Kaushik Bhattacharya

Multiscale modeling is essential for understanding the complex behavior of materials. However, accurately transferring all relevant information from one scale to another has remained an outstanding challenge. Neural operators, discretization-independent generalizations of neural networks, is proving to be a powerful tool in addressing this challenge. This article provides an introduction to neural operators, and illustrates their use in multiscale modeling of materials through three selected examples.

We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting, where homogenization theory provides a systematic approach to deriving macroscale constitutive laws, obviating the need to resolve the complex microstructure repeatedly. However, the unit-cell problems that define these constitutive models are typically not amenable to explicit evaluation. It is therefore of interest to learn constitutive models from data generated by the unit cell problem. Our proposed framework models homogenized constitutive laws with both memory- and microstructure-dependence using Markovian recurrent and Fourier neural operators. The homogenization problem for Kelvin–Voigt viscoelastic materials is studied to provide firm theoretical foundations for our model. The theoretical properties of the cell problem in this Kelvin–Voigt setting motivate the proposed learning framework, and are also used to prove a universal approximation theorem for the learned macroscale constitutive model. Numerical experiments show that the proposed learning framework accurately learns memory- and microstructure-dependent viscoelastic and elasto-viscoplastic constitutive models, beyond the setting of the theory. Furthermore, we show that the learned constitutive models can be successfully deployed in macroscale simulations of material deformation for different microstructures without retraining.

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.

Nematic elastomers are a particular class of liquid crystal elastomers (LCEs) that exhibit both liquid-crystalline order and rubber (entropic) elasticity. This combination makes them stimuli-responsive soft materials with a number of unusual thermo-mechanical properties. They have been proposed for various applications, including soft robotics, enhanced adhesion, and impact resistance. This paper presents a new experimental setup and a comprehensive dataset characterizing the soft behavior of nematic elastomers over a range of temperatures and strain rates. We also fit the results to a recently developed model of nematic elastomers.

Empirical rate-and-state friction laws are widely used in geophysics and engineering to simulate interface slip. They postulate that the friction coefficient depends on the local slip rate and a state variable that reflects the history of slip. Depending on the parameters, rate-and-state friction can be either rate-strengthening, leading to steady slip, or rate-weakening, leading to unsteady stick-slip behavior modeling earthquakes. Rate-and-state friction does not have a potential or variational formulation, making implicit solution approaches difficult and implementation numerically expensive. In this work, we propose a potential formulation for the rate-and-state friction. We formulate the potentials as neural networks and train them so that the resulting behavior emulates the empirical rate-and-state friction. We show that this potential formulation enables implicit time discretization leading to efficient numerical implementation.

We continue the development of a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations that we started in Akerson, Rajan and Bhattacharya (2024). We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive behavior that minimizes the difference between the experimental observation and the corresponding quantities computed with the model, while enforcing the balance laws. We formulate the forward problem as a boundary value problem corresponding to the experiment, and compute the sensitivity of the objective with respect to the model using the adjoint method. In this paper, we extend the approach to include contact and study dynamic indentation. Contact is a nonholonomic constraint, and we introduce a Lagrange multiplier and a slack variable to address it. We demonstrate the method on synthetic data before applying it to experimental observations on rolled homogeneous armor steel and a polycrystalline aluminum alloy.

Liquid crystal elastomers are rubbery solids that couple liquid crystalline order and deformation. This coupling leads to properties that are attractive for a number of applications in soft robotics and energy absorption. This paper is motivated by the latter application, and provides a systematic experimental study of a particular class of liquid crystal elastomers -- the isotropic genesis polydomain liquid crystal elastomers -- over a wide range of strain rates. An important aspect of this study is a novel tensile drop-tower that enables tensile strain rates of 100 s$^{-1}$ that are important to application but previously inaccessible. The paper also extends a recently proposed constitutive model to the high strain rate regime, and shows that it can be fit to describe the observed behavior across the spectrum of examined behavior.

Empirical rate-and-state friction laws are widely used in geophysics and engineering to simulate interface slip. They postulate that the friction coefficient depends on the local slip rate and a state variable that reflects the history of slip. Depending on the parameters, rate-and-state friction can be either rate-strengthening, leading to steady slip, or rate-weakening, leading to unsteady stick-slip behavior modeling earthquakes. Rate-and-state friction does not have a potential or variational formulation, making implicit solution approaches difficult and implementation numerically expensive. In this work, we propose a potential formulation for the rate-and-state friction. We formulate the potentials as neural networks and train them so that the resulting behavior emulates the empirical rate-and-state friction. We show that this potential formulation enables implicit time discretization leading to efficient numerical implementation.

Various mechanical phenomena depend on the length scale, and these have inspired a variety of nonlocal and higher gradient continuum theories. Mechanistically, it is believed that the length scale dependence arises due to an interplay between the length scale of heterogeneities in the material, the length scale of the material being probed and the phenomenon under study. In this paper, we seek to understand this interplay in a simple setting by studying the overall behavior of a one-dimensional periodic medium governed by strain gradient elasticity at the microstructural scale. We find through numerical experiments that the overall behavior is not described by a strain gradient elasticity. In other words, strain gradient theories are not invariant under averaging at this scale. We also find that the overall behavior may be described by a kernel-based nonlocal elasticity theory, but the kernel is highly oscillatory with slow decay. So we seek alternate characterization. First, we limit our interest to a range of length scales, and show that the behavior is described well by fractional strain gradient elasticity. Consequently, one can obtain various scaling laws with exponent between zero (classical elasticity) and one (strain-gradient elasticity). Second, we take a data-driven approach, and show that we can describe the overall behavior over a range of scales using a Fourier neural operator.

Abstract Constitutive relations close the balance laws of continuum mechanics and serve as a surrogate for a material in the design and engineering process. The problem of obtaining the constitutive relations is an indirect inverse problem where both the relation and the quantities that define the relation have to be inferred from experimental observations. The advent of full-field observation techniques promises a new ability to learn constitutive relations under realistic operational conditions. However, this is done in two steps, first by obtaining deformations from the images and then by obtaining the constitutive relation from deformations and forces. This leads to a variety of difficulties. In this article, we propose a novel approach that enables us to obtain constitutive relations directly from the raw data consisting of images and force measurements.

