Ellen M. Arruda

Auxetic lattices have demonstrated potential for impact mitigation thanks to their unique configurations. Building upon a prior theoretical framework, this study presents the experimental realization of a theoretically optimized, impact-mitigating bilayer auxetic metamaterial. However, physically realizing the idealized material parameters assumed in theoretical models remains a significant challenge. A central innovation of this work is the development of precise, custom digital polymer formulations, created by tuning the blending ratios of base 3D-printing photopolymers to realize theoretically optimal visco-elastic properties. To support this, we first characterized the broadband visco-elastic behavior of these candidate digital materials formed from a series of 3D-printable photopolymers using dynamic mechanical analysis (DMA). The data informed the development of a combined nonlinear visco-elastic constitutive model—integrating a multi-term Prony series with a neo-Hookean formulation—that accurately captures the intricate mechanical behaviors of real-world polymers. This model guided the selection of optimal digital formulations for fabricating an optimized bilayer metamaterial; its performance was then evaluated via drop-tower impact tests. The finite element predictions, using the nonlinear constitutive model, demonstrated excellent agreement with experiments, particularly throughout the critical loading phase across a wide range of impact severities. This validated our design’s effectiveness in achieving simultaneous force and impulse reductions and highlighted a transition from a material-dominated to a hybrid deformation regime governed cooperatively by material and structural properties. By successfully bridging the gap between computational design and physical realization, this work demonstrates a reliable methodology for designing the next generation of high-performance protective metamaterials.

Abstract Patellar osteochondral allograft (OCA) transplantation is widely used to treat large full-thickness cartilage defects, yet long-term failure and reoperation rates remain high. Although surface congruity and osseous integration are emphasized clinically, cartilage thickness and mechanical compatibility between donor and recipient are not considered. Our previous work suggests that cartilage thickness mismatch can amplify local deformation at the graft boundary, potentially compromising graft longevity. This study investigates how combined mismatches in cartilage thickness and mechanical properties influence the local strain environment at the patellar OCA interface. Simplified two-dimensional axisymmetric finite element models of patellar OCA repair were developed in ABAQUS. Donor-to-recipient cartilage thickness ratios ranging from 0.33 to 3.25 were evaluated together with donor-recipient Young’s modulus mismatches (2.5-7.0 MPa). Cartilage was modeled using homogeneous linear elastic and functionally graded material formulations to account for depth-dependent stiffness. A compressive pressure of 1.0 MPa was applied to represent patellofemoral joint loading, and peak compressive and shear strains were quantified at the graft boundary. Cartilage thickness mismatch produced localized high-strain regions (HSR) of compressive and shear strain at the donor-recipient interface that were absent in thickness-matched constructs. Strain amplification increased with both thickness and mechanical property mismatch. Compressive strain exhibited directional asymmetry, with donor-side-thicker configurations producing greater amplification than recipient-side-thicker configurations. Incorporating depth-dependent cartilage stiffness reduced peak strain magnitudes but did not eliminate mismatch-driven strain amplification. These findings demonstrate that cartilage thickness and mechanical disparity can create HSR at the patellar OCA graft boundary that may predispose grafts to impaired integration and long-term failure.

In this work, we characterized the material properties of an animal model of the rotator cuff tendon using full volume datasets of its intact and injured states. Unlike conventional approaches relying on surface strains or excised specimens, our framework leverages voxel-wise displacement data to infer constitutive behavior while preserving native architecture. Our experimental setup activated volumetric, tensile, and shear mechanisms given the tendon’s complex geometry. We implemented an approach to model inference termed variational system identification (VSI) to solve the weak form of the stress equilibrium equation using these full volume displacements, enabling identification of dominant deformation mechanisms. Three constitutive models were used for parameter inference: a neo-Hookean model, a modified Holzapfel-Gasser-Ogden (HGO) model with higher-order terms in the first and second invariants, and a reduced polynomial model based on the first, second, and fiber-related invariants. VSI-inferred parameters were further refined using an adjoint-based partial differential equation (PDE)-constrained optimization framework. The modified HGO model captures the tendon’s deformation mechanisms with reasonable accuracy, while the neo-Hookean model fails to reproduce key internal features, particularly the shear behavior in injured tendons. Surprisingly, the simplified polynomial model performs comparably to the modified HGO formulation using only three terms. These findings suggest that while current constitutive models do not fully replicate the complex internal mechanics of the tendon, they can capture key trends in intact and damaged tissue, using a homogeneous modeling approach. Continued model development is needed to bridge this gap and enable clinical-grade, predictive simulations of tendon injury and repair.

