Spatial confinement can induce geometrical frustration in condensed phases, giving rise to topological defects that confer materials with new and exotic properties. Here, we experimentally uncover the effect of confinement-induced defect strings termed 'grain boundary scars' on the behavior of dense two-dimensional assemblies of granular spinners, a canonical odd elastic solid. The spatial arrangement of these scars fundamentally reshapes the flows triggered by chiral activity. Specifically, they cause the topologically protected edge flows - a ubiquitous feature of confined spinner assemblies - to decouple from the bulk. Strikingly, increasing the net chiral activity of the system by tuning the ratio of counterclockwise to clockwise spinners caused spontaneous self-shearing. The resulting odd radial stresses led to a chiral activity-mediated reentrant melting transition at a fixed areal spinner density. Our findings open new avenues for exploiting geometrical frustration to elicit novel responses from odd elastic solids.

The theory of nonlinear elasticity has a long history, with contributions from great mathematicians including Euler, Lagrange, Cauchy, and many others and with critical applications in engineering and technology. The complex equations required for stress analyses in elastic solids have been the subject of extensive studies over many years, and effective and efficient systematic procedures have been developed to solve these equations. More recently, the rapid growth of computing technology and numerical methods has also guaranteed accurate and reliable solutions. In the formulation of nonlinear static and dynamic problems involving elastic solids, the most widely used form of the nonlinear strain tensor, namely, the Green strain tensor, is defined in terms of the deformation gradient. Another nonlinear strain tensor, the Euler–Almansi strain tensor, is also defined in a similar manner. It has now been found that on the basis of the linear Cauchy strain tensor and considering changes of the coordinate framework under finite deformations, a new nonlinear strain tensor can be defined consistently and differs from previously known nonlinear strain tensors. This new strain tensor, the nonlinear Cauchy strain tensor, offers a novel formulation of nonlinear elasticity in addition to the existing nonlinear strain tensors.

Non-Hermitian pseudo-gaps and higher-order skin modes in non-centrosymmetric, odd elastic solids

Abstract The lattice Boltzmann method (LBM) has been successfully applied to the simulation of fluid flows for over three decades. In recent years, it has also been extended to solid mechanics, particularly for elastodynamics. This work presents a comprehensive introduction to the moment chain LBM for solids, focusing on the two-relaxation-time (TRT) scheme. The method is based on a chain of balance equations, which allows for the simulation of wave propagation in elastic solids. The TRT scheme improves stability and accuracy, making it suitable for a wide range of material parameters. The method is applied to wave propagation in solids with an analysis of the energy dissipation. The results demonstrate the effectiveness of the moment chain LBM for simulating elastodynamics and highlight its potential for future applications in solid mechanics.

On the wave propagation in unbounded space-fractional elastic solids and identification of its intrinsic microstructure based on Lagrange lattice

Strain-stiffening in elastic solids reinforced by stiff wavy fibers

On universal deformations of compressible Cauchy elastic solids reinforced by inextensible fibers

We developed a model to predict the quality of fresh goji berries during storage by analyzing the correlations of their dielectric properties. The variations in these properties with storage temperature, time, and frequency were systematically characterized to inform the model. Leveraging these relationships, we developed a model to predict quality. The analysis integrated measurements of dielectric properties with assessments of texture and key physicochemical indicators. Results indicate that dielectric parameters exhibit significant frequency dependence. Complex impedance (Z), capacitance (Cp), and resistance (Rp) all decreased sharply with increasing frequency, with the most pronounced change observed in Cp. Conductance, G, and reactance, X, increased with frequency, reaching maximum increases of 360.86% and 87.79%, respectively. Under the specific test frequency of 163,280 Hz, a strong polynomial relationship was observed between the dielectric parameters and storage time, with all fitted models yielding Radj2 values above 0.94. The quality factor Q (a dimensionless number for the energy efficiency of a resonant circuit or medium) showed a near-perfect correlation with brittleness, while reactance, X, was correlated with springiness and cohesiveness, with correlation coefficients approaching 0.999 under the optimal test frequency. The constructed ANN model demonstrated high prediction accuracy for hardness, brittleness, elasticity, cohesiveness, chewiness, and soluble solids content (R2 > 0.97, MSE < 5%) but performed poorly in predicting adhesiveness, stickiness, and rebound elasticity (R2 < 0.9). The constructed LSSVM model showed good prediction performance for some indicators (hardness, springiness, cohesiveness, and SSC) (R2 > 0.94), but its prediction accuracy was low for brittleness and chewiness (R2 < 0.9). Overall, its performance and generalization ability were inferior to the ANN model. This study shows that ANN models based on dielectric properties establish a technical foundation for the non-destructive, automated monitoring of goji berry storage quality, thereby providing a critical tool for dynamic quality tracking and value assessment within integrated warehouse management systems.

