Computational plasticity model for hydrostatic pressure dependent foam materials

Abstract

A computational plasticity model for hydrostatic pressure dependent foam materials is presented. A new semi-associated flow rule is proposed for a three-parameter generalized initial yield criterion which is based on the second invariant of deviatoric tensor and the first invariant of spherical tensor. The parameters to determine the flow vector and the initial yield failure criterion are based on the three uniaxial strengths, which are obtained by uniaxial tension, compression and pure shear test respectively. Different from other wellknown flow rules which depends on the plastic Poisson ratio, this flow rule uses the standard strength values for plasticity flow and is more convenient and robust to be used. An implicit integration method by return mapping algorithm is carried out and the consistent tangent Jacobian matrix is also presented for the implicit integration. The plasticity model is implemented into the commercial finite element software ABAQUS for implicit finite element analysis. Simple numerical results are validated by the test results of foam materials. Nomenclature 1 I = spherical tensor invariant 2 J = deviatoric tensor invariant t  = tension strength c  = compression strength s  = shear strength 0 t  = initial yield tension strength 0 c  = initial yield compression strength 0 s  = initial yield shear strength   = plastic multiplier of the increment.p e  = equivalent plastic strain.  = coefficient of flow n = increment step number m = iteration step number k = coefficient of increment equivalent plastic strain G = shear modulus K = bulk modulus 2 N = flow tensor d σ = deviatoric stress tensor I = second order identity tensor 4 I = fourth order identity tensor. ε = increment of strain tensor  tr ε = increment of trial strain tensor p ε = increment of plastic strain tensor p d ε = increment of deviatoric plastic strain tensor p v ε = increment of volumetric plastic strain tensor y σ = hardening strength tensor 0 y σ = initial yield strength tensor r = hardening function vector y H = hardening parameter vector tr σ = trial stress tensor e D = elastic stiffness matrix ep D = elasto-plastic stiffness matrix.