Nikolaos Bouklas

The mechanics of single-chain stretching and rupture are central to understanding the resilience of biological polymers and designing strong and tough soft materials such as double-network gels and multi-network elastomers. In this work, we develop a statistical mechanics based model that enables one to determine the distribution of forces along the chain segments. By combining the force distribution with a tilted bond potential that captures the stretch energy stored in these bonds, we calculate the corresponding activation energy required for bond dissociation. This allows us to determine the probability of bond (and consequently chain) failure. The proposed approach is simple, direct, and readily adaptable for constructing higher-level coarse-grained descriptions of damage and fracture in polymer networks. We demonstrate this by applying the theory to two problems of practical interest: (1) toughening networks via sacrificial bond rupture in polymer chains and (2) incorporation of the local chain model into a 3-dimensional constitutive relation that captures damage in elastomers. The latter was implemented through the micro-sphere framework, which accounts for different chain orientations, as well as the computationally inexpensive eight chain model. The findings from this work provide a physically-based model to quantify the stretching and failure of a single chain and pave the way to the integration of local damage models into 3-dimensional networks.

The mechanics of single-chain stretching and rupture are central to understanding the resilience of biological polymers and designing strong and tough soft materials such as double-network gels and multi-network elastomers. In this work, we develop a statistical mechanics based model that enables one to determine the distribution of forces along the chain segments. By combining the force distribution with a tilted bond potential that captures the stretch energy stored in these bonds, we calculate the corresponding activation energy required for bond dissociation. This allows us to determine the probability of bond (and consequently chain) failure. The proposed approach is simple, direct, and readily adaptable for constructing higher-level coarse-grained descriptions of damage and fracture in polymer networks. We demonstrate this by applying the theory to two problems of practical interest: (1) toughening networks via sacrificial bond rupture in polymer chains and (2) incorporation of the local chain model into a 3-dimensional constitutive relation that captures damage in elastomers. The latter was implemented through the micro-sphere framework, which accounts for different chain orientations, as well as the computationally inexpensive eight chain model. The findings from this work provide a physically-based model to quantify the stretching and failure of a single chain and pave the way to the integration of local damage models into 3-dimensional networks.

A biohybrid coating for crack detection: when the substrate is damaged, the coating cracks, causing spores to germinate and fluoresce.

Clinically, the feel, touch, and shape of a solid tumor are important diagnostic methods for determining the malignant state of the disease. However, there are limited tools for quantifying the mechanics and the malignancy of the tumor in a physiologically realistic setting. Here, we developed a microfluidic rheometer - termed the microrheometer - that enables simultaneous measurements of tumor spheroid mechanics and their invasiveness into a 3D extracellular matrix (ECM). The microrheometer consists of a pneumatic pressure control unit for applying controlled static or cyclic compression to tumor spheroids, and a sample chamber for containing spheroid embedded ECM. The innovation here lies in the integration of a polyacrylamide membrane force sensor within the sample chamber, enabling a direct force measurement in a physiologically relevant setting. We found that both tumor stiffness and the viscoelastic properties of the tumor are closely correlated with tumor invasiveness. The microrheometer allowed us to measure tumor mechanics in a short time (less than a minute) and has the potential to be used clinically in the future. We note that the microrheometer here can be easily extended to studies of mechanics of single cell, nucleus, as well as other cell/tissue types.

This study aims to unravel the micro-mechanical underpinnings of the emergence of the fractocohesive length scale as a central concept in modern fracture mechanics. A thermodynamically consistent damage and fracture model for elastomers is developed, incorporating elements of polymer chain statistical mechanics. This approach enables the direct incorporation of polymer chain response into a continuum gradient enhanced damage formulation, that in turn allows a physically meaningful description of diffuse chain damage and corresponding fracture events. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation. Furthermore, we investigate flaw sensitivity and demonstrate that when flaw sizes are smaller than a critical length scale, the material response becomes largely insensitive to notch size. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage zone and representing the region where the irreversible dissipation process (i.e., bond scission) is happening. As this region is dictated in the proposed FED model through the introduction of a length scale associated with the non-local nature of the damage and fracture process, the emerging relationship of the two length scales is discussed, effectively connecting the microscopic characteristics of damage to the effective macroscopic response.