The modeling and design of linear viscoelastic metamaterials for impact mitigation remains challenging due to the complex interplay between structural geometry, viscoelastic damping, and nonlinear dynamic responses. Our study presents a data-driven framework that balances accuracy, interpretability, and computational efficiency for both forward modeling and inverse design. The mechanical properties of viscoelastic metamaterials are evaluated in terms of their transmitted peak force and impulse. By encoding structural geometries as binary void-shape features, we first develop a sparse linear model for the peak force in elastic metamaterials, which explicitly links dominant void geometries to peak force. We then extend this approach to viscoelastic responses by formulating them as functional transformations of elastic peak force modulated by viscoelasticity. Sparse regression identifies parsimonious nonlinear relationships, retaining only a few terms to describe viscoelastic responses. Furthermore, it enables inverse design with user-defined targets and efficiently mapping solutions to realizable microstructures via a combinatorial search. Our work offers a framework for rapid modeling and tailored design of viscoelastic metamaterials, enabling diverse metamaterials functions such as impact mitigation, wave manipulation and vibration control, and providing a potential pathway for designing other high-performance architected metamaterials.

In this work, we characterized the material properties of an animal model of the rotator cuff tendon using full volume datasets of both its intact and injured states by capturing internal strain behavior throughout the tendon. Our experimental setup, involving tension along the fiber direction, activated volumetric, tensile, and shear mechanisms due to the tendon's complex geometry. We implemented an approach to model inference that we refer to as variational system identification (VSI) to solve the weak form of the stress equilibrium equation using these full volume displacements. Three constitutive models were used for parameter inference: a neo-Hookean model, a modified Holzapfel-Gasser-Ogden (HGO) model with higher-order terms in the first and second invariants, and a reduced polynomial model consisting of terms based on the first, second, and fiber-related invariants. Inferred parameters were further refined using an adjoint-based partial differential equation (PDE)-constrained optimization framework. Our results show that the modified HGO model captures the tendon's deformation mechanisms with reasonable accuracy, while the neo-Hookean model fails to reproduce key internal features, particularly the shear behavior in the injured tendon. Surprisingly, the simplified polynomial model performed comparably to the modified HGO formulation using only three terms. These findings suggest that while current constitutive models do not fully replicate the complex internal mechanics of the tendon, they are capable of capturing key trends in both intact and damaged tissue, using a homogeneous modeling approach. Continued model development is needed to bridge this gap and enable clinical-grade, predictive simulations of tendon injury and repair.

In this work, we characterized the material properties of an animal model of the rotator cuff tendon using full volume datasets of both its intact and injured states by capturing internal strain behavior throughout the tendon. Our experimental setup, involving tension along the fiber direction, activated volumetric, tensile, and shear mechanisms due to the tendon's complex geometry. We implemented an approach to model inference that we refer to as variational system identification (VSI) to solve the weak form of the stress equilibrium equation using these full volume displacements. Three constitutive models were used for parameter inference: a neo-Hookean model, a modified Holzapfel-Gasser-Ogden (HGO) model with higher-order terms in the first and second invariants, and a reduced polynomial model consisting of terms based on the first, second, and fiber-related invariants. Inferred parameters were further refined using an adjoint-based partial differential equation (PDE)-constrained optimization framework. Our results show that the modified HGO model captures the tendon's deformation mechanisms with reasonable accuracy, while the neo-Hookean model fails to reproduce key internal features, particularly the shear behavior in the injured tendon. Surprisingly, the simplified polynomial model performed comparably to the modified HGO formulation using only three terms. These findings suggest that while current constitutive models do not fully replicate the complex internal mechanics of the tendon, they are capable of capturing key trends in both intact and damaged tissue, using a homogeneous modeling approach. Continued model development is needed to bridge this gap and enable clinical-grade, predictive simulations of tendon injury and repair.

Introduction Articular cartilage (AC) defects of the patellofemoral joint (PFJ) are clinically challenging and mechanically demanding. Osteochondral allograft (OCA) transplantation is the standard treatment for large cartilage injuries; however, little is known about intra-tissue mechanics after transplantation. Computational models suggest that cartilage thickness mismatch concentrates stresses at donor–recipient interfaces in OCA-treated patella, but direct experimental evidence is scarce. Local cartilage strain is closely linked to tissue health; therefore, the goal of this work was to provide a preliminary, full volume assessment of patellar cartilage mechanics before and after OCA transplantation. Methods A displacement-encoded MRI sequence was used to quantify full volume displacement and strain fields in human patellar AC before and after OCA transplantation under controlled indentation. Intact cadaveric patellae (n = 4) were prepared, with three serving as recipients and one as donor. Samples were cyclically compressed in a custom-built rig using nominal displacements of 1 and 2 mm. The complex phase data were unwrapped and converted to displacements; the Green–Lagrange strain tensor was computed using a finite element framework in FEniCS. Minimum principal strain ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi mathvariant="italic">min</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) and maximum shear strain ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> <mml:mi>s</mml:mi> <mml:mi>h</mml:mi> <mml:mi>e</mml:mi> <mml:mi>a</mml:mi> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) were analyzed. Donor–recipient step-off distance, representing cartilage-level geometric mismatch, was measured at the graft interface. Results Global displacement fields were similar between intact and OCA samples, with spherical indentation exhibiting through-thickness compression and lateral displacement in longitudinal and transverse directions. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi mathvariant="italic">min</mml:mi> </mml:msub> </mml:mrow> </mml:math> localized beneath the indenter, while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> <mml:mi>s</mml:mi> <mml:mi>h</mml:mi> <mml:mi>e</mml:mi> <mml:mi>a</mml:mi> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> concentrated near the articular surface. OCA-transplanted samples exhibited localized changes in strain distribution near portions of the graft rim, though these features varied across samples. Top-view percentile maps highlighted redistributed high-strain regions in some OCA samples. Exploratory step-off plots showed sample-specific directional trends between geometric mismatch and donor-recipient strain differences, though these trends were not consistent across all samples. Discussion This exploratory study provides the first experimental full volume displacement and strain distributions of patellar cartilage after OCA transplantation. The localized strain variations observed after transplantation should be interpreted descriptively, given the single-donor design and sub-physiological loading. These results establish an experimental foundation for validating computational models of the donor-recipient cartilage interaction and geometric mismatch following OCA transplantation and work investigating OCA mechanics under physiological loading.

Submaximal loading during routine activities is an understudied contributor to evolving mechanics preceding acute Anterior Cruciate Ligament (ACL) injury. This study characterizes the history-dependent mechanical response of the anteromedial (AM) bundle of the ACL subjected to repeated submaximal low-strain cyclic loading and intermittent recovery periods. This loading regime represents early-stage behavior often referred to as preconditioning, which is important for achieving steady-state mechanics but also for understanding the onset of irreversible changes. Digital image correlation (DIC) reveals the development of localized inelastic deformation in regions corresponding to clinically observed acute ACL tears. Complementary repeated cycle-recovery (RCR) experiments reveal that inelastic deformation and normalized hysteresis follow a dual-regime pattern, with pronounced early-cycle attenuation followed by a linear-log response. These findings indicate that submaximal loading induces irreversible mechanical changes on short time scales and establishes a mechanistic link between physiological relevant load histories and increased site-specific susceptibility of the ACL.