Surgeons perpetually innovating with a singular goal of improving patient-reported outcomes (PROs) have always been at the forefront of incorporating emerging horizons of basic sciences. The three aces, i.e., asepsis, anesthesia, and antibiotics, have put surgeons on winning table of healthcare stakes. Popular adoption of laparoscopic and other minimally invasive surgical sciences (MISS), have delivered the “Trump Suit” equivalent of bridge card game to surgeons, making them ambassadors of innovative application of science married to basic science fields such as computers, information technology, optics, pigment-based imaging in vivo during surgeries, motion picture editing, machine learning, and social sciences. Societal acceptance of these polymath traits of surgeon is reflected in universal adoption of MISS. This popular acceptance came ahead of any signatures of approval from peer review boards (PRBs) and without any level of evidence. This popular acceptance-based application of MISS was debated and given the scientific approval at the most prestigious global congress of surgeons following a “Presidential debate” between two science icons, Richard Satava and Bruce McFadyen. The congress was 2008 annual meet of “Society of Gastrointestinal and Endoscopic Surgeons (SAGES).”[1] The debate was titled, “Evidence-Based Surgery Is for Those Willing to Follow Behind—New Advances Can’t Wait” at SAGES 2008.[2] The polymath surgeon-scientist, dismissed as “boys with toys,” has been finally enabled to pursue research-based innovations.[3] This pursuit by surgeon aimed at improving PROs is an understanding that PRBs mirror the clearance from chair of surgery, akin to dealer having license to declare “Trump” in a game of “bridge whist.”[4,5] Such pursuits are rewarding not only for surgeon but science and society as well. The recognition by SAGES of the importance of limiting surgical energy to hemostasis and avoiding dissection outside established anatomical planes prompted the development of guidelines for the safe use of surgical energy, culminating in an invited editorial in surgical endoscopy, the leading journal of MISS.[6,7] The editorial described the traits of a scientist-surgeon having knowledge of basic sciences that can be translated to clinical benefits. These traits of translational science-driven surgeons are encapsulated to an acronym Imagineer, used now a self-descriptive word.[7] Surgeon-scientists distinguish themselves from clinicians by seamlessly integrating knowledge from both laboratory and clinical settings to identify research opportunities that enhance patient care and community health. A surgeon-scientist is defined as a surgeon actively engaged in translational research across a broad spectrum of fields.[8] The scientist-surgeon, aptly termed the “Imagineer,” has spearheaded the translation of fundamental research on microbiome, sterile inflammatory pathways, dietary molecules such as curcumin, and yoga into clinical applications, yielding robust evidence of benefits for postoperative convalescence defining PROs. An unfavorable ecosystem reflected in conduct of PRB stifles such pursuits, hindering advancements in science, the most common alibi being a demand for absolute proof in microconstituents of an idea at the foundation of hypothesis. The surgeon-scientist’s Imagineering, the innovative work, often lifesaving, can be hindered by the challenges of meeting PRB compliance rigidity. The experience with PRB reminds of Emerson who said, Society is always taken by surprise at any new example of common sense. What we trust and how we act should be more important for century-old harmless practices, rather than spending resources to find statistical algorithms for the trust. Beneficially applied basic science and trusted knowledge in surgical practice cannot always be reduced to numbers, text, or images, much to annoyance of statistics-grounded PRB.[9] Prevailing ecosystem of PRB has been seen to discourage younger aspiring surgeons to pursue academics and research. As the dwindling number of surgeon-scientists reduces the pool of potential mentors, aspiring young surgeon-scientists face an uncertain landscape. Many medical students and surgery residents, initially enthusiastic about developing a research program are often deterred by the significant challenges surgeon-scientists encounter, opting instead for clinical careers without a research focus. Following the rote learning-based education, they graduate to establish independent practice. Thus, prioritizing to have a better work–life balance, relinquishing the demands of research and writing that require evenings and weekends.[10] Thomas Sowell prophesized, “Too much of what is called ‘education’ is little more than an expensive isolation from reality.” Surgeons have gained their status of surgeon-scientist from being restricted to the management of diseases called external, i.e., on body surface as dictated by physician guilds, self-anointing themselves as internists with sole rights for internal medicine.[11] The future of research depends on our ability to nurture and support surgeon-scientist. In prevailing perceptions of PRBs not being favourable to surgeon-scientist, surgery leadership has expressed concerns being headlined as, “The extinction of Surgeon-Scientist,” “The surgeon-scientist a dying breed,” “Endangered academia” and A role for the surgeon-scientist? What does the “evidence’ tell us?” etc.[12] Postoperative convalescence-associated PRO pathways require integration of the emerging basic science understanding in surgical research. The surgeon-scientists with their unique understanding of translational science research need to be nurtured by supportive PRB. The concerns about ecosystem for research expressed in Western literature are an apt pointer toward Indian counterparts, which is insulated from such critique due to its overbearing statute with mandates intimidating enough for a careerist surgeon. It took a Nobel laureate of Indian descent to scratch the surface in saying that India cannot be a nursery of talent for research due to its cumbersome research environment.[13] Cover of an article is explicitly explanatory [Figure 1]. Many factors for this inconducive and cumbersome ecosystem have been discussed. What the young scientists fear to express, needs some introduction here. The choice of words to address concerns, i.e. ’Academic Bullying’ and ’Envy of Excellence’, though unconventional, convey, the helplessness of true idea generators. Several high-profile science institutions have been rocked by spate of bullying allegations.[14] Factors such as abrasive supervision, ostracism, gossip to target credibility, spreading malicious rumors, misinformation about achievements, hierarchical exclusion from formal networks, and sabotaging career pathways have been reported in these institutions. Bullying is seen in all walks of life, but the data are scary for academic science. The reported annual incidence of 25%–40% is significantly higher than 10%–14% among working population and 2%–19% for other universities. Most worrisome figures have been reported from neonatal intensive care units, more than half of almost 400 doctors and nurses having experienced bullying.[14]Figure 1: Illustration by Daniel Stolle“Envy of excellence” is even a worse nightmare for an aspiring surgeon scientist. It involves mobbing and systematic targeting and harassment of independent thinkers, high-achieving scientist-surgeons. Westhues describes it as group ganging with psychological aggression and isolation in influential academic committees.[15] This too, has been reported having higher prevalence in medical academia, with The Lancet journal sending a shout for global committee on Academic Behavior Ethics.[16] The issue remains alive as most of the addressing mechanisms have failed as these envious bullies leave no trace/trail.[17] Statistics is another common harassment tool in PRB interactions. This despite best of tools available online with highest degree of analysis in artificial intelligence-enabled or handheld pocket gadgets. iPhone being a favorite of most even at PRB meets. While Statistics is the grammar of science (Pearson), if tortured long enough, the data will confess to anything (Ronald Coase), revealing the suggestive, but concealing the vital (Aaron Levenstein). Still, statisticians prevail in PRB, falling in love with their models (George EP Box), using statistics like a lamp post, more for support than illumination (Andrew Lang). Our proposal to use natural probiotic bath (with Dahee, Indian fermented milk) as a potential tool to reduce risk of surgical site infections, raised a concern by PRB, what if some consenting study volunteer dies of MI (we are still searching literature, if it meant myocardial infarction or Milk intoxication!). Surprisingly, it was about using milk to make tea, mentioned in the famous “Lady Tasting Tea” experiment. The experiment designed by Muriel Bristol, a colleague of Fisher’s, who claimed she could taste the difference between tea made with milk added before or after brewing. The study, which used 8 cups of tea, tested her claim and laid the foundation for modern statistical hypothesis testing. Fischer later developed the analysis of variance, ANOVA, followed by the book that guides PRB experts, “The design of Experiments.” We many in scientific community follow the colonial mindsets and teaching forgetting that the best of mathematics and science travelled to Arab during the Islamic occupation of India. Many believe that there was no civilization with geographical domain roots 2000 years back, no ’believers’ of any kind 1500 years back, no Indian human records or history before invasions from its northwest or seas, no Indian fighting for independence before a specific person arrived and no scholarship beyond the dictates of few after 1947. The facts otherwise speak for themselves. The Arabs translated Indian books and carried it to Europe, undergoing renaissance from dark ages.[18] The mathematical fields were the best that humanity has ever had.[19] Indian renaissance will need studies beyond the dictated of the last 12 centuries to reconnect with our more advanced methods of scientific studies to redeem our own heritage in science.[20] Francesca Bray, Professor Emeritus at the University of Edinburgh, reminds us that the books that we refer to and cite were written by English or Dutch; they preferred to say they were the ones bringing progress and we believe them.[21] India believes in inclusion of wisdom from all sources. We must use the best from colonial education, but at the same time stop being skeptical of advance science having existed in Bharat, that is, India. Our skepticism should not be biased, finding unrelated fault lines in our own while ignoring a believer in racial intelligence difference, one who was eugenicist, supported scientific racism, and is also famous for his “sexy son hypothesis.”[22] The PRB and institutions need to redeem science from mockery of obstructive peer reviews. Let the surgeon-scientist thrive! Voltaire, a witty thinker, had this to say during the European Renaissance, “Our wretched species is so made that those who walk on the well-trodden path always throw stones at those who are showing a new road. Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well. Every man is a creature of the age in which he lives, and few are able to raise themselves above the ideas of the time.” Disclosure This article was written by experiences and observations of changing mentor profile and their attitudes toward curious and sincere postgraduates starting their journey of professional life. The ‘trials and tribulations’ they face, their frustration with the prevailing research ecosystem, potentially leads them to surrender at the altar of PRB rigid structures. The peer ecosystem, mandated to navigate enthusiasm for research amongst younger generation, ends up putting the procedural cart before the surgeon-scientist horse. Their approach mirrors the procrustean cutting humans to size of the bed, akin to a polite adage, “trim the foot to fit the shoe”. The ecosystem results in defeating the self-belief of surgeon-scientist, thus eliminating the possibilities of their dreams or thinking out of the box. It is a timely call for introspection by our generation, whether we are being as good mentors as we had! We at Ganga Ram Hospital, Delhi, are blessed to have had guidance of such mentors in Late Prof. KC Mahajan and Prof. Kusum Verma now. A cartoon posted on social media by one of the authors excelling in academics with witty humor, crystalized the chain of observation leading to, thoughts of other authors [Figure 2]. Starting the title and a sentence with lower case is a reminder to make some Dutch friends.Figure 2: Peer review versus pear review

