The phenomenological theory of elastic—plastic response is reconsidered in the light of recent opinion regarding the constitutive character of the constituent elastic and plastic deformations. The primary role of dissipation in the physics of plastic evolution is emphasized and shown to lead to the clarification of a number of open questions. Particular attention is given to the invariance properties of the elastic and plastic deformations, to the kinematics of discontinuities, and to the role of material symmetry in restricting constitutive equations for elastic response, yield and plastic evolution.

A non-equilibrium theory of isothermal and diffusionless evolution of incoherent interfaces within a plastically deforming solid is developed. The irreversible dynamics of the interface are driven by its normal motion, incoherency (slip and misorientation), and an intrinsic plastic flow;and purely by plastic deformation in the bulk away from the interface. Using the continuum theory for defect distribution (in bulk and over the interface) we formulate a general kinematical framework, derive relevant balance laws and jump conditions, and prescribe a thermodynamically consistent constitutive/kinetic structure for interface evolution.

The coupled motion of a closed non-circular grain boundary (GB) in a bicrystal, with both isotropic and anisotropic GB energies, is studied using the level set method. The kinetic relations, obtained within the framework of linear irreversible thermodynamics, govern the overall dynamics including normal motion (migration) of the GB, viscous sliding along the GB, and tangential motion of the grains which is geometrically coupled with the migration. The shape accommodation necessary to maintain coherency of relatively rotating and non-deforming grains is accomplished by allowing for diffusion along the GB. We solve the governing equations for the coupled motion to determine the shape and the misorientation evolution of an isolated GB under various constitutive assumptions. First, assuming both GB energy and kinetic coefficients to be isotropic, we study the interplay between kinetic coefficients for initially circular, near-circular, and non-circular GBs, as well as the role of stress and initial conditions on the GB dynamics. Next, we study the influence of anisotropy in GB energy, mobility, and geometric coupling for various combinations of parameters and initial conditions. Allowing for geometric coupling can in fact lead to distinctly different shapes than what are usually predicted on the basis of migration alone. Our numerical scheme provides a general framework to study these and other related problems of GB motion.

The dual conservation laws of elasticity are systematically re-examined by using both Noether's variational approach and Coleman-Noll-Gurtin's thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy-momentum tensor. Some previously unknown and yet interesting results in elasticity theory have been discovered. As an example, we note the following duality condition between the configuration force (energy-momentum tensor) P and the dual configuration force (dual energy-momentum tensor) L, P À L ¼ ðP : FÞ1 À rðP Á xÞ:This and other results derived in this paper may lead to a better understanding of configurational mechanics and therefore of mechanics of defects. (2000): 35L65, 37K05, 49S05, 58E30 Mathematics Subject Classification

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various kinematical quantities, such as area change and curvature, on the elastic and inelastic strains is discussed. This is essential for the development of general constitutive models. In order to fully explore the coupling between elastic and different inelastic deformations, the surface balance laws for mass, momentum, energy and entropy are examined in the context of the multiplicative decomposition. Based on the second law of thermodynamics, the general constitutive relations are then derived. Two cases are considered: Independent inelastic strains, and inelastic strains that are functions of temperature and concentration. The constitutive relations are illustrated by several nonlinear examples on growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells. The formulation is fully expressed in curvilinear coordinates leading to compact and elegant expressions for the kinematics, balance laws and constitutive relations. (183) and consider only inelastic dilatation (â αβ = J in A αβ ) according to Sec. 3.3. Contracting (184) with a αβ and using the relations from Sec. 3.3 thus yields the evolution laẇfor J in . For a generalized viscoelastic solid, see Fig. 2b, evolution law (184) needs to be solved forâ αβ