High-resolution electronic tactile displays stand to transform haptics for remote machine operation, virtual reality, and digital information access for people who are blind or visually impaired. Yet, increasing the resolution of these displays requires increasing the number of individually addressable actuators while simultaneously reducing their total surface area, power consumption, and weight, challenges most evidently reflected in the dearth of affordable multiline braille displays. Blending principles from soft robotics, microfluidics, and nonlinear mechanics, we introduce a 10-dot-by-10-dot array of 2-millimeter-diameter, combustion-powered, eversible soft actuators that individually rise in 0.24 milliseconds to repeatably produce display patterns. Our rubber architecture is hermetically sealed and demonstrates resistance to liquid and dirt ingress. We demonstrate complete actuation cycles in an untethered tactile display prototype. Our platform technology extends the capabilities of tactile displays to environments that are inaccessible to traditional actuation modalities.

Early detection of fatigue cracking is crucial to extend the life‐cycle of materials and structures. To reduce the risk of fatigue, parts are often over‐engineered or retired early, leading to material waste. Current methods for crack detection, including strain sensors or ultrasonic testing, can be costly, require regular maintenance, and do not respond to cracks directly via a repair mechanism. People are leveraging biology to create materials that can sense and respond. Engineered living materials have been primarily limited to porous matrices and hydrogels, which facilitate viability of organisms. We present an engineered living coating that can be applied to conventional structural materials to detect cracks. The coating integrates bacterial spores into a tailored synthetic matrix. This biohybrid coating approach unlocks potential, beyond crack detection, for crack mitigation through leveraging the biological component. This study: 1) describes the design of a spore‐polymer coating for in situ crack detection for structural materials and 2) demonstrates detection for different loading mechanisms, geometries, and materials. This work demonstrates how living materials can be used to enhance conventional materials and creates a valuable approach for crack detection. Our coating will reduce waste, increase product lifespan, and improve safety by preventing failure due to cracks.

The main objective of this work is to shed light on the effect of fiber plasticity on the macroscopic response and domain formation in soft biological composites. This goal is pursued by analyzing the plane-strain response of two-phase laminates. In the context of this problem, the effect of fiber plasticity is accounted for by allowing the elastically stiffer layers (``fiber'' phase) to also yield plastically and by taking the soft layers (``matrix'' phase) to be purely elastic solids. The analysis is carried out at finite elastic and plastic strains, but it is restricted to unidirectional, non-monotonic loading paths, applied by initially increasing the macroscopic stretch along the direction of the layers up to a prescribed maximum value and then decreasing the same stretch down to a minimum value. A simple expression is derived for the critical conditions at which the homogenized behavior of the laminate loses strong ellipticity for the first time along the loading path. The relevance of this result stems from the fact that the loss of macroscopic ellipticity of these composites is known to coincide with the onset of bifurcations of the long-wavelength type. It follows from this result that, just like hyperelastic laminates, elastoplastic laminates may lose macroscopic ellipticity whenever their incremental strength in shear perpendicular to the layers vanishes for the first time. For situations in which loss of macroscopic ellipticity does take place, a corresponding post-bifurcation solution for the homogenized behavior of the laminate is computed. The deformed state of the material described by this solution is characterized by twin lamellar domains that are formed at a length scale much larger than the width of the original, microscopic layers, but still much smaller than the overall dimensions of the macroscopic specimen under consideration.

Multi-material 3D printing, particularly through polymer jetting, enables the fabrication of digital materials by mixing distinct photopolymers at the micron scale within a single build to create a composite with tunable mechanical properties. This work presents an integrated experimental and computational investigation into the composition-dependent mechanical behavior of 3D printed digital materials. We experimentally characterize five formulations, combining soft and rigid UV-cured polymers under uniaxial tension and torsion across three strain and twist rates. The results reveal nonlinear and rate-dependent responses that strongly depend on composition. To model this behavior, we develop a physics-augmented neural network (PANN) that combines a partially input convex neural network (pICNN) for learning the composition-dependent hyperelastic strain energy function with a quasi-linear viscoelastic (QLV) formulation for time-dependent response. The pICNN ensures convexity with respect to strain invariants while allowing non-convex dependence on composition. To enhance interpretability, we apply $L_0$ sparsification. For the time-dependent response, we introduce a multilayer perceptron (MLP) to predict viscoelastic relaxation parameters from composition. The proposed model accurately captures the nonlinear, rate-dependent behavior of 3D printed digital materials in both uniaxial tension and torsion, achieving high predictive accuracy for interpolated material compositions. This approach provides a scalable framework for automated, composition-aware constitutive model discovery for multi-material 3D printing.

