Effects of a nonlocal microstructure on peeling of thin films.

In this work, starting from an approach previously proposed by the Authors, we put forward an extension to the large deformation regime of the dimensionally-reduced formulation for peridynamic thin plates, including both hyperelasticity and fracture. In particular, the model, validated against numerical simulations, addresses the problem of the peeling in nonlocal thin films, which when attached to a soft substrate highlights how nonlocality of the peeled-off layer might greatly influence the whole structural response and induce some unforeseen mechanical behaviours that could be useful for engineering applications. Through a key benchmark example, we in fact demonstrate that de-localization of damage and less destructive failure modes take place, these effects suggesting the possibility of ad hoc conceiving specific networks of nonlocal interactions between material particles, corresponding to lattice-equivalent structure of the nonlocal model treated, of interest in designing new material systems and interfaces with enhanced toughness and adhesive properties.

Benchmarking physics-informed frameworks for data-driven hyperelasticity.

Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics constraints. Recently, frameworks that automatically satisfy these requirements have been proposed. Here we review, extend, and compare three promising data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE). Our formulation expands the strain energy potentials in terms of sums of convex non-decreasing functions of invariants and linear combinations of these. The expansion of the energy is shared across all three methods and guarantees the automatic satisfaction of objectivity, material symmetries, and polyconvexity, essential within the context of hyperelasticity. To benchmark the methods, we train them against rubber and skin stress-strain data. All three approaches capture the data almost perfectly, without overfitting, and have some capacity to extrapolate. This is in contrast to unconstrained neural networks which fail to make physically meaningful predictions outside the training range. Interestingly, the methods find different energy functions even though the prediction on the stress data is nearly identical. The most notable differences are observed in the second derivatives, which could impact performance of numerical solvers. On the rich data used in these benchmarks, the models show the anticipated trade-off between number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the flexibility and accuracy of other data-driven methods without compromising on the physics. These methods are ideal options to model arbitrary hyperelastic material behavior.

Anisotropic Hyperelastic Strain Energy Function for Carbon Fiber Woven Fabrics.

The present paper introduces an innovative strain energy function (SEF) for incompressible anisotropic fiber-reinforced materials. This SEF is specifically designed to understand the mechanical behavior of carbon fiber-woven fabric. The considered model combines polyconvex invariants forming an integrity basisin polynomial form, which is inspired by the application of Noether's theorem. A single solution can be obtained during the identification because of the relationship between the SEF we have constructed and the material parameters, which are linearly dependent. The six material parameters were precisely determined through a comparison between the closed-form solutions from our model and the corresponding tensile experimental data with different stretching ratios, with determination coefficients consistently reaching a remarkable value of 0.99. When considering only uniaxial tensile tests, our model can be simplified from a quadratic polynomial to a linear polynomial, thereby reducing the number of material parameters required from six to four, while the fidelity of the model's predictive accuracy remains unaltered. The comparison between the results of numerical calculations and experiments proves the efficiency and accuracy of the method.

Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations.

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

Synthetic fibrous hydrogels as a platform to decipher cell-matrix mechanical interactions.

Cells continuously sense external forces from their microenvironment, the extracellular matrix (ECM). In turn, they generate contractile forces, which stiffen and remodel this matrix. Although this bidirectional mechanical exchange is crucial for many cell functions, it remains poorly understood. Key challenges are that the majority of available matrices for such studies, either natural or synthetic, are difficult to control or lack biological relevance. Here, we use a synthetic, yet highly biomimetic hydrogel based on polyisocyanide (PIC) polymers to investigate the effects of the fibrous architecture and the nonlinear mechanics on cell-matrix interactions. Live-cell rheology was combined with advanced microscopy-based approaches to understand the mechanisms behind cell-induced matrix stiffening and plastic remodeling. We demonstrate how cell-mediated fiber remodeling and the propagation of fiber displacements are modulated by adjusting the biological and mechanical properties of this material. Moreover, we validate the biological relevance of our results by demonstrating that cellular tractions in PIC gels develop analogously to those in the natural ECM. This study highlights the potential of PIC gels to disentangle complex bidirectional cell-matrix interactions and to improve the design of materials for mechanobiology studies.

Numerical simulation of mechanical tests on a living skin using anisotropic hyperelastic law.

The skin is a living tissue that behaves in a hyperelastic and anisotropic way. A constitutive law called HGO-Yeoh is proposed to model the skin by improving the classical HGO constitutive law. This model is implemented in a finite element code FER "Finite Element Research" to benefit from its tools, including the bipotential contact method, a very efficient function coupling contact and friction. Identifying the skin-related material parameters is done through an optimisation procedure using analytic and experimental data. A tensile test is simulated using the codes FER and ANSYS. Then, the results are compared with the experimental data. Finally, a simulation of an indentation test using a bipotential contact law is done.

