A peridynamics-like framework to analyze structures

Abstract

Largely motivated by the advantages of peridynamics, the purpose of the thesis is to propose a derivative-free continuum mechanics framework for solving a broad class of problems in solid mechanics, particularly focusing on modeling the failure of concrete and analysing the architected beams and plates. The most important finding of this work is perhaps the proposal of a derivative-free directionality term that is derived based on a stochastic projection technique. The directionality term, which recovers the classical gradient in an infinitesimal limit, can be seen as a non-local counterpart to the deformation gradient. Within this derivative-free set up, a constitutive model for concrete-like composite materials is proposed in Chapter 2. The constitutive relation affords a way of incorporating information pertaining to the different constituents depending on their volume measures, within the continuum setting. Much like peridynamics, the integro-differential nature of the balance laws naturally helps in the simulation of non-linear and discontinuous phenomena such as fracture. However, unlike the most popular non-ordinary state based peridynamics, our proposal offers a constitutive relation of its own, thereby eschewing the constitutive correspondence route and the issues that crop up in the process. The method is specifically applied to the simulation of inelastic deformation and damage in concrete.