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Efficient numerical integration of an elastic-plastic damage law within a mixed velocity-pressure formulation. (English) Zbl 1499.74023

Summary: This study focuses on numerical integration of constitutive laws in numerical modeling of cold materials processing that involves large plastic strain together with ductile damage. A mixed velocity-pressure formulation is used to handle the incompressibility of plastic deformation. A Lemaitre damage model where dissipative phenomena are coupled is considered. Numerical aspects of the constitutive equations are addressed in detail. Three integration algorithms with different levels of coupling of damage with elastic-plastic behavior are presented and discussed in terms of accuracy and computational cost. The implicit gradient formulation with a non-local damage variable is used to regularize the localization phenomenon and thus to ensure the objectivity of numerical results for damage prediction problems. A tensile test on a plane plate specimen, where damage and plastic strain tend to localize in well-known shear bands, successfully shows both the objectivity and effectiveness of the developed approach.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
74R05 Brittle damage
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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