Development of a peridynamic plate theory

• Grant number: 24/20862-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2025
• End date: March 31, 2028
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Adair Roberto Aguiar
• Grantee: Lucas Almeida Rocha
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In the peridynamic theory, the concept of interaction between particles separated by finite distances 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 edge of a crack or the material interface that may appear as a result of the deformation of a solid. In this project we will use the peridynamic theory to model thin plates. We will consider a particular class of homogeneous peridynamic solids and will expand the displacement field asymptotically in terms of the thickness coordinate, following classical arguments of thin plate theory. We will then reduce the equation of motion to a system of equations for the determination of the expansion coefficients. We will apply this theory in the formulation of problems in structural engineering and biomechanics. The scope of the project is in line with the scope of our previous works in peridynamics and asymptotic methods, and its results will advance our recent efforts in constructing a peridynamic plate theory.