State based peridynamic modeling of dynamic fractureJ.T. Foster1, S.A. Silling2 and W.W. Chen3
1 Sandia National Laboratories, Penetration Technology, Albuquerque, NM, USA
2 Sandia National Laboratories, Multiscale Dynamic Materials Modeling, Albuquerque, NM, USA
3 Purdue University, Schools of Aeronautics & Astronautics and Materials Engineering, West Lafayette, IN, USA
Published online: 15 September 2009
Peridynamics is a continuum reformulation of the classical partial differential equations of motion. The divergence of the stress field term in the conservation of linear momentum equation is replaced with an integral functional, which handles material constitutive response. The peridynamic model is a non-local theory. The original peridynamic formulation used a functional that relates forces on neighboring material points through a pair-wise linear potential or “bond”. This had some drawbacks including a resulting Poisson ratio of 1/4. Recent developments have improved upon the original formulation through the use of peridynamic force-vector states. These force-vector states handle the constitutive behavior of the material allowing neighboring material points to interact with each other in any fashion desired, not just pair-wise. These recent developments also allow classical constitutive models (formulated in terms of stress-strain relationships) to be converted to force-vector states in a straightforward manner. The integral formulation of peridynamics allows for straightforward modeling of crack initiation and propagation because the integrals can be evaluated over discontinuities unlike partial differential equations. By analyzing the energy required to break all “bonds” across a plane of unit area (energy release rate), one can determine the critical energy density required to irreversibly fail a single “bond”. By failing individual “bonds”, this allows cracks to initiate, coalesce, and propagate without a prescribed external crack law. This is demonstrated using experimentally collected fracture toughness measurements to evaluate the energy release rate. This energy release rate is used to derive the fracture model input and a classic viscoplastic constitutive law is used to model the deformation around the failure. Simulations are compared to experimental results.
© EDP Sciences 2009