# Peridynamics-Based Meshless Modeling

Peridynamics based idealization of a solid with a crack

Peridynamics (PD) is a recently introduced non-local reformulation of classical elasticity theory for modeling materials with discontinuities such as cracks [1]. The theory replaces the partial differential equations of classical solid mechanics with integro-differential equations. The equations are based on a model which treats the internal forces within a body as a network of interactions between material points. The governing equation for the peridynamics material points is given by the local conservation of linear momentum as:

The numerical discretization of the governing equation can be cast into a meshless particle (Lagrangian-type) approach, which allows for simulation of discontinuities like crack without any need for re-meshing the domain. The mathematical structure of the PD approach automatically enables simulation of cracks propagation and failure, without the need for complicated crack path algorithms like that of XFEM or cohesive element method.

PD framework can also be used to model multiphysics problems, by expanding the constitutive model to include thermal, electrical and diffusive effects. ACT has developed PD based models for prediction of damage phenomenon in two areas:

1. Corrosion fatigue damage in metals
2. Progressive damage in thick composites

Corrosion fatigue is a damage phenomenon resulting due to material degradation under combined action of cyclic loads and corrosive environments. The corrosion damage phenomenon is a function of material microstructure, mechanical loading and environmental conditions; and its propagation depends on nature of complex interactions at several time and length scales.

Fiber-reinforced composites on the other hand exhibit complex failure mechanisms due to their inherent anisotropy (fiber, matrix phases) and damage aspects like matrix cracking, fiber breakage, fiber-matrix shear and delamination. The exact nature of damage evolution and failure depends on complex interactions between the fiber, matrix phases of each ply and inter-ply interactions, in response to the loading environment.

ACT has developed novel PD based methods to model damage evolution in both the aforementioned scenarios. These models which are based on novel scientific principles link the behavior of material and different scale and provide fundamental insights on damage behavior. The resulting computational framework provides a means to evaluate damage phenomenon in structural components as function of loading and environmental conditions.

ACT’s simulation of crack propagation in composite lamina using meshless peridynamics approach

ACT’s simulation of corrosion pit growth using meshless peridynamics approach

[1] Silling S. A., Journal of the Mechanics and Physics of Solids, 48:175–209 (2000).