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A thermodynamically consistent peridynamics model for visco-plasticity and damage. (English) Zbl 1440.74035
Summary: This article presents a unified visco-plastic-damage model in the peridynamics set-up which may be applied across different regime of strain rates and temperatures. In the model, we introduce two internal variables, one describing plastic flow and other the damage in the material. Exploiting the idea of master balance, in addition to the conventional momentum balances, we postulate micro-force balances for both plastic flow and damage evolution in terms of additional peridynamic force states. The equations of motion are in the form of integro-differential equations and do not require continuity of field variables. Using the idea of energy equivalence and entropy equivalence, constitutive relations for the peridynamic force states are determined. The proposed peridynamic visco-plastic-damage model may be thought as a non-trivial extension of the recently developed peridynamic visco-plasticity model [the second author et al., “A dynamic flow rule for viscoplasticity in polycrystalline solids under high strain rates”, Int. J. Non-Linear Mech. 95, 10–18 (2017; doi:10.1016/j.ijnonlinmec.2017.05.010)]. The current scheme couples the visco-plasticity and damage in a thermo-dynamically consistent manner and provides temperature evolution which reflects contribution from both plasticity and damage. The efficacy of the model is demonstrated through simulations of the adiabatic shear band propagation as observed in Kalthoff-Winkler experiment and the shear plugging failure of Weldox 460 E steel plates along with the determination of the ballistic limit.

MSC:
74A45 Theories of fracture and damage
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
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