Constitutive relations close the balance laws of continuum mechanics and serves as the surrogate for a material in the design and engineering process. The problem of obtaining the constitutive relations is an indirect inverse problem where both the relation and the quantities that define the relation have to be inferred from experimental observations. The advent of full-field observation techniques promises a new ability of learning constitutive relations in realistic operational conditions. However, this is done in two steps, first obtaining deformations from the images, and then obtaining the constitutive relation from deformations and forces. This leads to a variety of difficulties. In this paper, we propose a novel approach that enables us to obtain constitutive relation directly from the raw data consisting of images and force measurements.

The role of grain size in determining fracture toughness in metals is incompletely understood with apparently contradictory experimental observations. We study this grain-size dependence computationally by building a model that combines the phase-field formulation of fracture mechanics with dislocation density-based crystal plasticity. We apply the model to cleavage fracture of body-centered cubic materials in plane strain conditions, and find non-monotonic grain-size dependence of plastic-brittle transgranular fracture. We find two mechanisms at play. The first is the nucleation of failure due to cross-slip in critically located grains within transgranular band of localized deformation, and this follows the classical Hall-Petch law that predicts a higher failure stress for smaller grains. The second is the resistance to the propagation of a mode I crack, where grain boundaries can potentially pin a crack, and this follows an inverse Hall-Petch law with higher toughness for larger grains. The result of the competition between the two mechanisms gives rise to non-monotonic behavior and reconciles the apparently contradictory experimental observations.

Photomechanically active materials undergo reversible deformation on illumination, making them ideal for remote, tether-free actuation. Much of the work on these materials has focused on one-dimensional structures, such as strips. In this paper, we explore photomechanically active two-dimensional structures such as sheets and shells. When illuminated, such structures undergo spontaneous bending due to the limited penetration of light. However, the geometry of the shell constrains possible deformation modes: changes in Gauss curvature lead to in-plane stretching, against which shells are very stiff. Therefore, there is a complex coupling between the photomechanical actuation and the mechanical behavior of a shell. We develop and implement a novel approach to study photomechananically active shells. This method is a discrete shell model which captures the interplay between actuation, stretching, bending, and geometric changes. Through a series of examples, we explore these complex interactions, demonstrating how one can design shells that deform to follow the source of illumination.

We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this sharp interface problem, prove its convergence as the regularization length approaches 0 and present an efficient numerical implementation. We illustrate the strengths of our approach through a series of numerical examples.

The role of grain size in determining fracture toughness in metals is incompletely understood with apparently contradictory experimental observations. We study this grain-size dependence computationally by building a model that combines the phase-field formulation of fracture mechanics with dislocation density-based crystal plasticity. We apply the model to cleavage fracture of body-centered cubic materials in plane strain conditions, and find non-monotonic grain-size dependence of plastic-brittle transgranular fracture. We find two mechanisms at play. The first is the nucleation of failure due to cross-slip in critically located grains within transgranular band of localized deformation, and this follows the classical Hall-Petch law that predicts a higher failure stress for smaller grains. The second is the resistance to the propagation of a mode I crack, where grain boundaries can potentially pin a crack, and this follows an inverse Hall-Petch law with higher toughness for larger grains. The result of the competition between the two mechanisms gives rise to non-monotonic behavior and reconciles the apparently contradictory experimental observations.

This study examines the gravitational collapse of an overdense dark matter region in a coupled scalar field dark energy scenario within a flat FLRW background. It finds that, depending on the initial conditions, some overdense regions avoid collapse and expand eternally with the background. The interior overdense region follows a closed FLRW metric, while its boundary is described by generalized Vaidya spacetime, which allows flux across the boundary while preserving the homogeneity of dark energy inside. Dark matter evolves as cold dark matter, but in non-minimal coupling, the modified Klein-Gordon equation alters dark energy evolution. The results highlight the impact of coupled dark energy on dark matter virialization and cosmic structure formation.

This paper presents a novel and versatile tensile testing system based on the drop weight technique, specifically designed for materials that can undergo significant tensile deformation , such as elastomers . The core apparatus comprises of a hanging slender bar, from which a steel sleeve (referred to as the striker) is released under controlled conditions. Accelerated in free fall , the striker impacts a stationary plate, initially held in place by a mechanical detent. The specimen, secured by a gripping system between the hanging bar and the stationary support, undergoes controlled stretching at a nearly constant velocity upon the release of the detent triggered by the striker’s impact. Full-field strain measurement is obtained using a high-speed camera in conjunction with digital image correlation . Additionally, strategically located piezoresistive force sensors enable real-time force measurements. By achieving strain rates ranging from 100 s −1 to 500 s −1 , this system addresses a notable gap in the literature concerning intermediate strain rate testing for soft materials.

We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive behavior that minimizes the difference between the experimental observation and the corresponding quantities computed with the model, while enforcing the balance laws. We formulate the forward problem as a boundary value problem corresponding to the experiment, and compute the sensitivity of the objective with respect to model using the adjoint method. The resulting method is robust and can be applied to constitutive models with arbitrary complexity. We focus on elasto-viscoplasticity, but the approach can be extended to other settings. In this part one, we formulate the method and demonstrate it using synthetic data on two problems, one quasistatic and the other dynamic.

Photomechanically active materials undergo reversible deformation on illumination, making them ideal for remote, tether-free actuation. Much of the work on these materials has focused on one-dimensional structures, such as strips. In this paper, we explore photomechanically active two-dimensional structures such as sheets and shells. When illuminated, such structures undergo spontaneous bending due to the limited penetration of light. However, the geometry of the shell constrains possible deformation modes: changes in Gauss curvature lead to in-plane stretching, against which shells are very stiff. Therefore, there is a complex coupling between the photomechanical actuation and the mechanical behavior of a shell. We develop and implement a novel approach to study photomechananically active shells. This method is a discrete shell model which captures the interplay between actuation, stretching, bending, and geometric changes. Through a series of examples, we explore these complex interactions, demonstrating how one can design shells that deform to follow the source of illumination.

Liquid crystal elastomers (LCEs) containing light-sensitive molecules exhibit large reversible deformation when subjected to illumination. Here, we investigate the role of optical penetration depth on this photomechanical response. We present a model of the photomechanical behavior of photoactive LCE strips under illumination that goes beyond the common assumption of shallow penetration. This model reveals how the optical penetration depth and the consequent photomechanically induced deformation can depend on the concentration of photoactive molecules, their absorption cross-sections, and the intensity of illumination. Through a series of examples, we show that the penetration depth can quantitatively and qualitatively affect the photomechanical response of a strip. Shallow illumination leads to monotone curvature change while deep penetration can lead to non-monotone response with illumination duration. Further, the flapping behavior (a cyclic wave-like motion) of doubly clamped and buckled strips that has been proposed for locomotion can reverse direction with sufficiently large penetration depth. This opens the possibility of creating wireless light-driven photomechanical actuators and swimmers whose direction of motion can be controlled by light intensity and frequency.

Reversible dry adhesion is exploited by lizards and insects in nature, and is of interest to robotics and bio-medicine. In this paper, we use numerical simulation to study how the soft elasticity of liquid crystal elastomers can affect its adhesion and provide a technological opportunity. Liquid crystal elastomers are cross-linked elastomer networks with liquid crystal mesogens incorporated into the main or side chain. Polydomain liquid crystalline (nematic) elastomers exhibit unusual mechanical properties like soft elasticity, where the material deforms at nearly constant stress, due to the reorientation of mesogens. Our study reveals that the soft elasticity of nematic elastomers dramatically affects the interfacial stress distribution at the interface of a nematic elastomer cylinder adhered to a rigid substrate. The stress near the edge of the nematic cylinder under tensile load deviates from the singular behavior predicted for linear elastic materials, and the maximum normal stress reduces dramatically. This suggests that nematic elastomers should display extremely high, but controllable adhesion, consistent with the available experimental observations.

Abstract We study solute‐laden flow through permeable geological formations with a focus on surface reactions that lead to changes in flow and formation. As the fluid flows through the permeable medium, it reacts with the medium, thereby changing the morphology and properties of the medium; this in turn, affects the flow conditions and chemistry. These phenomena occur at various lengths and time scales and make the problem extremely complex. Multiscale modeling addresses this complexity by dividing the problem into those at individual scales, and systematically passing information from one scale to another. However, accurate implementation of these multiscale methods is still prohibitively expensive. We present a methodology to overcome this challenge that is computationally efficient and quantitatively accurate. We introduce a surrogate for the solution operator of the lower scale problem in the form of a recurrent neural operator, train it using one‐time off‐line data generated by repeated solutions of the lower scale problem, and then use this surrogate in application‐scale calculations. The result is the accuracy of concurrent multiscale methods, at a cost comparable to those of classical models. We study various examples, and show the efficacy of this method in understanding the evolution of the morphology, properties and flow conditions over time in geological formations.

Neural network based models have emerged as a powerful tool in multiscale modeling of materials. One promising approach is to use a neural network based model, trained using data generated from repeated solution of an expensive small scale model, as a surrogate for the small scale model in application scale simulations. Such approaches have been shown to have the potential accuracy of concurrent multiscale methods like FE2, but at the cost comparable to empirical methods like classical constitutive models or parameter passing. A key question is to understand how much and what kind of data is necessary to obtain an accurate surrogate. This paper examines this question for history dependent elastic-plastic behavior of an architected metamaterial modeled as a truss. We introduce an iterative approach where we use the rich arbitrary class of trajectories to train an initial model, but then iteratively update the class of trajectories with those that arise in large scale simulation and use transfer learning to update the model. We show that such an approach converges to a highly accurate surrogate, and one that is transferable.

This paper presents a novel and versatile tensile testing system based on the drop weight technique, specifically designed for materials that can undergo significant tensile deformation, such as elastomers. The core apparatus comprises of a hanging slender bar, from which a steel sleeve (referred to as the striker) is released under controlled conditions. Accelerated in free fall, the striker impacts a stationary plate, initially held in place by a mechanical detent. The specimen, secured by a gripping system between the hanging bar and the stationary support, undergoes controlled stretching at a nearly constant velocity upon the release of the detent triggered by the striker's impact. Full-field strain measurement is obtained using a high-speed camera in conjunction with digital image correlation. Additionally, strategically located piezoresistive force sensors enable real-time force measurements. By achieving strain rates ranging from 100 s-1 to 500 s-1, this system addresses a notable gap in the literature concerning intermediate strain rate testing for soft materials.

We constrain the parameters of the $k$-essence scalar field model with inverse square and exponential potentials using data sets including Pantheon+SHOES and the Dark Energy Survey (DES) of Type Ia supernovae, Baryon Acoustic Oscillation (BAO) data from SDSS and DESI surveys, and direct measurements of the Hubble parameter and redshift obtained from the differential age method (CC). We also provide a brief perspective on the dynamical evolution of both models and derive stability constraints on the model parameters, which are then used to set appropriate priors. We adopt a Bayesian inference procedure to estimate the model parameters that best fit the data. A comprehensive analysis in light of observational data shows that the $k$-essence model fits well across all data combinations. However, according to the BIC criterion, the $Λ$CDM model provides a slightly better fit compared to the $k$-essence model.

Liquid crystal elastomers are cross-linked elastomer networks with liquid crystal mesogens incorporated into the main or side chain. Polydomain liquid crystalline (nematic) elastomers exhibit unusual mechanical properties like soft elasticity, where the material deforms at nearly constant stress, due to the reorientation of mesogens. In this paper, we use numerical simulation to study the implication of the remarkable elastic softness on a classical problem of adhesion. This study reveals that the soft elasticity of nematic elastomers dramatically affects the interfacial stress distribution at the interface of a nematic elastomer cylinder adhered to a rigid substrate. The stress near the edge of the nematic cylinder under tensile load deviates from the singular behavior predicted for linear elastic materials, and the maximum normal stress reduces dramatically. Moreover, the location of maximum interfacial stress shifts from the edge to the center of the nematic cylinder when the applied tensile force goes beyond a critical value. We discuss the implications for adhesion. The results are consistent with the available experimental data.

This paper explores the evolution of the overdense region of dark matter in the presence of a nonminimally coupled scalar field which is used to model quintessence and phantomlike dark energy. We focus on algebraic coupling, where the interaction Lagrangian is independent of the derivatives of the scalar field. To make our model more relativistic, like the minimal coupling scenario we studied earlier, we consider a spacetime structure that is internally closed Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime and externally the generalized Vaidya spacetime. This structure allows nonzero matter flux at the boundary of the overdense region. Our investigation reveals that an increment of the coupling strength causes dark energy to cluster with dark matter at a certain cosmological scale where the influence of dark energy cannot be ignored. This phenomenon arises from the specific nature of the nonminimal coupling considered in this paper. While the evolution of matter's energy density remains unchanged, the scalar field's Klein-Gordon equation is modified, causing dark energy to deviate from its homogeneous state and cluster with dark matter. Similar to minimal coupling scenarios, closed spherical regions do not collapse within certain parameter ranges, exhibiting eternal expansion within the spatially flat FLRW spacetime and acting as voids with decreasing matter density. The study extends our understanding of the cosmological scenarios where the virialization of the overdense regions of dark matter is influenced by the nonminimally coupled dark energy.

