An extended peridynamic approach for deformation and fracture analysis

Abstract

An extended bond-based peridynamic approach is proposed for quantitative analysis of elastic deformation and simulation of both quasi-static and dynamic crack propagation. A continuous function is uniquely introduced in the commonly used peridynamic constitutive model by considering the internal length effect of long-range forces. Moreover, a local damping is incorporated into the peridynamic equations of motion, and the step-by-step loading algorithms and non-equilibrium criterion for particle systems are developed specifically for quasi-static problems. The effective calculation field of material points in the numerical peridynamic discretization is discussed as well. Analysis of quantitative elastic deformation and quasi-static fracture behavior of the model is verified through simulating the uniaxial tension and compression of a slab, bending and failure of a cantilever beam, and quasi-static propagation of mode I and mode II cracks in a plate. The numerical examples show that the present approach is capable of quantitatively calculating the elastic deformation and accurately predicting the critical failure load and crack propagation paths. To further demonstrate the capabilities of the proposed model, dynamic fracture of a brittle plate under high-rate loading is simulated, in which the experimentally-observed phenomena, such as successive branching, are captured naturally as a consequence of the solution.