Fast transient dynamic plane stress analysis of orthotropic Hill-type solids at finite elastoplastic strains

Abstract

The objective of this work is the geometrically nonlinear plane stress analysis of orthotropic Hill type elastoplastic solids under short term dynamic loading conditions. Thereby, the underlying motivation is the necessity to model the anisotropic behaviour of metal specimens which is due to the manufacturing procedure in terms of an orthotropic yield condition. To this end, the classical von Mises condition in the framework of multiplicative elastoplasticity is substituted by a yield criterion which invokes a second order anisotropy tensor acting on the deviatoric stresses in the plastic intermediate configuration. A reparametrization of this model reveals its relation to the classical criterion originally proposed by Hill in the geometrically linear setting. Moreover an element technology is outlined recovering the plane stress response of arbitrary 3D constitutive models without any plane stress specific modifications in the large strain regime. The intriguing influence of certain types of orthotropy on the failure patterns of thin metal sheets under plane stress uniaxial extension is investigated numerically. Thereby, an explicit time stepping procedure designed to incorporate the developed plane stress element is employed to trace the short term response predictions of the investigated specimens.