Estudo e implantação numérica da teoria de Biot para meios elastoplásticos e uso de estratégias de otimização para o processamento

Abstract

This work presents a strategy for the coupled poro-elasto-plastic formulation. The Finite Element Method (FEM) is used to solve the differential equations, interpolating displacement and pore pressure fields. This problem is solved fully coupled, based on an only one system of equations. The nonlinear problem is globally solved by the Newton-Raphson procedure, and the Closest Point algorithm is implemented for the returning map in the elasto-plastic models. Based on a computational module that has already been developed (PORO), which is written using C++ language and Object-Oriented Programming (OOP), this work expands this program creating new classes for different elasto-plastic constitutive models. The program is verified by classical examples in the literature such as the poro-elastic column and the problem of Schiffman. Some strategies for optimization the computational cost are presented, which use specialized math libraries (MKL) and code parallelization (OpenMP).