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Small strain elasto-plastic multiphase-field model. (English) Zbl 1314.74013

Summary: A small strain plasticity model, based on the principles of continuum mechanics, is incorporated into a phase-field model for heterogeneous microstructures in polycrystalline and multiphase material systems [B. Nestler et al., “Multicomponent alloy solidification: phase-field modeling and simulations”, Phys. Rev. E 71, No. 4, Article ID 041609, 6 p. (2005; doi:10.1103/PhysRevE.71.041609)]. Thereby, the displacement field is computed by solving the local momentum balance dynamically [R. Spatschek et al., “Phase field modeling of fracture and stress-induced phase transitions”, Phys. Rev. E 75, No. 6, Article ID 066111, 14 p. (2007; doi:10.1103/PhysRevE.75.066111)] using the finite difference method on a staggered grid. The elastic contribution is expressed as the linear approximation according to the Cauchy stress tensor. In order to calculate the plastic strain, the Prandtl-Reuss model is implemented consisting of an associated flow rule in combination with the von Mises yield criterion and a linear isotropic hardening approximation. Simulations are performed illustrating the evolution of the stress and plastic strain using a radial return mapping algorithm for single phase system and two phase microstructures. As an example for interface evolution coupling with elasto-plastic effects, we present crack propagation simulations in ductile material.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74N15 Analysis of microstructure in solids
74E15 Crystalline structure
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