Dynamic fracture modeling with a meshfree peridynamic code

Abstract

The peridynamic model is an alternate theory of continuum mechanics that is specifically oriented toward modeling problems, in which cracks or other discontinuities emerge spontaneously as a body deforms under load. In this study, a code that implements this theory is applied to the Kalthoff-Winkler dynamic single-fracture experiment in a tough steel specimen. Many problems of fundamental importance in mechanics involve the spontaneous emergence of discontinuities, such as cracks, in the interior of a body. The classical theory of continuum mechanics is in some ways suited to modeling this type of problem because the theory uses partial differential equations as a mathematical description. Although much work has been devoted to special techniques aimed at working around this problem—particularly in the theory of fracture mechanics—these techniques are not fully satisfactory either in principle or in practice as general descriptions of fracture. This difficulty is inherited by numerical methods that implement the classical theory, including almost all finite-element and finite-difference codes in common usage.