Energy-based limit criteria for anisotropic elastic materials with constraints

Abstract

The main aim of this paper is to investigate the influence of internal restrictions on the form of the energy-based limit condition. Some restrictions may be imposed in the elastic as well as in the limit states. Spectral decomposition of symmetric linear operators in a space with two different scalar products is applied. An algorithm for accounting for the considered restrictions in the limit condition is proposed. It was shown that as long as the energy scalar product is defined properly in the elastic range, the limit condition having the energy-based interpretation can be found. Examining the material with such an internal structure that there are stresses which do not cause any strain, the space with passive stresses and locked strains has to be introduced. The limit condition in this case has two parts, one connected with active part of stresses which has energy-based interpretation and the second one connected with passive stresses. The algorithm how to introduce this part of stresses to the limit condition has been proposed. As examples, the energy-based form of the Schmid law for single slip is derived and fiber-reinforced materials are analyzed.