A non-intrusive iterative generalized finite element method for multiscale coupling of 3-D solid and shell models

Li, H.; Avecillas-Leon, J.; Shauer, Nathan; Duarte, C. Armando

doi:10.1016/j.cma.2022.115408

Computer Methods in Applied Mechanics and Engineering

2022

DOI: 10.1016/j.cma.2022.115408

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A non-intrusive iterative generalized finite element method for multiscale coupling of 3-D solid and shell models

H. Li

J. Avecillas-Leon

Nathan Shauer

et al.

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2024

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Cited by 4 publications

References 49 publications

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On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

Gomes,

Barros

2024

Numerical Meth Engineering

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A strategy that combines the global‐local version of the generalized finite element method (GFEM) with a mixed‐dimensional coupling iterative method is proposed to simulate two‐dimensional crack propagation in structures globally represented by Timoshenko‐frame models. The region of interest called the local problem, where the crack propagates, is represented by a 2D elasticity model, where a fine mesh of plane stress/strain elements and special enrichment functions are used to describe this phenomenon accurately. A model of Timoshenko‐frame elements simulates the overall behavior of the structure. A coarse mesh of plane stress/strain elements provides a bridge between these two representation scales. The mixed‐dimensional coupling method imposes displacement compatibility and stress equilibrium at the interface between the two different element types by an iterative procedure based on the principle of virtual work. After establishing the constraint equations for the interface, the 2D elasticity model is related to the small‐scale model by the global‐local enrichment strategy of GFEM. In such a strategy, the numerical solutions of the local problem subjected to boundary conditions derived from the global‐scale problem enrich the approximation of this same global problem in an iterative procedure. Each step of the crack propagation requires a new sequence of this iterative global‐local procedure. On the other hand, the constraint equation for the interface is defined only once. The crack representation in a confined region by the global‐local strategy avoids a remeshing that would require new constraint equations. Two numerical problems illustrate the proposed strategy and assess the influence of the analysis parameters.

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On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

Gomes,

Barros

2024

Numerical Meth Engineering

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An adaptive global–local generalized FEM for multiscale advection–diffusion problems

He,

Valocchi,

Duarte

2024

Computer Methods in Applied Mechanics and Engineering

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On the implementation in Abaqus of the global–local iterative coupling and acceleration techniques

Bettinotti,

Guinard,

Véron

et al. 2024

Finite Elements in Analysis and Design

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A non-intrusive iterative generalized finite element method for multiscale coupling of 3-D solid and shell models

Cited by 4 publications

References 49 publications

On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

An adaptive global–local generalized FEM for multiscale advection–diffusion problems

On the implementation in Abaqus of the global–local iterative coupling and acceleration techniques

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