Abstract A novel variational formulation is developed for natural frequency analysis of couple stress elastic continua. This formulation is based on extremization of a correlated action of the primary variables in the frequency domain. To reduce continuity requirements from $${C}^{1}$$ C 1 to $${C}^{0}$$ C 0 , Lagrange multipliers are employed to satisfy curvature–displacement compatibility and the essential boundary conditions on rotations in a variational sense, thus resulting in a mixed formulation with displacement and couple stress vectors as primary field variables. Using this variational framework to create a weak form, a two-dimensional finite element method is developed to carry out size-dependent natural frequency analysis of cubic elastic solids for the first time under consistent couple stress theory. The elements used are linear constant strain triangles with additional degrees of freedom on the edges, where tangential components of couple stress are assigned. Elements of this variety are referred to as edge elements or vector finite elements and have a distinct benefit in this case of ensuring the divergence free nature of couple stresses. Two fundamental computational examples are considered under plane strain conditions. First, a slender cantilever beam is examined for an isotropic material, along with corresponding single crystal aluminum and copper beams to explore the effects of anisotropy. A Rayleigh quotient analysis is carried out to quantify couple stress contributions to frequencies and mode shapes, and a modal participation analysis is performed to quantify how each mode contributes to motion in the coordinate directions. Finally, a hollow circular cylinder, both closed and with a small opening, is studied for the isotropic material and single crystal copper. Interesting results show a shift toward isotropic behavior for the copper cylinder and a reduction in the influence of the opening for both materials as the couple stress length parameter increases. With the ongoing push for new technologies on the micro- and nano-scale for applications in sensing, actuating and energy harvesting, the physical phenomena studied in this paper are important to consider for predicting mechanical behavior in this domain. In particular, understanding the role of size-dependent response becomes critical for effective design.

This paper is devoted to the modelling of nonlocality in continuum physics through constitutive functions that depend on suitable gradients. For definiteness, the attention is addressed to elastic solids, heat conductors, and magnetic solids. Models are developed where both the requirements of the second law of thermodynamics and the balance equations are satisfied for the constitutive functions that involve gradients of strain, temperature, heat flux, and magnetization. Concerning elastic and magnetic solids, it is shown that, depending on the chosen variables, the standard symmetry property of the stress holds identically. The models so developed are free from any hyperstress tensor frequently considered in the literature.

ABSTRACT The present work aims to gain new insights into thermal stresses and force states in peridynamic elastic solids. The key findings from this study are: (1) A general micro‐potential‐based formulation is developed for peridynamic thermal stresses in elastic solids. It provides a route to develop and verify micro‐bond potential functions for materials with a known relationship between thermal stress and strain. As an example, a specific micro‐bond potential is introduced, and the corresponding peridynamic thermal stresses are derived, which take the same form as the linear relationship between stresses and strains in the classical theory of thermoelasticity. It indicates that the specific micro‐bond potential is applicable to linear thermoelasticity and might be further used to develop bond failure criteria for linear thermoelastic solids. (2) A peridynamic projection tensor is defined for the first time, based on which an exact relation between stresses and force states is established. This would provide a powerful way to incorporate more material models in peridynamics. (3) The peridynamic linear thermoelastic‐elastic correspondence principle is first developed by inspection of the constitutive force states and the basic peridynamic momentum equation. Peridynamic hypothetical body forces are formulated by taking into account the temperature effect on the motion. On this basis, the displacement solution to a linear thermoelastic problem could be replaced by a solution to a corresponding isothermal problem provided that the solid was subject to an additional hypothetical peridynamic body force. Besides, study shows that for material points away from solid boundaries, the hypothetical peridynamic body forces converge to those defined in the classical theory of linear thermoelasticity as the horizon approaches zero. The effectiveness of the present work is demonstrated through numerical examples, highlighting its ability to provide good predictions for displacements and thermal stresses in linear thermoelastic solids.

