Numerical studies of unidimensional peridynamic problems

Abstract

The peridynamic theory is an extension of the classical continuum mechanics theory and is based on long-range interaction forces between material points separated by finite distances, which are usually smaller than a parameter l called horizon. These forces depend upon the relative displacements and positions between material points within a body rather than the spatial derivatives of displacements, which are used in classical constitutive relations, allowing modeling of discontinuities such as cracks. This work concerns analysis of 1D problems within the context of peridynamics through numerical methods, with the purpose of gaining understanding in future analysis of 2D and 3D problems.