Thermoelasticity of bodies with microstructure and microtemperatures

AbstractThis paper is concerned with a linear theory of thermodynamics for elastic materials with microstructure, whose microelements possess microtemperatures. It is shown that there exists the coupling of microrotation vector field with the microtemperatures even for isotropic bodies. Uniqueness and continuous dependence results are presented. The theory is used to establish the solution corresponding to a concentrated heat source acting in an unbounded continuum

On the torsion of chiral bars in gradient elasticity

AbstractThis paper contains a study of the problem of torsion of chiral bars with arbitrary cross-sections in the context of the linear theory of gradient elasticity. The solution is expressed in terms of solutions of four auxiliary plane problems characterized by loads which depend only on the constitutive coefficients. It is shown that, in general, the torsion produces extension (or contraction) and bending effects. The results are used to investigate the torsion of a homogeneous circular bar. In contrast with the case of achiral circular cylinders, the torsion and extension cannot be treated independently of each other

Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices

In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral. Therefore, influence of the chiral effect cannot be properly characterized by existing theories for 2D chiral solids. To circumvent this difficulty, based on reinterpretation of isotropic tensors in a 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. A single material parameter related to chirality is introduced to characterize the coupling between the bulk deformation and the internal rotation which is a fundamental feature of 2D chiral solids. Coherently, the proposed continuum theory is also derived for a triangular chiral lattice from a homogenization procedure, from which the effective material constants of the lattice are analytically determined. The unique behavior in the chiral lattice is demonstrated through the analyses of a static tension problem and a plane wave propagation problem. The results, which cannot be predicted by the non-chiral model, are validated by the exact solution of the discrete model.Comment: 33 pages, 7 figure

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations