A Multilevel Technique based on Nested Local Meshes for Nonlinear Mechanics

Abstract

In this paper an adaptive multilevel mesh refinement method, coupled with the Zienkiewicz and Zhu a posteriori error estimator, is applied to solids mechanics with the objective of conducting reliable nonlinear studies in acceptable computational times and memory space. The approach presented in this paper is first validated on linear behaviour, on two and three dimensional simulations. Then nonlinear behaviour is studied. Advantages and limitations of the local defect correction method in solids mechanics problems in terms of error level, CPU time and memory space are discussed. This kind of resolution is also compared with the classical finite element resolution.

An automatic multilevel refinement technique based on nested local meshes for nonlinear mechanics

“…Moreover, the use of refinement ratio greater than 2 could be attractive in the sense that it could allow us to obtain the same error level with less sub-grids [13]. In [12,13], it had been shown that for a refinement ratio of 4, the mesh convergence remains in Oðd h fine Þ. That is why we decide to compare our LDC method applied on an initial mesh of size h i =2, with 1 to 7 sub-grids of refinement ratio 2 to 1 to 4 sub-grids of refinement ratio 4.…”

“…For more details about the own effects on the cladding of the pellet hourglass configuration, the reader is referred to [12,13].…”

“…This paper is based upon Barbié et al [12] but the current version includes results obtained from additional research on the efficiency of the coupled LDC-ZZ method for linear behaviour (see also [13]), a further study on three-dimensional test case where different initial meshes are compared and an extended work concerning the nonlinear test case, particularly with the use of refinement ratio greater than 2.…”

Strategies involving the local defect correction multi-level refinement method for solving three-dimensional linear elastic problems

“…These initial results suggest that the LDC solver may be also efficient with more complex structural mechanics behaviour, such as nonlinear path-dependent behaviour. This method has in fact already been successfully applied to ''one-time-step'' nonlinear behaviour (see [77]) and give promising results.…”