Stable and efficient procedures for temporal integration of dynamic problems: application to phase field models

• Grant number: 21/11577-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2022
• End date: February 28, 2023
• Field of knowledge: Engineering - Mechanical Engineering
• Principal Investigator: Marco Lucio Bittencourt
• Grantee: Rodrigo Santos Nogueira Júnior
• Host Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project aims to develop procedures for temporal integration for the analysis of dynamic problems related to the equation of motion of a mechanical system and a phase-field model of equations nonlinear differentials for the evolution of fracture, damage, and fatigue. These models are discretized by the High Order Finite Element Method (MEF-AO) and the equations obtained must be integrated over time using stable and efficient procedures. Initial testing of new versions of implicit and explicit temporal integrators in one-dimensional linear problems showed a performance gain of up to 10 times when compared to conventional procedures. However, stability problems were identified, which implied the need for a greater number of integration steps. It is intended to investigate under what conditions these new versions of the Newmark and centered difference methods achieve stability. After identifying the stability regions, the methods will be applied to problems with two-dimensional equations involving the equation of linear motion and a system of equations non-linear analysis for damage and fracture evolution. The entire project will be developed using Matlab software and the program(hp)2FEM for solving mechanical problems using the MEF-AO.(AU)