An Elastoplastic Constitutive Model Based on the Cosserat Continuum Theory

Abstract

In order to describe the mechanical response of metal foams, a phenomenological elastoplastic constitutive model is proposed based on the Cosserat continuum theory. Since metal foams involve complex structures in geometry, simple models based on the conventional scheme are of no use in the sense that the models do not capture the specific features of the internal structures. Following a series of experimental and analytical investigations on metals foams, basic equations required for a generalized continuum theory are stated, and then an elastoplastic constitutive model is formulated. The model features are as follows; simple linear elasticity models both for stress and couple stress, and a single yield function accounting for material compressibility and length-scale dependence. The constitutive model naturally approaches to the conventional one when the couple stress terms diminish, and there are only three material parameters particular to the couple stress component. Applying the mixed-type element discretization technique to the virtual work principle, we obtain the finite element equation, which is regarded as one of the simplest extensions from the conventional scheme. A bending process simulation is carried out to demonstrate the effect of couple stress on the mechanical responses.