Peridynamics damage model through phase field theory

• Published in: International journal of mechanical sciences Vol. 128-129; pp. 181 - 193
• Main Authors: Roy, Pranesh, Pathrikar, Anil, Deepu, S.P., Roy, Debasish
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-08-2017
• Subjects: Constitutive correspondence; Crack branching; Crack propagation; Kalthoff-Winkler experiment; Peridynamics; Phase field; Crack branching; Peridynamics; Kalthoff-Winkler experiment; Constitutive correspondence; Phase field; Crack propagation
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2017.04.016

We attempt a reformulation of the phase field theory in the framework of peridynamics (PD) to arrive at a continuum damage model. This obtains a better criterion for bond breaking in PD, marking a departure from the inherently ad-hoc bond-stretch-based or bond-energy-based conditions and thus allowing for the body to physically break into parts which a phase field model cannot by itself accomplish. Moreover, posed within the PD setup, the integral equation for the phase field eases the smoothness restrictions on the field variable. Taking advantages from both the worlds, the proposed scheme thus offers a better computational approach to problems involving cracks or discontinuities. Starting with Hamilton's principle, an equation of the Ginzburg-Landau type with dissipative correction is arrived at as a model for the phase field evolution. A constitutive correspondence route is followed to incorporate classical constitutive relations within our PD model. Numerical simulations of dynamic crack propagation (including branching) and the Kalthoff-Winkler experiment are also provided. To demonstrate how the model naturally prevents interpenetration, a mode II delamination simulation is presented. A brief discussion on the convergence of PD equations to the classical theory is provided in Appendix I.
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•A peridynamics damage model is proposed with the phase field as damage parameter.•Phase field equations are reconstructed in the framework of peridynamics which eases the smoothness requirement of the field variables.•A rational criterion for bond breaking in tension is suggested to simulate fracture.•Our method naturally prevents matter interpenetration.•Numerical illustrations on dynamic crack branching, Kalthoff-Winkler experiment and prevention of interpenetration are provided.