Three-dimensional model for cyclic, rate-independent and compressible response of aluminium

A three-dimensional rate-independent framework consistent with thermodynamics is presented to study the dissipative response of metals. The entropy inequality is transformed into equality by introducing a non-negative, continuous rate of dissipation function. The constitutive relation that relates the Hencky strain and Cauchy stress is parametrized by replacement stress, instead of the plastic strain, for reasons discussed. The evolution equation for the replacement stress is obtained such that among the possible processes, the one that maximizes the rate of dissipation is realized so that thermodynamic equilibrium is achieved in the shortest possible time. Appropriate 3D constitutive functions to model aluminium are prescribed for the dissipation function and a Gibbs-like potential. The variation of the transverse strain as a function of the uniaxial strain differs between the present formulation and classical plasticity. Consistent with some of the experimental observations, the material tends to be compressible in the present formulation during plastic deformations. Thus, further experimental investigations are required to choose the appropriate constitutive relation.