相关论文: Connecting weakly nonlinear elasticity theories of…

In the theory of weakly non-linear elasticity, Hamilton et al. [J. Acoust. Soc. Am. \textbf{116} (2004) 41] identified $W = \mu I_2 + (A/3)I_3 + D I_2^2$ as the fourth-order expansion of the strain-energy density for incompressible…

We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion…

The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…

Strain energy density is calculated for a network of flexible chains with weak excluded-volume interactions (whose energy is small compared with thermal energy). Constitutive equations are developed for an incompressible network of chains…

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…

The holographic duality has proven successful in linking seemingly unrelated problems in physics.Recently, intriguing correspondences between the physics of soft matter and gravity are emerging,including strong similarities between the…

A theory is developed for evaluation of nonlinear elastic moduli of composite materials with nonlinear inclusions dispersed in another nonlinear material (matrix). We elaborate a method aimed for determination of elastic parameters of a…

The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…

We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…

The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…

Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model…

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…

We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while…

The stress-strain relationship of biological soft tissues affected by Marfan's syndrome is believed to be non-convex. More specifically, Haughton and Merodio recently proposed a strain-energy density leading to localized strain softening,…

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…