In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials, they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening. This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. We discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials, they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening. This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. We discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

Abstract The resistance to volumetric deformations displayed by polymer networks is largely due to secondary and tertiary interactions between neighboring polymer chains. These interactions are both entropic and enthalpic in nature but are fundamentally different from the entropic forces that resist shearing in these networks. In this paper, we introduce a new depiction of elastomers as a crosslinked Van der Waals fluid. Starting from first principles, we develop constitutive equations that are implemented in a continuum model as well as a discrete network model. Our models predict that the failure of polymer networks may be driven by an instability in the underlying polymer bulk ‘fluid’ or by the breaking of polymer chains, depending on the loading path taken. The results of this study indicate that material failure in elastomers exposed to a purely triaxial state, such as in a poker chip experiment, may be driven by an entirely different mode of instability than those deformed in pure shear, such as in a uniaxial tension experiment.

Clinically, the feel, touch, and shape of a solid tumor are important diagnostic methods for determining the malignant state of the disease. However, there are limited tools for quantifying the mechanics and the malignancy of the tumor in a physiologically realistic setting. Here, we developed a microfluidic rheometer - termed the microrheometer - that enables simultaneous measurements of breast tumor spheroid mechanics and their invasiveness into a 3D extracellular matrix (ECM). The microrheometer consists of a pneumatic pressure control unit for applying controlled static or cyclic compression to tumor spheroids, and a sample chamber for containing spheroid embedded ECM. The innovation here lies in the integration of a polyacrylamide membrane force sensor within the sample chamber, enabling a direct force measurement in a physiologically relevant setting. We found that both breast tumor stiffness and the viscoelastic properties of the tumor are closely correlated with tumor invasiveness. The microrheometer allowed us to measure tumor mechanics in a short time (less than a minute) and has the potential to be used clinically in the future. We note that the microrheometer here can be easily extended to studies of mechanics of single cell, nucleus, as well as other cell/tissue types.

We propose a Stein variational gradient descent (SVGD) method to concurrently sparsify, train, and provide uncertainty quantification (UQ) of a complexly parameterized model, such as a neural network (NN). It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed concurrent, condensed SVGD (ccSVGD) method can provide UQ on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a mechanical response representation problem in solid mechanics.

We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed condensed Stein variational gradient (cSVGD) method provides uncertainty quantification on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a representation problem in solid mechanics.

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiment, verification, and validation.

Abstract Recently, the phase-field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft materials, the convergence of the phase-field method becomes challenging, especially in scenarios of unstable crack growth. To overcome these numerical difficulties, several approaches have been introduced, with artificial viscosity being the most widely utilized. This study investigates the energy release rate due to crack propagation in hyperelastic nearly-incompressible materials and compares the phase-field method and a novel gradient-enhanced damage (GED) approach. First, we simulate unstable loading scenarios using the phase-field method, which leads to convergence problems. To address these issues, we introduce artificial viscosity to stabilize the problem and analyze its impact on the energy release rate utilizing a domain J-integral approach giving quantitative measurements during crack propagation. It is observed that the measured energy released rate during crack propagation does not comply with the imposed critical energy release rate, and shows non-monotonic behavior. In the second part of the paper, we introduce a novel stretch-based GED model as an alternative to the phase-field method for modeling crack evolution in elastomers. It is demonstrated that in this method, the energy release rate can be obtained as an output of the simulation rather than as an input which could be useful in the exploration of rate-dependent responses, as one could directly impose chain-level criteria for damage initiation. We show that while this novel approach provides reasonable results for fracture simulations, it still suffers from some numerical issues that strain-based GED formulations are known to be susceptible to.

Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft materials, the convergence of the phase-field method becomes challenging, especially in scenarios of unstable crack growth. To overcome these numerical difficulties, several approaches have been introduced, with artificial viscosity being among the most widely utilized. This study investigates the energy release rate due to crack propagation in hyperelastic nearly-incompressible materials and compares the phase-field method and a novel gradient-enhanced damage (GED) approach. First, we simulate unstable loading scenarios using the phase-field method, which leads to convergence problems. To address these issues, we introduce artificial viscosity to stabilize the problem and analyze its impact on the energy release rate utilizing a domain J-integral approach giving quantitative measurements during crack propagation. It is observed that the measured energy released rate during crack propagation does not comply with the imposed critical energy release rate, and shows non-monotonic behavior. In the second part of the paper, we introduce a novel stretch-based GED model as an alternative to the phase-field method for modeling crack evolution in elastomers. It is demonstrated that in this method, the energy release rate can be obtained as an output of the simulation rather than as an input which could be useful in the exploration of rate-dependent responses, as one could directly impose chain-level criteria for damage initiation. We show that while this novel approach provides reasonable results for fracture simulations, it still suffers from some numerical issues that strain-based GED formulations are known to be susceptible to.

