![]() ![]() Considering the tension–compression asymmetry, a new history variable is developed to enforce the irreversibility condition of crack propagation. In particular, the formulation is posed in an updated Lagrangian framework and the constitutive update is realized with a return-mapping algorithm. Our model considers the dynamic finite deformation with both strain hardening and strain rate hardening by the Johnson–Cook plasticity model. In this paper, we present a coupled phase field model to simulate fracture in these situations. High-speed impact problems usually undergo a form of highly localized plastic deformation under high strain rate with intense shock waves.
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