Instability and Phase Mixtures in Peridynamic Elasticity

• Grant number: 19/15086-4
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2019
• End date: November 28, 2019
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Adair Roberto Aguiar
• Grantee: Alan Bourscheidt Seitenfuss
• Supervisor: Gianniroyer-Carfagni
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Università degli Studi di Parma, Italy
• Associated to the scholarship: 17/23669-4 - A contribution to the development of the theory of peridynamic elasticity, BP.DR

Abstract

Ericksen's bar problem consists of the equilibrium of a finite-length bar pulled at the ends without body force. Its response is governed by a non-monotonic stress-strain constitutive relation. For this problem, there exists an uncountable number of inhomogeneous, energyminimizing equilibrium solutions for the bar, which involves phase transitions and the formation of equilibrium mixtures. We want to study these phenomena in the context of peridynamics, which is a nonlocal theory of continuum mechanics that considers the interaction of material points due to forces acting at a finite distance. An advantage of this theory is that the balance of linear momentum remains valid on a continuum in which discontinuities may appear as a result of deformation, such as phase boundaries. Also, peridynamics provides a natural settingto model long-range forces that are important in nanoscale applications and biomechanics. This project consists of determining the role of the boundary conditions and constitutive hypotheses on the behavior of an elastic peridynamic bar. For this, we will consider an Ericksen's bar problem in the context of the elastic peridynamic theory, a trilinear stress-strain constitutive relation and, an adaptive dynamic relaxation method to search for approximate solutions. In addition, we will consider an infinite peridynamic bar, with similar trilinear material, and superpose an homogeneous deformation with a small incremental displacement. This projectis part of the project DR/FAPESP #2017/23669-4, and is related to the project Visitor fromAbroad/FAPESP, Proc. #2016/12217-2.