Armor is known to protect underlying targets by reducing force transmission during impact events. However, the kinetic energy associated with an impact, often underappreciated, can be as destructive as the force, causing relative motion in the target and consequent damage. Therefore, efficient protective gear and packaging should be lightweight and effective at both force reduction and energy mitigation. Although auxetic lattices have been studied as lightweight alternatives for force reduction, the simultaneous optimization of force reduction and energy dissipation in impact mitigation, through geometric configurations and material selection, has not been addressed. In the present study, we demonstrate that a 2D auxetic lattice, optimized for the slenderness ratio of its struts and for elastic and viscoelastic material properties, can not only reduce the transmitted peak force but also significantly mitigate energy. By employing a multi-step optimization method integrated with Finite Element (FE) analysis, we achieve an optimal auxetic lattice design that simultaneously considers both peak force and energy mitigation. Our results are further validated through theoretical analyses from existing literature.

In this work, we evaluate the mechanical response of rotator cuff tendons with high-grade partial thickness tears through a recently developed full volume measurement technique that resolves through-thickness behavior. As opposed to traditional strain measurement methods, which examine surfaces of the tendon or localized two-dimensional regions, we have probed three-dimensional strains including internal locations via magnetic resonance imaging. Differences between the intact and torn states have been considered in an ex-vivo ovine model of the rotator cuff. The torn condition depicts sliding between cut/uncut tissue regions, with high shear strain concentrations at the boundaries of detached/attached tissue portions. At both submaximal and supramaximal force levels, the internal and inferior bands of the tendon show high shear strain magnitudes, which could indicate regions of high risk for tear propagation. Geometrical features which could explain strain distribution differences in their intact and torn conditions are also analyzed. Through the understanding of full volume displacement and strain distributions, our study elucidates why two-dimensional values might not represent the global behavior of the injured tendon, critical components of the Lagrangian strain tensor which have not been probed before, and important implications for surgical repairs.

This work introduces novel structural design concepts for large aperture RF antennas that can be manufactured in space, overcoming the limitations of traditional launch loads and deployability. The spacecraft is designed to be mass-efficient, stable, and resilient with high precision. To this end, a form-finding approach is deployed to obtain the optimal design of the netband that supports the reflective mesh. The netband is tensioned and supported via eight truss spokes optimized to endow the coupled truss-netband system with the required precision, mass efficiency, and resiliency. The RF antenna design and its substructures are prototyped and statically and dynamically tested to validate the design concepts and metrics.

The precision of space structures is sensitive to high-temperature variation during on-orbit operations. This work develops zero thermal expansion (ZTE) metamaterials that can be integrated into space structures to restrict large thermal deformation under precision requirements. The proposed bi-material ZTE metamaterial beams show extremely low coefficients of thermal expansion (CTE) for a wide temperature variation. Static and dynamic analyses are conducted on the designed metamaterials for performance evaluation. The proposed ZTE beam elements are integrated into a 48-meter rib of a space RF antenna to enhance its thermal precision over a wide temperature range. Further, experimental validation of the ZTE truss beam design is conducted in a thermal chamber to demonstrate its low thermal deformation compared to a reference aluminum truss beam.

Highly precise space structures are sensitive to vibration during on-orbit operation. This work develops metamaterials that can be integrated into space structures, namely dissipative metamaterial beams for vibration mitigation. The proposed dissipative phononic crystal beam with twisted viscoelastic inclusions presents high structural damping over a large space-level temperature range. The developed novel metamaterials can be implemented in the next-generation space structures, which can be manufactured and assembled in space to enhance their spatiotemporal precision.

This work introduces innovative design concepts for solar arrays that can be manufactured in space, overcoming the limitations of conventional launch loads and deployability. The spacecraft is designed to be mass-efficient, stable, precise, and highly resilient. To achieve this, thin plate structures with creases are integrated into the design to support the solar cells while enhancing stiffness and improving the spacecraft's resilience to damage. Numerical analysis demonstrates that creasing the plate that supports the solar cells significantly increases its stiffness with minimal increase in total mass, thereby improving the precision of the solar array. The 1 MW solar array design is optimized for mass efficiency and precision. A scaled-down model is fabricated using additive manufacturing and validated experimentally using modal analysis. The comparison between the eigenmodes and eigenfrequencies obtained from experiments and numerical simulations shows a high level of agreement.