A BSTRACT Artificial intelligence (AI) is transforming the field of colonoscopy by enhancing diagnostic precision, improving detection rates of polyps, and optimizing procedural efficiency. Recent advances such as computer-aided detection (CADe) and computer-aided diagnosis (CADx) play crucial roles in improving adenoma detection rates (ADRs) and differentiating between benign and malignant polyps in real time. CADe systems alert endoscopists to small or flat lesions often missed in traditional procedures, leading to increased ADR and consistent quality across providers. CADx further supports this by accurately characterizing polyps, reducing the need for histopathological analysis on benign lesions, and contributing to better patient outcomes. In addition, AI-driven polyp characterization, quality metrics, workflow optimization, and three-dimensional visualization techniques improve real-time decision-making, procedural efficiency, and endoscopist training. These technologies ensure a more thorough examination of the colon, lower healthcare costs, and enhance patient-centered care. As AI continues to integrate into clinical practice, it presents significant potential for advancing the safety, efficacy, and personalization of colonoscopy.

It is known that in Friedmann-Lemaitre-Robertson-Walker cosmology one has more number of dynamical equations, compared to the number of unknown variables. This fact makes some equations redundant. The situation becomes complicated because all the relevant differential equations in cosmology are not of the same order. In this article we study the fate of the redundant equations. We show that this redundancy is inevitable in general relativity. It is shown that this redundancy is primarily responsible for a special role of one of the Friedmann equations, which constrains the initial values of the problem. Our method of analyzing the dynamical structure of the theories relies on an operational approach and can be generalized further.

Neural network based models have emerged as a powerful tool in multiscale modeling of materials. One promising approach is to use a neural network based model, trained using data generated from repeated solution of an expensive small scale model, as a surrogate for the small scale model in application scale simulations. Such approaches have been shown to have the potential accuracy of concurrent multiscale methods like FE2, but at the cost comparable to empirical methods like classical constitutive models or parameter passing. A key question is to understand how much and what kind of data is necessary to obtain an accurate surrogate. This paper examines this question for history dependent elastic-plastic behavior of an architected metamaterial modeled as a truss. We introduce an iterative approach where we use the rich arbitrary class of trajectories to train an initial model, but then iteratively update the class of trajectories with those that arise in large scale simulation and use transfer learning to update the model. We show that such an approach converges to a highly accurate surrogate, and one that is transferable.

This paper explores the evolution of the over-dense region of dark matter in the presence of a non-minimally coupled scalar field which is used to model quintessence and phantom-like dark energy. We focus on algebraic coupling, where the interaction Lagrangian is independent of the derivatives of the scalar field. To make our model more relativistic, like the minimal coupling scenario we studied earlier, we consider a spacetime structure that is internally closed Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime and externally the generalized Vaidya spacetime. This structure allows non-zero matter flux at the boundary of the over-dense region. Our investigation reveals that an increment of the coupling strength causes dark energy to cluster with dark matter at a certain cosmological scale where the influence of dark energy cannot be ignored. This phenomenon arises from the specific nature of the non-minimal coupling considered in this paper. While the evolution of matter's energy density remains unchanged, the scalar field's Klein-Gordon equation is modified, causing dark energy to deviate from its homogeneous state and cluster with dark matter. Similar to minimal coupling scenarios, closed spherical regions do not collapse within certain parameter ranges, exhibiting eternal expansion within the spatially flat FLRW spacetime acting as voids with decreasing matter density. The study extends our understanding of the cosmological scenarios where the virialization of the over-dense regions of dark matter is influenced by the non-minimally coupled dark energy.

We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation of Lagrangian with respect to independent variables, which produces modified scalar field and Friedmann equations. Using dynamical stability approach in different types of interaction models with two types of scalar field potential, we explore this coupled framework. Implementing detailed analysis, we can conclude our models can able to produce stable late-time cosmic acceleration.