APPLICATIONS OF A GENERALIZED COMPLEMENTARY ENERGY PRINCIPLE FOR THE EQUILIBRIUM-ANALYSIS OF SOFTENING STRUCTURES

An interpretation for computational solution is given for a new global extremum principle that models a generalized form of elastic/softenin g structural behavior. The principle and its interpretation are expres sed in a form that accommodates arbitrary heterogeneity and anisotropy in the structural material. Also the stress-strain properties that re flect evolution of local softening are represented in the model by a s et of parameters defined over the field of the structure. Thus, the mo del may be used to predict the general behavior of solid structures ha ving non-uniform stress / strain fields that evolve with change in ext ernal load. A discretized version of the principle used for computatio n is based on a consistent, mixed-form finite element interpretation o f the principle as stated for the general softening continuum. Example computational solutions are provided covering the evolution of soften ing for a uniformly loaded homogeneous sheet with a hole, and simulati ons of a sheet with various configurations of softer or stiffer inclus ions in an otherwise uniform structure.