Cellular contractility, migration, and extracellular matrix (ECM) mechanics are critical for a wide range of biological processes including embryonic development, wound healing, tissue morphogenesis, and regeneration. Even though the distinct response of cells near the tissue periphery has been previously observed in cell-laden microtissues, including faster kinetics and more prominent cell-ECM interactions, there are currently no models that can fully combine coupled surface and bulk mechanics and kinetics to recapitulate the morphogenic response of these constructs. Mailand et al. (Biophys J 117(5):975–986, 2019) had shown the importance of active elastocapillarity in cell-laden microtissues, but modeling the distinct mechanosensitive migration of cells on the periphery and the interior of highly deforming tissues has not been possible thus far, especially in the presence of active elastocapillary effects. This paper presents a framework for understanding the interplay between cellular contractility, migration, and ECM mechanics in dynamically morphing soft tissues accounting for distinct cellular responses in the bulk and the surface of tissues. The major novelty of this approach is that it enables modeling the distinct migratory and contractile response of cells residing on the tissue surface and the bulk, where concurrently the morphing soft tissues undergo large deformations driven by cell contractility. Additionally, the simulation results capture the changes in shape and cell concentration for wounded and intact microtissues, enabling the interpretation of experimental data. The numerical procedure that accounts for mechanosensitive stress generation, large deformations, diffusive migration in the bulk and a distinct mechanism for diffusive migration on deforming surfaces is inspired from recent work on bulk and surface poroelasticity of hydrogels involving elastocapillary effects, but in this work, a two-field weak form is proposed and is able to alleviate numerical instabilities that were observed in the original method that utilized a three-field mixed finite element formulation.

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure-property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. We demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

Most scientific machine learning (SciML) applications of neural networks involve hundreds to thousands of parameters, and hence, uncertainty quantification for such models is plagued by the curse of dimensionality. Using physical applications, we show that $L_0$ sparsification prior to Stein variational gradient descent ($L_0$+SVGD) is a more robust and efficient means of uncertainty quantification, in terms of computational cost and performance than the direct application of SGVD or projected SGVD methods. Specifically, $L_0$+SVGD demonstrates superior resilience to noise, the ability to perform well in extrapolated regions, and a faster convergence rate to an optimal solution.

Collagen scaffolds seeded with human chondrocytes have shown great potential for cartilage repair and regeneration. However, these porous scaffolds buckle under low compressive forces, creating regions of highly localized deformations that can cause cell death and deteriorate the integrity of the engineered tissue. We perform three-dimensional (3D) tomography-based characterization to track the evolution of collagen scaffolds’ microstructure under large deformation. The results illustrate how instabilities produce a spatially varying compaction across the specimens, with more pronounced collapse near the free boundaries. We discover that, independent of differences in pore-size distributions, all collagen scaffolds examined displayed strong auxetic behavior i.e., their transverse area contracts under compression, as a result of the instability cascade. This feature, typically characteristic of engineered metamaterials, is of critical importance for the performance of collagen scaffolds in tissue engineering, especially regarding the persistent challenge of lateral integration in cartilage constructs.

A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress-strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data. Supplementary Information: The online version contains supplementary material available at 10.1007/s00466-024-02497-x.

In this study, we present a methodology to predict the macroscopic yield surface of metals and metallic alloys with general crystallographic textures. In previous work, we have established the use of partially input convex neural networks (pICNN) as macroscopic yield functions of crystal plasticity simulations. However, this work was performed with an over-abundance of data, and on limited crystallographic textures. Here, we extend this study to approach more realistic material states (i.e., complex crystallographic textures), and consider data-availability as a major driver for our approach. We present our modified framework capable of handling generalized material states and demonstrate its effectiveness on samples with multi-modal textures deformed under plane stress conditions. We further describe an adaptive algorithm for the generation of training data as informed by the shape of yield surfaces to reduce the time for both the generation of training data as well as pICNN training. Finally, we will discuss errors in both training and test datasets, limitations, and future extensibility.

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure-property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. We demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiments, verification, and validation.

