Nonelastic strains in solids—an inverse characterization from measured boundary data

Abstract

Nonelastic strains include the strains caused by thermal expansion, phase transformation, plastic deformation and misfit interface, etc. The nonelastic strains, if given, can be replaced by fictitious body forces and surface tractions. The problem is then treated as an elasticity problem. Such a problem is called a forward problem. There is a body of well-developed knowledge dealing with the forward problems. In this paper, we consider the so-called inverse problems. Overspecified boundary values (both tractions and displacements) are used to calculate the nonelastic strains. Although these surface data are not sufficient to determine the exact distribution of the nonelastic strains, some important characteristic quantities associated with the nonelastic strains are obtained. These quantities include lower bounds of the magnitude of the nonelastic strains (in terms of L 2 norm) and elastic energy, etc. The method is applied to a dislocation problem where we compute the Burger's vector from measured residual surface displacements. Another application is found in determining the material properties of a solid with microscopic defects.