Intermodal coupling spectroscopy of mechanical modes in microcantilevers.

Atomic force microscopy (AFM) is highly regarded as a lens peering into the next discoveries of nanotechnology. Fundamental research in atomic interactions, molecular reactions, and biological cell behaviour are key focal points, demanding a continuous increase in resolution and sensitivity. While renowned fields such as optomechanics have marched towards outstanding signal-to-noise ratios, these improvements have yet to find a practical way to AFM. As a solution, we investigate here a mechanism in which individual mechanical eigenmodes of a microcantilever couple to one another, mimicking optomechanical techniques to reduce thermal noise. We have a look at the most commonly used modes in AFM, starting with the first two flexural modes of cantilevers and asses the impact of an amplified coupling between them. In the following, we expand our investigation to the sea of eigenmodes available in the same structure and find a maximum coupling of 9.38 × 103 Hz/nm between two torsional modes. Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware.

Programmable soft valves for digital and analog control.

In soft devices, complex actuation sequences and precise force control typically require hard electronic valves and microcontrollers. Existing designs for entirely soft pneumatic control systems are capable of either digital or analog operation, but not both, and are limited by speed of actuation, range of pressure, time required for fabrication, or loss of power through pull-down resistors. Using the nonlinear mechanics intrinsic to structures composed of soft materials-in this case, by leveraging membrane inversion and tube kinking-two modular soft components are developed: a piston actuator and a bistable pneumatic switch. These two components combine to create valves capable of analog pressure regulation, simplified digital logic, controlled oscillation, nonvolatile memory storage, linear actuation, and interfacing with human users in both digital and analog formats. Three demonstrations showcase the capabilities of systems constructed from these valves: 1) a wearable glove capable of analog control of a soft artificial robotic hand based on input from a human user's fingers, 2) a human-controlled cushion matrix designed for use in medical care, and 3) an untethered robot which travels a distance dynamically programmed at the time of operation to retrieve an object. This work illustrates pathways for complementary digital and analog control of soft robots using a unified valve design.

Biaxial mechanics of thermally denaturing skin - Part 2: Modeling.

Understanding the response of skin to superphysiological temperatures is critical to the diagnosis and prognosis of thermal injuries, and to the development of temperature-based medical therapeutics. Unfortunately, this understanding has been hindered by our incomplete knowledge about the nonlinear coupling between skin temperature and its mechanics. In Part I of this study we experimentally demonstrated a complex interdependence of time, temperature, direction, and load in skin's response to superphysiological temperatures. In Part II of our study, we test two different models of skin's thermo-mechanics to explain our observations. In both models we assume that skin's response to superphysiological temperatures is governed by the denaturation of its highly collageneous microstructure. Thus, we capture skin's native mechanics via a microstructurally-motivated strain energy function which includes probability distributions for collagen fiber orientation and waviness. In the first model, we capture skin's response to superphysiological temperatures as a transition between two states that link the kinetics of collagen fiber denaturation to fiber coiling and to the transformation of each fiber's constitutive behavior from purely elastic to viscoelastic. In the second model, we capture skin's response to superphysiological temperatures instead via three states in which a sequence of two reactions link the kinetics of collagen fiber denaturation to fiber coiling, followed by a state of fiber damage. Given the success of both models in qualitatively and quantitatively capturing our observations, we expect that our work will provide guidance for future experiments that could probe each model's assumptions toward a better understanding of skin's coupled thermo-mechanics and that our work will be used to guide the engineering design of heat treatment therapies. STATEMENT OF SIGNIFICANCE: Quantifying and modeling skin thermo-mechanics is critical to our understanding of skin physiology, pathophysiology, as well as heat-based treatments. This work addresses a lack of theoretical and computational models of the coupled thermo-mechanics of skin. Our model accounts for skin microstructure through modeling the probability of fiber orientation and fiber stress-free states. Denaturing induces changes in the stress-free configuration of collagen, as well as changes in fiber stiffness and viscoelastic properties. We propose two competing models that fit all of our experimental observations. These models will enable future developments of thermal-therapeutics, prevention and management of skin thermal injuries, and set a foundation for improved mechanistic models of skin thermo-mechanics.

Nonlinear elasticity of biological basement membrane revealed by rapid inflation and deflation.

Basement membrane (BM) is a thin layer of extracellular matrix that surrounds most animal tissues, serving as a physical barrier while allowing nutrient exchange. Although they have important roles in tissue structural integrity, physical properties of BMs remain largely uncharacterized, which limits our understanding of their mechanical functions. Here, we perform pressure-controlled inflation and deflation to directly measure the nonlinear mechanics of BMs in situ. We show that the BMs behave as a permeable, hyperelastic material whose mechanical properties and permeability can be measured in a model-independent manner. Furthermore, we find that BMs exhibit a remarkable nonlinear stiffening behavior, in contrast to the reconstituted Matrigel. This nonlinear stiffening behavior helps the BMs to avoid the snap-through instability (or structural softening) widely observed during the inflation of most elastomeric balloons and thus maintain sufficient confining stress to the enclosed tissues during their growth.