During cancer pathogenesis, cell-generated mechanical stresses lead to dramatic alterations in the mechanical and organizational properties of the extracellular matrix (ECM). To date, contraction of the ECM is largely attributed to local mechanical stresses generated during cell invasion, but the impact of "elastocapillary" effects from surface tension on the tumor periphery has not been examined. Here, we embed glioblastoma cell spheroids within collagen gels, as a model of tumors within the ECM. We then modulate the surface tension of the spheroids, such that the spheroid contracts or expands. Surprisingly, in both cases, at the far-field, the ECM is contracted toward the spheroids prior to cellular migration from the spheroid into the ECM. Through computational simulation, we demonstrate that contraction of the ECM arises from a balance of spheroid surface tension, cell-ECM interactions, and time-dependent, poroelastic effects of the gel. This leads to the accumulation of ECM near the periphery of the spheroid and the contraction of the ECM without regard to the expansion or contraction of the spheroid. These results highlight the role of tissue-level surface stresses and fluid flow within the ECM in the regulation of cell-ECM interactions.

Bacteria experience substantial physical forces in their natural environment, including forces caused by osmotic pressure, growth in constrained spaces, and fluid shear. The cell envelope is the primary load-carrying structure of bacteria, but the mechanical properties of the cell envelope are poorly understood; reports of Young’s modulus of the cell envelope of Escherichia coli range from 2 to 18 MPa. We developed a microfluidic system to apply mechanical loads to hundreds of bacteria at once and demonstrated the utility of the approach for evaluating whole-cell stiffness. Here, we extend this technique to determine Young’s modulus of the cell envelope of E. coli and of the pathogens Vibrio cholerae and Staphylococcus aureus . An optimization-based inverse finite element analysis was used to determine the cell envelope Young’s modulus from observed deformations. The Young’s modulus values of the cell envelope were 2.06 ± 0.04 MPa for E. coli, 0.84 ± 0.02 MPa for E. coli treated with a chemical (A22) known to reduce cell stiffness, 0.12 ± 0.03 MPa for V. cholerae, and 1.52 ± 0.06 MPa for S. aureus (mean ± SD). The microfluidic approach allows examination of hundreds of cells at once and is readily applied to Gram-negative and Gram-positive organisms as well as rod-shaped and cocci cells, allowing further examination of the structural causes behind differences in cell envelope Young’s modulus among bacterial species and strains.

ABSTRACT Bacteria experience substantial physical forces in their natural environment including forces caused by osmotic pressure, growth in constrained spaces, and fluid shear. The cell envelope is the primary load-carrying structure of bacteria, but the mechanical properties of the cell envelope are poorly understood; reports of Young’s modulus of the cell envelope of E. coli are widely range from 2 MPa to 18 MPa. We have developed a microfluidic system to apply mechanical loads to hundreds of bacteria at once and demonstrated the utility of the approach for evaluating whole-cell stiffness. Here we extend this technique to determine Young’s modulus of the cell envelope of E. coli and of the pathogens V. cholerae and S. aureus. An optimization-based inverse finite element analysis was used to determine the cell envelope Young’s modulus from observed deformations. The Young’s modulus of the cell envelope was 2.06 ± 0.04 MPa for E. coli , 0.84 ± 0.02 MPa for E. coli treated with a chemical known to reduce cell stiffness, 0.12 ± 0.03 MPa for V. cholerae , and 1.52 ± 0.06 MPa for S. aureus (mean ± SD). The microfluidic approach allows examining hundreds of cells at once and is readily applied to Gram-negative and Gram-positive organisms as well as rod-shaped and cocci cells, allowing further examination of the structural causes of differences in cell envelope Young’s modulus among bacteria species and strains.

We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface diffusion kinetics. This type of coupling can manifests as an integral aspect in diverse engineering processes encountered in optical interference coatings, tissue engineering, soft electronics, and can prove important in design process for the next generation of sensors and actuators, especially as the focus is shifted to systems in smaller lengthscales. The intricate interplay between solvent diffusion and deformation of the film is governed by surface poroelasticity, and the viscoelastic deformation of the substrate. While existing methodologies offer tools for studying coupled poroelasticity involving solvent diffusion and network deformation, there exists a gap in understanding how coupled poroelastic processes occurring in a film attached to the boundary of a highly deformable solid can influence its response. In this study, we introduce a non-equilibrium thermodynamics formulation encompassing the multiphysical processes of surface poroelasticity and bulk viscoelasticity, complemented by a corresponding finite element implementation. Our approach captures the complex dynamics between the finite deformation of the substrate and solvent diffusion on the surface. This work contributes valuable insights, particularly in scenarios where the coupling of surface diffusion kinetics and substrate elasticity is an important design factor.