Shank3 oligomerization governs material properties of the postsynaptic density condensate and synaptic plasticity.

Surface-polyconvex models for soft elastic solids

Abstract We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of Yavari and Goriely (Proc. R. Soc. A 472(2196):20160690, 2016), who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent).

Abstract Most theories and applications of elasticity rely on an energy function that depends on the strains from which the stresses can be derived. This is the traditional setting of Green elasticity, also known as hyper-elasticity. However, in its original form the theory of elasticity does not assume the existence of a strain energy function. In this case, called Cauchy elasticity, stresses are directly related to the strains. Since the emergence of modern elasticity in the 1940s, research on Cauchy elasticity has been relatively limited. One possible reason for this is that for Cauchy materials, the net work performed by stress along a closed path in the strain space may be nonzero. Therefore, such materials may require access to both energy sources and sinks. This characteristic has led some mechanicians to question the viability of Cauchy elasticity as a physically plausible theory of elasticity. In this paper, motivated by its relevance to recent applications, such as the modeling of active solids, we revisit Cauchy elasticity in a modern form. First, we show that in the general theory of anisotropic Cauchy elasticity, stress can be expressed in terms of six functions, that we call Edelen-Darboux potentials. For isotropic Cauchy materials, this number reduces to three, while for incompressible isotropic Cauchy elasticity, only two such potentials are required. Second, we show that in Cauchy elasticity, the link between balance laws and symmetries is lost, in general, since Noether’s theorem does not apply. In particular, we show that, unlike hyperleasticity, objectivity is not equivalent to the balance of angular momentum. Third, we formulate the balance laws of Cauchy elasticity covariantly and derive a generalized Doyle–Ericksen formula. Fourth, the material symmetry and work theorems of Cauchy elasticity are revisited, based on the stress-work 1-form that emerges as a fundamental quantity in Cauchy elasticity. The stress-work 1-form allows for a classification via Darboux’s theorem that leads to a classification of Cauchy elastic solids based on their generalized energy functions. Fifth, we discuss the relevance of Carathéodory’s theorem on accessibility property of Pfaffian equations. Sixth, we show that Cauchy elasticity has an intrinsic geometric hystresis, which is the net work of stress in cyclic deformations. If the orientation of a cyclic deformation is reversed, the sign of the net work of stress changes, from which we conclude that stress in Cauchy elasticity is neither dissipative nor conservative. Seventh, we establish connections between Cauchy elasticity and the existing constitutive equations for active solids. Eighth, linear anisotropic Cauchy elasticity is examined in detail, and simple displacement-control loadings are proposed for each symmetry class to characterize the corresponding antisymmetric elastic constants. Ninth, we discuss both isotropic and anisotropic Cauchy anelasticity and show that the existing solutions for stress fields of distributed eigenstrains (and particularly defects) in hyperelastic solids can be readily extended to Cauchy elasticity. Tenth, we introduce Cosserat–Cauchy materials and demonstrate that an anisotropic three-dimensional Cosserat–Cauchy elastic solid has at most twenty four generalized energy functions.

