NUMERICAL AND THEORETICAL STUDY OF THE PROPERTIES OF A LINEAR ELASTIC PERIDYNAMIC MATERIAL

Abstract

The peridynamic theory is a generalization of classical continuum mechanics and takes into account the interaction between material points separated by a finite distance within a peridynamic horizon . The parameter corresponds to a length scale and is treated as a material property related to the microstructure of the body. This work concerns a study of the properties of a linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which considers both length and relative angle changes, and is based upon a free energy function that contains four material constants. Using convergence results of the peridynamic theory to the classical linear elasticity theory in the limit of vanishing sequences of and a correspondence argument between the proposed free energy function and the strain energy density function from the classical theory, expressions were obtained relating three peridynamic constants to the classical elasticity constants of an isotropic linearly elastic material. To evaluate the fourth peridynamic material constant, the correspondence argument is used together with the deformation field of an elastic beam subjected to pure bending. This work also concerns the validation of the proposed linearly elastic peridynamic model through numerical simulations of mechanical problems formulated in the context of both the classical linear elasticity and peridynamic theories. Simulation results will be presented at the meeting.