Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model wave propagation stressed media. Although third-order tensors have been determined based on first principles previous studies, their current definition is an expansion of thermodynamic energy terms the Lagrangian strain near natural, or zero pressure, reference state. T...

In classical elasticity theory the stress-field of a dislocation is characterized by $1/r$-type singularity. When such considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces order parameter, resulting in non-physical (and discretization-dependent) predictions interaction between dislocations and phase-, twin- or gra...

Abstract: In this paper we solve a simple dead load problem for an isotropic constrained material according to the linearized finite theory of elasticity. We show that the solution of such a problem can be obtained by linearizing with respect to the displacement gradient the solution of the corresponding problem in finite elasticity for an isotropic material subject to the same constraint, exac...

Intermediate filaments are common structural elements found in abundance in all metazoan cells, where they form networks that contribute to the elasticity. Here, we report measurements of the linear and nonlinear viscoelasticity of networks of two distinct intermediate filaments, vimentin and neurofilaments. Both exhibit predominantly elastic behavior with strong nonlinear strain stiffening. We...

A method is proposed herein to build beam equations for materials featuring higher-grade elasticity. As it based on the minimization of constitutive equation gap, static admissibility conditions are taken into account so that naturally converges usual resulting from Cauchy elasticity when dimensions large enough. The exemplified, Euler–Bernoulli beams, first-strain gradient and second-strain el...

It is well known that glassy polymer nanocomposites (PNC) exhibit heterogeneous mechanical properties, with a distinct polymer/nanoparticle (NP) interfacial region. The interphase rigidity in particular can significantly influence the overall response of PNCs. Continuum theories typically describe behavior such to depend only on deformation and, thus, they discard strong internal gradients with...

Several finite elastic strain measures are evaluated for use in constitutive models of crystalline elasticity and elasto-plasticity. These include the Green material strain tensor, the Eulerian material strain tensor, and the logarithmic material strain tensor, all of which are referred to locally relaxed coordinates invariant under spatial rotations. New applications of logarithmic strain-base...

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of  nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the me...

In this study, the small scale effect on the linear free-field vibration of a nano-circular plate has been investigated using nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effects, the governing differential equation based on the nonlocal elasticity theo...

Rheology is science which treats the deformation and flow of materials. The science of rheology is applied to the physics, chemistry, engineering, medicine, dentistry, pharmacy, biology and so on. Classical theory of elasticity treats the elastic solid which is accordant to Hooke’s law [1]. The stress is directly proportional to strain in deformations and is not dependent of the rate of strain....