Electroplasticization of Liquid Crystal Polymer Networks.

Shape-shifting liquid crystal networks (LCNs) can transform their morphology and properties in response to external stimuli. These active and adaptive polymer materials can have impact in a diversity of fields, including haptic displays, energy harvesting, biomedicine, and soft robotics. Electrically driven transformations in LCN coatings are particularly promising for application in electronic devices, in which electrodes are easily integrated and allow for patterning of the functional response. The morphing of these coatings, which are glassy in the absence of an electric field, relies on a complex interplay between polymer viscoelasticity, liquid crystal order, and electric field properties. Morphological transformations require the material to undergo a glass transition that plasticizes the polymer sufficiently to enable volumetric and shape changes. Understanding how an alternating current can plasticize very stiff, densely cross-linked networks remains an unresolved challenge. Here, we use a nanoscale strain detection method to elucidate this electric-field-induced devitrification of LCNs. We find how a high-frequency alternating field gives rise to pronounced nanomechanical changes at a critical frequency, which signals the electrical glass transition. Across this transition, collective motion of the liquid crystal molecules causes the network to yield from within, leading to network weakening and subsequent nonlinear expansion. These results unambiguously prove the existence of electroplasticization. Fine-tuning the induced emergence of plasticity will not only enhance the surface functionality but also enable more efficient conversion of electrical energy into mechanical work.

Nonlinear viscoelastic constitutive model for bovine liver tissue.

Soft tissue mechanical characterisation is important in many areas of medical research. Examples span from surgery training, device design and testing, sudden injury and disease diagnosis. The liver is of particular interest, as it is the most commonly injured organ in frontal and side motor vehicle crashes, and also assessed for inflammation and fibrosis in chronic liver diseases. Hence, an extensive rheological characterisation of liver tissue would contribute to advancements in these areas, which are dependent upon underlying biomechanical models. The aim of this paper is to define a liver constitutive equation that is able to characterise the nonlinear viscoelastic behaviour of liver tissue under a range of deformations and frequencies. The tissue response to large amplitude oscillatory shear (1-50%) under varying preloads (1-20%) and frequencies (0.5-2 Hz) is modelled using viscoelastic-adapted forms of the Mooney-Rivlin, Ogden and exponential models. These models are fit to the data using classical or modified objective norms. The results show that all three models are suitable for capturing the initial nonlinear regime, with the latter two being capable of capturing, simultaneously, the whole deformation range tested. The work presented here provides a comprehensive analysis across several material models and norms, leading to an identifiable constitutive equation that describes the nonlinear viscoelastic behaviour of the liver.

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces.

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 µm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Agonistic and antagonistic roles of fibroblasts and cardiomyocytes on viscoelastic stiffening of engineered human myocardium.

Cardiomyocyte and stroma cell cross-talk is essential for the formation of collagen-based engineered heart muscle, including engineered human myocardium (EHM). Fibroblasts are a main component of the myocardial stroma. We hypothesize that fibroblasts, by compacting the surrounding collagen network, support the self-organization of cardiomyocytes into a functional syncytium. With a focus on early self-organization processes in EHM, we studied the molecular and biophysical adaptations mediated by defined populations of fibroblasts and embryonic stem cell-derived cardiomyocytes in a collagen type I hydrogel. After a short phase of cell-independent collagen gelation (30 min), tissue compaction was progressively mediated by fibroblasts. Fibroblast-mediated tissue stiffening was attenuated in the presence of cardiomyocytes allowing for the assembly of stably contracting, force-generating EHM within 4 weeks. Comparative RNA-sequencing data corroborated that fibroblasts are particularly sensitive to the tissue compaction process, resulting in the fast activation of transcription profiles, supporting heart muscle development and extracellular matrix synthesis. Large amplitude oscillatory shear (LAOS) measurements revealed nonlinear strain stiffening at physiological strain amplitudes (>2%), which was reduced in the presence of cells. The nonlinear stress-strain response could be characterized by a mathematical model. Collectively, our study defines the interplay between fibroblasts and cardiomyocytes during human heart muscle self-organization in vitro and underscores the relevance of fibroblasts in the biological engineering of a cardiomyogenesis-supporting viscoelastic stroma. We anticipate that the established mathematical model will facilitate future attempts to optimize EHM for in vitro (disease modelling) and in vivo applications (heart repair).

Magnetic resonance elastography in nonlinear viscoelastic materials under load.

