Related papers: Strain tensor selection and the elastic theory of …
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
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…
Ordinarily, the stress tensor that one derives for a Madelung fluid is not regarded as being coupled to a strain tensor, which is consistent with the fluid hypothesis. However, based upon earlier work regarding the geometric nature of the…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
An analytical solution in a closed form is obtained for the three-dimensional elastic strain distribution in an unlimited medium containing an inclusion with a coordinate-dependent lattice mismatch (an eigenstrain). Quantum dots consisting…
A continuum mechanical theory incorporating an extension of Finsler geometry is formulated for fibrous soft solids. Especially if of biologic origin, such solids are nonlinear elastic with evolving microstructures. For example, elongated…
When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been observed in…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…
Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
We give conditions on the strain-energy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated with the…
A general framework is developed to study the deformation and stress response in F{\"o}ppl-von K{\'a}rm{\'a}n shallow shells for a given distribution of defects, such as dislocations, disclinations, and interstitials, and metric anomalies,…
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…
We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…
Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown…
Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components…
Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
In this paper we study the twist disclination within the elastoplastic defect theory. Using the stress function method, we found exact analytical solutions for all characteristic fields of a straight twist disclination in an infinitely…
The elastic tensor provides valuable insight into the mechanical behavior of a material with lattice strain, such as disordered binary alloys. Traditional stress-strain methods have made it possible to compute elastic constants for ordered…