In-space manufacturing is an advantage to the designer by liberating them from the constraints of launch loads and limitations on stowed volumes. Additionally, a structure manufactured entirely in space obviates the need for design checks based on the influence of gravity and eliminates parasitic mass resulting from deploying mechanisms. As a consequence, the primary concern for the designer shifts towards addressing accelerations during maneuvering, thermal gradients (including the effect of partial shadowing), and other vibrations during service, including those of actuators. This paper focuses on the design and optimization of a de-novo 1MW solar array structure intended for full in-space manufacturing. Specifically, a design optimization problem is introduced for a hexagonal solar array spanning 66 meters in width, comprised of a creased, thin, elastic plate on a Kagome bi-layer network. Six design variables have been identified, consisting of one discrete variable and five continuous variables. The present work proposes frameworks for global structural optimization in designing in-space manufacturable structures.

The study presented in this article examines a solar array structure that is intended to be fully manufactured and assembled in space. Consequently, the design of such a structure need not consider the launch loads, usually up to ten times Earth’s gravity. The solar array design is optimized to be highly mass-efficient and ensures high precision even under space-level acceleration loading. This paper focuses on the thermomechanical analysis of the structure and the mechanical response of the array while it goes through eclipses in orbit. The study considers large temperature differences to simulate a full eclipse and investigates the resulting von Mises stresses and displacements. The research found that the solar array’s optimized design maintains the required structural precision under extreme thermal loading. The numerical models for the thermo-mechanical behavior of the solar array were validated by experimentally testing a 3D-printed scaled-down model of a section of the array. The simulations show very good agreement with the experimental results.

Crumpling, folding and introducing creases will increase the transverse stiffness of thin, elastic plates. In this study, fundamental frequency is used as a measure of the stiffness of the plate. A comprehensive study is introduced to show the effect of ordered, pyramidal crumples on the fundamental frequencies of these plates. It is observed that by introducing nine ordered creases in a square sheet of side 6in, an increase of 124% in the fundamental frequency is achieved with only a 0.5% increase in the total mass when compared to a flat plate. A structural optimization formulation is introduced to show that, under the constraints of the problem, a unique and unordered creasing in a thin plate can be obtained that maximizes the fundamental frequency of the structure. The results show a 176% increase in frequency with only 0.84% increase in mass compared to a flat sheet.

Rotator cuff tears constitute a vast majority of shoulder-related injuries, occurring in a wide population range and increasing in incidence with age. Current treatments for full thickness tears use suture to secure the ruptured tendon back to its native attachment site and often retear due to improper enthesis regeneration. To reduce the occurrence of retear, our laboratory developed an engineered tendon graft for rotator cuff repair (ETG-RC) to serve as an underlayment to traditional suture repair. We hypothesize the ETG-RC will aid in the repair of the torn rotator cuff tendon by promoting the regeneration of a functional enthesis. This devitalized graft fabricated from ovine-derived bone marrow stromal cells was evaluated for biomechanical and histomorphology properties in an ovine infraspinatus rotator cuff repair model. Compared with a current standard practice Suture-Only model, the ETG-RC repair showed comparable high strain-to-failure forces, greater fibrocartilage deposition, regeneration of zonal gradients, and Shapey's fibers formation, indicative of enthesis regeneration. Enthesis regeneration after rotator cuff repair should repair mechanical properties and alleviate the need for subsequent surgeries required due to retear. The ETG-RC could potentially be used for repairing other tendon injuries throughout the body.