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy's equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of [Formula: see text] Pa in unloaded state, the biased stiffness increases to 9767.5 [Formula: see text]1949.9 Pa under a load of [Formula: see text] 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

Enabling and Localizing Omnidirectional Nonlinear Deformation in Liquid Crystalline Elastomers.

Liquid crystalline elastomers (LCEs) are widely recognized for their exceptional promise as actuating materials. Here, the comparatively less celebrated but also compelling nonlinear response of these materials to mechanical load is examined. Prior examinations of planarly aligned LCEs exhibit unidirectional nonlinear deformation to mechanical loads. A methodology is presented to realize surface-templated homeotropic orientation in LCEs and omnidirectional nonlinearity in mechanical deformation. Inkjet printing of the homeotropic alignment surface localizes regions of homeotropic and planar orientation within a monolithic LCE element. The local control of the self-assembly and orientation of the LCE, when subject to rational design, yield functional materials continuous in composition with discontinuous mechanical deformation. The variation in mechanical deformation in the film can enable the realization of nontrivial performance. For example, a patterned LCE is prepared and shown to exhibit a near-zero Poisson's ratio. Further, it is demonstrated that the local control of deformation can enable the fabrication of rugged, flexible electronic devices. An additively manufactured device withstands complex mechanical deformations that would normally cause catastrophic failure.

Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.

A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.

Imaging the Molecular Motions of Autonomous Repair in a Self-Healing Polymer.

Self-healing polymers can significantly extend the service life of materials and structures by autonomously repairing damage. Intrinsic healing holds great promise as a design strategy to mitigate the risks of damage by delaying or preventing catastrophic failure. However, experimentally resolving the microscopic mechanisms of intrinsic repair has proven highly challenging. This work demonstrates how optical micromechanical mapping enables the quantitative imaging of these molecular-scale dynamics with high spatiotemporal resolution. This approach allows disentangling delocalized viscoplastic relaxation and localized cohesion-restoring rebonding processes that occur simultaneously upon damage to a self-healing polymer. Moreover, frequency- and temperature-dependent imaging provides a way to pinpoint the repair modes in the relaxation spectrum of the quiescent material. These results give rise to a complete picture of autonomous repair that will guide the rational design of improved self-healing materials.

A fibril-based structural constitutive theory reveals the dominant role of network characteristics on the mechanical behavior of fibroblast-compacted collagen gels.

In this paper, we present a general, fibril-based structural constitutive theory which accounts for three material aspects of crosslinked filamentous materials: the single fibrillar force response, the fibrillar network model, and the effects of alterations to the fibrillar network. In the case of the single fibrillar response, we develop a formula that covers the entropic and enthalpic deformation regions, and introduce the relaxation phase to explain the observed force decay after crosslink breakage. For the filamentous network model, we characterize the constituent element of the fibrillar network in terms its end-to-end distance vector and its contour length, then decompose the vector orientation into an isotropic random term and a specific alignment, paving the way for an expanded formalism from principal deformation to general 3D deformation; and, more important, we define a critical core quantity over which macroscale mechanical characteristics can be integrated: the ratio of the initial end-to-end distance to the contour length (and its probability function). For network alterations, we quantitatively treat changes in constituent elements and relate these changes to the alteration of network characteristics. Singular in its physical rigor and clarity, this constitutive theory can reproduce and predict a wide range of nonlinear mechanical behavior in materials composed of a crosslinked filamentous network, including: stress relaxation (with dual relaxation coefficients as typically observed in soft tissues); hysteresis with decreasing maximum stress under serial cyclic loading; strain-stiffening under uniaxial tension; the rupture point of the structure as a whole; various effects of biaxial tensile loading; strain-stiffening under simple shearing; the so-called "negative normal stress" phenomenon; and enthalpic elastic behaviors of the constituent element. Applied to compacted collagen gels, the theory demonstrates that collagen fibrils behave as enthalpic elasticas with linear elasticity within the gels, and that the macroscale nonlinearity of the gels originates from the curved fibrillar network. Meanwhile, the underlying factors that determine the mechanical properties of the gels are clarified. Finally, the implications of this study on the enhancement of the mechanical properties of compacted collagen gels and on the cellular mechanics with this model tissue are discussed.

Evaluation of the strain-line patterns in a human left ventricle: a simulation study.

The aim of this paper is to emphasise the role of the primary strain-line patterns in a human left ventricle (LV) within the complex system that is the heart. In particular, a protocol is proposed for the measurement of the principal strain lines (PSL) in the walls of the LV; this protocol is tested by means of a computational model which resembles a human LV. When the analysis is focused on the epicardial surface, PSL can be used to derive information on the directions of muscle fibres during the entire cardiac cycle, not only the systolic phase.