Adaptive fem-spim coupling for phase-field modelling of fracture

• Autor(a) principal: Larissa Novelli
• Data de Publicação: 2023
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/60104
• topic: Phase-field; Meshfree methods; Smoothed point interpolation method; Coupled models; Adaptivity; Engenharia de estruturas; Mecânica da fratura

This thesis proposes an adaptive coupling between the Finite Element Method (FEM) and the different versions of the meshfree method Smoothed Point Interpolation Method (SPIM), for the discretisation of phase-field models applied to the crack propagation problem. For these applications, the weak-weakened form, adopted for the displacement problem in SPIM, was extended to the phase-field problem and the gradient smoothing, adopted for the calculation of the derivative of the shape functions, was applied to the phase-field variable. The strategy aims to reduce the computational cost while maintaining the inherent advantages of each method. The study began with the use of models in which the mesh is previously refined in the crack region. In these initial studies, two distinct alternatives were adopted, namely: the entire domain with the SPIM meshfree method and prior FEM-SPIM coupling, with SPIM in the crack propagation region. In the adaptive strategy, the domain is initially discretised with a coarse FEM mesh, from which the crack propagation region is detected, and this region is replaced by SPIM and refined if necessary. The entire process is carried out automatically and the user must inform only a few parameters of the adaptive strategy. The implementation is general so that different formats can be adopted for SPIM smoothing domains and different constitutive models of phase-field. Numerical simulations were performed seeking to demonstrate the accuracy and stability of the proposed strategy. The results obtained were able to correctly simulate crack propagation in brittle and quasi-brittle fracture models and the load-displacement curves showed good agreement with the experimental and numerical reference results.