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Development of nonlocal theory in solid mechanics

Grant number: 19/00428-7
Support type:Regular Research Grants
Duration: May 01, 2019 - April 30, 2021
Field of knowledge:Engineering - Civil Engineering
Principal Investigator:Adair Roberto Aguiar
Grantee:Adair Roberto Aguiar
Home Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated scholarship(s):19/12102-9 - Support for the implementation of computational code for numerical simulation of nonlinear peridynamic problems, BP.TT
19/12546-4 - Support for the implementation of computational code for numerical simulation of linear peridynamic problems, BP.TT

Abstract

Nonlocal theories have been proposed to model the behavior of solids in the vicinity of singular points, such as crack tips and points on interfaces between different materials. In particular, in the peridynamic theory the concept of interaction between particles separated by finite distances between them is used to rewrite the equation of motion in terms of the corresponding interaction forces. These forces are given in terms of the relative displacements between the particles, which makes it possible to apply the resulting governing equation directly onto a surface of discontinuity, such as the edges of a crack or the material interfaces that may appear as a result of the deformation of a solid. In this project we will continue the development of a peridynamic theory that is physically plausible and mathematically amenable to analysis. We will also continue to investigate the loss of elipticity in orthotropic materials. This project is complementary to the project MCTI/CNPQ 28/2018 - Universal/Faixa B, Proc. 420099/2018-2, and is related to the project FAPESP - Bolsa de Doutorado no País, Proc. 2017/23669-4. (AU)