关键词: 黏弹性, 塑性, 应力更新算法, 一致切线算子, 有限元法

Abstract: A coupled viscoelastic-plastic model is composed of viscoelastic model and a series of plastic elements, which can be regarded as a limit condition of the viscoelastic-viscoplastic model when the viscosity-related parameter of viscoplasticity is close to 0. This model provides an alternative scheme for analysing the structural collapse of viscoelastic materials by numerical solution at the certain circumstance. First, the strain increment was decomposed into viscoelastic part and plastic part in this viscoelastic-plastic model. Then the integral type viscoelastic constitutive equations were linearized over the time interval, by taking the history of viscoelastic strains into consideration. Meanwhile, the shear and bulk modules were clearly defined, which are functions of the time increment. The recurrence formulas for stresses on viscoelastic strains were deduced as well. The numerical integration of viscoelastic-plastic constitutive equation was transformed into the similar format with the general elastic-plastic circumstance. The plastic part of the viscoelastic-plastic model was assumed as the hyperbolic Drucker-Prager plasticity with isotropic hardening. Finally, the fully implicit stress update algorithm and the associated consistent tangent operator, as well as the final formulas, were derived by the combination of the viscoelastic predictor and the plastic return mapping. The comparison and analysis of numerical examples indicate that the algorithm had a good convergence, since only the simple function calculation was performed in each iteration process. After two iterations, the value of yield function reached to 10?10 degree, and the stress point returned to the yield surface.

Key words: viscoelasticity, plasticity, return mapping algorithm, consistent tangent operator, FEM