Bond Graph Modeling of Continuous Solids in Finite Strain Elastic-Plastic Deformation

Abstract

The physical systems modeling theory of bond graphs may be employed to represent the hysteretic deformation of continuous solids infinite strain elastic-plastic deformation. Second and fourth order tensors represent stress power conjugate variables and transformer or gyrator moduli, respectively, with corresponding inner products generalizing the power flow and modulation calculations of scalar and vector bond graphs. Capacitors and resistors of a tensor type suitably represent strain energy storage, associated flow rules in plasticity, and other familiar concepts. An important application of this simulation technique arises in constitutive modeling studies of nonlinear materials.