Related papers: Generalized Hooke's law for isotropic second gradi…
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…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
From the principle of maximum entropy for a closed system in thermal equilibrium, for the first instance a clear relation is shown to exist between total entropy S (in terms of arrangements of particles) and the classical expression for the…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli…
In this chapter, criteria for existence of propagating optical modes which are transversely bound at the interface of two materials are studied. In particular, quite general cases are considered, where the materials involved are assumed to…
Soft materials such as rubber and hydrogels are commonly used in industry for their excellent hyperelastic behaviour. There are various types of constitutive models for soft materials, and phenomenological models are very popular for finite…
Fibre-reinforced elastomers are lightweight and strong materials that can sustain large deformations. When filled with magnetic particles, their effective mechanical response can be modified by an external magnetic field. In the present…
We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function…
A homogenization method to model a stack of second generation (2G) High Temperature Superconducting (HTS) tapes under AC applied transport current or magnetic field has been obtained. The idea is to find an anisotropic bulk equivalent for…
We describe a theoretical and computational approach to calculate the vibrational, elastic, and thermal properties of materials from the low-temperature quantum regime to the high-temperature anharmonic regime. This approach is based on…
Here we study the wave propagation and stability of general relativistic non-resistive dissipative second-order magnetohydrodynamic equations in curved space-time. We solve the Boltzmann equation for a system of particles and antiparticles…
We discuss general 2-fluid hydrodynamic equations for complex fluids, where one kind is a simple Newtonian fluid, while the other is either liquid-crystalline or polymeric/elastomeric, thus being applicable to lyotropic liquid crystals,…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…
In this work, we provide an overview of general solutions for displacement fields in static problems of isotropic strain gradient elasticity (SGE). We not only review existing solutions but also derive new representations, showing that all…
Deformation of material lines drives transport and dissipation in many industrial and natural flows. Here we report an exact Eulerian formula for the stretching rate of a material line, also known as the topological entropy, in a prototype…
Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are…
The theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous…
We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic…