Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations (PDE) of classical continuum theories with integro-differential equations (IDE). We apply Finite Element Methods (FEM) as well as Discontinuous Galerkin Methods (DGM) to implement the peridynamic model. Since the integro-differential equations remain valid in the presence of discontin...

Adviser: Florin Bobaru Damage and failure in composite materials under dynamic loading has been extensively studied in experiments for several decades. Composite materials exhibit various damage and failure patterns under different loading rates, such as splitting and branching. Classical models cannot directly be applied to problems with discontinuous fields. A new nonlocal continuum model, pe...

This paper first considers the approximation of peridynamics by strain-gradient models in the linear, one-dimensional setting. Strain-gradient expansions that approximate the peridynamic dispersion relation using Taylor series are compared to strain-gradient models that approximate the peridynamic elastic energy. The dynamic and energetic expansions differ from each other, and neither captures ...

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Most physical processes are the result of collective interactions across disparate length and time scales. The dynamic fracture of brittle solids is a particularly interesting collective interaction connecting large and small length scales. With the application of enough stress or strain to a sample of brittle material, atomistic-scale bonds will eventually snap, leading to fracture of the macr...

Using peridynamic simulations, a vast range of materials with di erent properties, from polymethyl methacrylate to titanium alloy can be simulated [5]. The results significantly depend on the models and numerical schemes that are employed. Di erent models for bonds, time integration schemes and the summation of forces between particles are employed. Furthermore, several parameters such as the i...

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blo...