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An implicit time integration scheme for inelastic constitutive equations with internal state variables. (English) Zbl 0584.73108

In a broad class of inelastic constitutive models for the deformation of metals the inelastic strain rates are functions of the current state of stress and internal state variables only. All known models are in some regions of application mathematically stiff and therefore difficult to integrate. The unconditionally stable implicit Euler rule is used for integration. It leads to a system of highly nonlinear algebraic equations which have to be solved by an iterative process. The general Newton- Raphson method, which converges under very broad conditions, requires repeated solution of the finite element system and is infeasible for large inelastic problems. But for the inelastic strains and internal state variables the Jacobian can be computed analytically and therefore the NRI can be used. For the stresses the Jacobian cannot be computed analytically and therefore the accelerated Jacobi iteration is used. A new method for computing the relaxation parameter is introduced which increases the rate of convergence significantly. The new algorithm is applied on Hart’s model. A comparison with prior computations using an approximation is made.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65D30 Numerical integration
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids

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