Multiscale analysis of localized, nonlinear, three-dimensional thermo-structural effects

Generalized Finite Element Method (GFEM);extended finite element method;multiphysics;multiscale;parallel;thermomechanical;thermoelasticity;thermoplasticity;plasticity;heterogeneous materials

Plews, Julia A.

关键词: Generalized Finite Element Method (GFEM);    extended finite element method;    multiphysics;    multiscale;    parallel;    thermomechanical;    thermoelasticity;    thermoplasticity;    plasticity;    heterogeneous materials;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/88953/PLEWS-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

There are a wide range of computational modeling challenges associated with structures subjected to sharp, local heating effects. Problems of this nature are prevalent in diverse engineering applications such as structural analysis of hypersonic flight vehicles in extreme environments, computational modeling of weld processes, and development of semiconductor processing technology. Complex temperature gradients in the materials cause three-dimensional, localized, intense thermomechanical stress/strain variation and residual deformations, making multiphysics analysis necessary to accurately predict structural response. Localized damage or deformation may impact global structural behavior, yet bridging spatial scales between local- and structural-scale response is a nontrivial task. Because of these issues, standard finite element analysis techniques lead to cumbersome and prohibitively expensive numerical simulations for this class of problems.This study proposes a Generalized or eXtended Finite Element Method (G/XFEM) for analyzing three-dimensional solid, coupled physics problems exhibiting localized heating and thermomechanical effects. The method is based on the GFEM with global–local enrichment functions (GFEMgl), which involves the solution of interdependent coarse- (global) and fine-scale (local) problems. The global problem captures coarse-scale behavior, while local problems resolve sharp solution features in regions where fine-scale phenomena may govern the overall structural response. To address the intrinsic coupling of scales, local solution information is embedded in the global solution space via a partition of unity approach. This method extends the capabilities of traditional hp-adaptive FEM or GFEM—consisting of heavy mesh refinement (h) and local high-order polynomial approximations (p)—to one-way coupled thermo-structural problems, providing meshing flexibility while remaining accurate and efficient. Linear thermoelasticity and nonlinear thermoplasticity problems are considered, involving both steady-state and transient heating effects.The GFEMgl is further extended to capture multiscale thermal and thermomechanical effects induced by material-scale heterogeneity, which may also impact structural behavior at the coarse scale. Due to the extraordinary level of fidelity required to resolve fine-scale effects at the global scale, strategies for distributing large workloads on a parallel computer and improving the computational efficiency of the proposed method are needed. Studies have shown that the GFEMgl benefits from straightforward parallelism. However, inexact, coarse-scale boundary conditions on fine-scale may lead to large errors in global solutions. Traditional strategies aimed at improving or otherwise lessening the effect of poor local boundary conditions in the GFEMgl may be impractically expensive in the problems of interest, such as transient or nonlinear simulations involving many time or load steps. Thus, inexpensive and optimized approaches for improving boundary conditions on local problems in both linear and nonlinear problems are identified.The performance of the method is assessed on representative, large-scale, nonlinear, coupled thermo-structural problems exhibiting phenomena spanning global (structural) and local (component or even material) scales.