Study on the dynamics of a single cavitation bubble in a compressible spherical liquid confined by an elastic solid

This article is the final part of a three-part series that develops a self-consistent theoretical framework describing the electromechanics of arbitrarily curved lipid membranes at the continuum scale. Owing to their small thickness, lipid membranes are commonly modeled as two-dimensional surfaces. However, this approach breaks down when considering their electromechanical behavior as it requires accounting for their finite thickness. To address this, we developed a new dimension reduction procedure in part I [Y. A. D. Omar et al. Phys. Rev. E 109, 054401 (2024)10.1103/PhysRevE.109.054401] to derive effective surface theories that explicitly capture the finite thickness of lipid membranes. We applied this method to dimensionally reduce Gauss' law and the electromechanical balance laws and referred to the resulting theory as (2+δ)-dimensional, where δ indicates the membrane thickness. However, the (2+δ)-dimensional balance laws for thin bodies derived in part II [Y. A. D. Omar et al., Phys. Rev. E 112, 024406 (2025)10.1103/75tt-k2f5] are general, and specific constitutive material models must be incorporated to specialize them to lipid membranes. In this work, we devise appropriate three-dimensional constitutive models that capture the material behavior of lipid membranes, which flow along their in-plane directions like viscous fluids but bend out-of-plane like elastic solids. The viscous material behavior is recovered by considering a three-dimensional Newtonian fluid model, leading to the same viscous stresses as strictly two-dimensional models of lipid membranes. The elastic resistance to bending is recovered by imposing a free energy penalty on local volume changes. While this material model does give rise to the characteristic bending resistance of lipid membranes, it differs in its higher-order curvature terms from the two-dimensional Canham-Helfrich-Evans theory. Furthermore, since lipid membranes only exhibit small midsurface stretch, they are often considered midsurface-area incompressible. In this work, this is captured by introducing reactive stresses that give rise to an effective surface tension. Finally, we use the viscous, elastic, and reactive stresses to derive the equations of motion and boundary conditions describing the electromechanics of lipid membranes. We conclude this article by providing the equations of motion and coupling and boundary conditions for a charged lipid membrane embedded in an electrolyte solution.

On a new class of implicit constitutive relation for quasi-incompressible and compressible isotropic nonlinear elastic solids

Presented herein is a novel approach to apply the finite element method (FEM) to the forced vibration analysis of a two-axially preloaded plate with two constituent materials standing on a rigid foundation under a time-variable angled force based on a piecewise homogeneous body model. The article is pioneering the application of the FEM to analyze the mentioned problem, marking a significant advancement in the understanding of multilayered composite structures in engineering dynamics. First, the geometry of the problem and the physical considerations are explained in detail. Next, a mathematical solution process is developed in the context of the theory of linearized waves in elastic solids under a preloaded state according to the variational calculus. The solution algorithm is validated by presenting an error analysis thanks to norm functions and the convergence analysis compared to the available studies. Next, a thorough numerical discussion is performed to highlight how various factors involving the initial deformation state, the angles of inclined force, and the resonance frequency, together with the thickness ratio and the frequency response of the system, affect its forced vibration behaviors. Numerical results demonstrate that while increasing the vertical length of the body exceeds the resonance frequency of the system, increasing the horizontal lengths promotes that mode. Also, it is shown that when the Young modulus of the lower layer is bigger than that of the upper layer, the stability of the system increases.

Abstract Dry adhesion between solids relies on direct surface–surface interactions (such as van der Waals forces) that require intimate contact. In contrast, capillary adhesion occurs when a liquid bridge forms between surfaces and generates attractive forces through the line force and negative Laplace pressure. At first glance, these two adhesion mechanisms appear mutually exclusive or at least fundamentally different in origins, raising the question: When a liquid bridge brings two solid surfaces into contact, does the system exhibit dry or capillary adhesion as the bridge size becomes small? We show that the answer depends on whether the liquid energetically spreads at the solid–solid interface and, in either case, the minimization of total free energy suggests that the system adopts the maximum adhesion possible. Specifically, when the liquid spreads, the system asymptotically exhibits capillary adhesion; otherwise, dry adhesion eventually prevails. Naturally, the term “small” for the liquid bridge should be defined relative to the characteristic size of the specific system. We then elucidate the capillary and dry adhesion interplay by examining two representative systems: the adhesion of a folded elastica loop and the adhesion of a rigid sphere on a linearly elastic half-space. The corresponding small parameters are defined by a combination of geometry and elasticity. In particular, in the second system, we demonstrate the emergence of modified Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov limits in systems of both dry and capillary adhesion, with a continuous transition governed by an effective liquid volume that we define.