A large deformation theory for rate-dependent elastic-plastic materials with combined isotropic and kinematic hardening

作者：Henann David L; Anand Lallit^*

来源：International Journal of Plasticity, 2009, 25(10): 1833-1878.

DOI：10.1016/j.ijplas.2008.11.008

• Large deformation viscoplasticity
• Isotropic hardening
• Kinematic hardening
• Time-integration procedure
• Finite elements

We have developed a large deformation viscoplasticity theory with combined isotropic and kinematic hardening based on the dual decompositions F = F(e)F(p) [Kroner, E., 1960. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Archive for Rational Mechanics and Analysis 4, 273-334] and F(p) = F(en)(p)F(dis)(p) [Lion, A., 2000. Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models. International Journal of Plasticity 16, 469-494]. The elastic distortion F(e) contributes to a standard elastic free-energy psi((e)), while F(en)(p), the energetic part of F(p), contributes to a defect energy psi((p)) - these two additive contributions to the total free energy in turn lead to the standard Cauchy stress and a back-stress. Since F(e) = FF(p-1) and F(en)(p) = F(p)F(dis)(p-1), the evolution of the Cauchy stress and the back-stress in a deformation-driven problem is governed by evolution equations for F(p) and F(dis)(p) - the two flow rules of the theory.
We have also developed a simple, stable, semi-implicit time-integration procedure for the constitutive theory for implementation in displacement-based finite element programs. The procedure that we develop is "simple" in the sense that it only involves the solution of one non-linear equation, rather than a system of non-linear equations. We show that our time-integration procedure is stable for relatively large time steps, is first-order accurate, and is objective.

• 出版日期2009-10