Parallel Elastoplastic Models of Inelastic Material Behavior

Abstract

Parallel mathematical models are presented and analyzed as a basis for representing the mechanical behavior of inelastic materials. These models are developed within the framework of incremental elastoplasticity theory. The models are shown to simply represent strain hardening through the adjustment of internal stresses within internal elements of the model, to capture Bauschinger's effect during stress reversal, and to provide hysteretic loops in closed stress cycles. The models are shown to provide stable, nonassociated plastic flow for frictional materials such as geologic materials, i.e., to obey Drucker's stability postulate. A simple parallel model for rock is presented that gives the same response as a conventional elastoplastic material model when used to fit idealized uniaxial strain and triaxial compression test data. However, the two models give much different results in triaxial extension after initial hardening occurred on the compression side first. It is believed that this modeling concept holds significant promise for improving mathematical models of the inelastic mechanical behavior of a variety of engineering materials.