Cyclic Behavior of Simple Models in Hypoplasticity and Plasticity with Nonlinear Kinematic Hardening

Abstract

The paper gives insights into modeling and well-posedness analysis driven by cyclic behavior of particular rate-independent constitutive equations based on the framework of hypoplasticity and on the elastoplastic concept with nonlinear kinematic hardening. Compared to the classical concept of elastoplasticity, in hypoplasticity there is no need to decompose the deformation into elastic and plastic parts. The two different types of nonlinear approaches show some similarities in the structure of the constitutive relations, which are relevant for describing irreversible material properties. These models exhibit unlimited ratchetting under cyclic loading. In numerical simulation it will be demonstrated, how a shakedown behavior under cyclic loading can be achieved with a slightly enhanced simple hypoplastic equations proposed by Bauer

Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity

“…In this way we also make a close link to barodesy models [18]. The existence of an exact solution made it possible to describe analytically various scenarios of the behavior of stress paths obtained from monotonic compression, extension, and isochoric deformations [7,19,20,21].…”