FAST TRANSIENT DYNAMIC PLANE-STRESS ANALYSIS OF ORTHOTROPIC HILL-TYPESOLIDS AT FINITE ELASTOPLASTIC STRAINS

The objective of this work is the geometrically nonlinear plane stress analysis of orthotropic Hill type elastoplastic solids under short te rm dynamic loading conditions. Thereby, the underlying motivation is t he necessity to model the anisotropic behaviour of metal specimens whi ch is due to the manufacturing procedure in terms of an orthotropic yi eld condition. To this end, the classical von Mises condition in the f ramework 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 repa rametrization of this model reveals its relation to the classical crit erion originally proposed by Hill in the geometrically linear setting. Moreover an element technology is outlined recovering the plane stres s response of arbitrary 3D constitutive models without any plane stres s specific modifications in the large strain regime. The intriguing in fluence of certain types of orthotropy on the failure patterns of thin metal sheets under plane stress uniaxial extension is investigated nu merically. Thereby, an explicit time stepping procedure designed to in corporate the developed plane stress element is employed to trace the short term response predictions of the investigated specimens.