Approximately 300,000 anterior cruciate ligament (ACL) tears occur annually in the United States, half of which lead to the onset of knee osteoarthritis within 10 years of injury. Repetitive loading is known to result in fatigue damage of both ligament and tendon in the form of collagen unravelling, which can lead to structural failure. However, the relationship between tissue's structural, compositional, and mechanical changes are poorly understood. Herein we show that repetitive submaximal loading of cadaver knees causes an increase in co-localised induction of collagen unravelling and tissue compliance, especially in regions of greater mineralisation at the ACL femoral enthesis. Upon 100 cycles of 4× bodyweight knee loading, the ACL exhibited greater unravelled collagen in highly mineralized regions across varying levels of stiffness domains as compared to unloaded controls. A decrease in the total area of the most rigid domain, and an increase in the total area of the most compliant domain was also found. The results highlight fatigue-driven changes in both protein structure and mechanics in the more mineralized regions of the ACL enthesis, a known site of clinical ACL failure. The results provide a starting point for designing studies to limit ligament overuse injury.

A unique type of domain-wall solitons, fractional topological solitons, have been recently theoretically shown to arise in minimal surface ribbons and demonstrate topological robustness. Here we study these fractional topological solitons experimentally using 3D printed helicoid ribbons and computationally using finite-element analysis (FEA). We show that these fractional solitons propagate at constant speed despite the strong dissipation in the viscoelastic material the ribbon consists of, and this speed can be sensitively controlled by an axial load. The nonlinear viscoelastic FEA quantitatively captures fine features of this fractional soliton. The results verify the predicted fractional solitons, and more importantly, open a new pathway of realizing and controlling topological fractional excitations in systems with complex material features including nonlinearity and viscoelasticity.

Osteochondral allograft implantation is a form of cartilage transplant in which a cylindrical graft of cartilage and subchondral bone from a donor is implanted into a patient's prepared articular defect site. No standard exists for matching the cartilage thickness of the donor and recipient. The goal of this study was to use finite element (FE) analysis to identify the effect of cartilage thickness mismatches between donor and recipient cartilage on cartilage stresses in patellar transplants. Two types of FE models were used: patient-specific 3D models and simplified 2D models. 3D models highlighted which geometric features produced high-stress regions in the patellar cartilage and provided ranges for the parameter sweeps that were conducted with 2D models. 2D models revealed that larger thickness mismatches, thicker recipient cartilage, and a donor-to-recipient cartilage thickness ratio (DRCR) < 1 led to higher stresses at the interface between the donor and recipient cartilage. A surface angle between the donor-recipient cartilage interface and cartilage surface normal near the graft boundary increased stresses when DRCR > 1, with the largest increase observed for an angle of 15°. A surface angle decreased stresses when DRCR < 1. Clinical Significance: This study highlights a potential mechanism to explain the high rates of failure of patellar OCAs. Additionally, the relationship between geometric features and stresses explored in this study led to a hypothetical scoring system that indicates which transplanted patellar grafts may have a higher risk of failure.

&lt;div&gt;Abstract&lt;p&gt;Understanding the molecular alterations that confer cancer cells with motile, metastatic properties is needed to improve patient survival. Here, we report that p38γ motogen-activated protein kinase regulates breast cancer cell motility and metastasis, in part, by controlling expression of the metastasis-associated small GTPase RhoC. This p38γ–RhoC regulatory connection was mediated by a novel mechanism of modulating RhoC ubiquitination. This relationship persisted across multiple cell lines and in clinical breast cancer specimens. Using a computational mechanical model based on the finite element method, we showed that p38γ-mediated cytoskeletal changes are sufficient to control cell motility. This model predicted novel dynamics of leading edge actin protrusions, which were experimentally verified and established to be closely related to cell shape and cytoskeletal morphology. Clinical relevance was supported by evidence that elevated expression of p38γ is associated with lower overall survival of patients with breast cancer. Taken together, our results offer a detailed characterization of how p38γ contributes to breast cancer progression. Herein we present a new mechanics-based analysis of cell motility, and report on the discovery of a leading edge behavior in motile cells to accommodate modified cytoskeletal architecture. In summary, these findings not only identify a novel mechanism for regulating RhoC expression but also advance p38γ as a candidate therapeutic target. &lt;i&gt;Cancer Res; 71(20); 6338–49. ©2011 AACR&lt;/i&gt;.&lt;/p&gt;&lt;/div&gt;

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