A contribution to the development of the theory of peridynamic elasticity

Abstract

Peridynamics is a nonlocal theory of continuum mechanics that considers the interaction of material points due to forces acting at a finite distance. In contrast to the classical theory, the balance of linear momentum does not involve spatial derivatives and remains valid on a surface of discontinuity, such as a crack, or a continuum in which discontinuities may appear as a result of deformation, such as a phase boundary. Also, peridynamics provides a natural setting to model long-range forces that are important in nanoscale applications and biomechanics. This project will contribute to the development of the peridynamic elasticity theory. The project is divided in two main parts. The first part consists of completing an investigation on the validation of expressions obtained for material constants of a linear elastic peridynamic material. The second part consists of determining the role of the boundary conditions and constitutive hypotheses on the behavior of an elastic peridynamic bar. In particular, it is our intention to consider the Ericksen bar problem in the context of the elastic peridynamic theory and to use an adaptive dynamic relaxation method to search for approximate solutions. This project is complementary to the project MCTI/CNPQ/Universal 14/2014 - Track B, Proc. #444896/2014-7, and is related to the projects Research Fellowship Abroad/FAPESP, Proc. #2010/11969-4, BEPE-IC/FAPESP, Proc. #2016/23777-9, and Visitor from Abroad/FAPESP, Proc. #2016/12217-2. (AU)