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Communication Dans Un Congrès Année : 2016

MultiGrid fi nite diff erence solver for brittle fracture simulation using phase field method in heterogeneous materials

Résumé

The prediction of brittle fracture initiation and propagation in heterogeneous structures is one of the main challenging problems in the fi eld of solid failure mechanics. Nowadays with the development of X-Ray tomography, it is possible to account for the real micro structure in a computational model. Recently, a new phase field method proposed by Miehe et al. [1] has been developed for describing the brittle fracture propagation, and Nguyen et al. [2] introduced a modi ed algorithm to simplify the computation of strain tensor split, which makes the problem linear. However, due to the complexity of the heterogeneous structure, its simulation requires dense grids for the very local description of the actual material topology. The effciency of the MultiGrid fi nite di erence method allows a computational cost that depends linearly on the number of unknowns. This off ers great opportunities to simulate the brittle fracture in strongly heterogeneous materials. According to previous work by Bo y et al. [3] and Gu et al. [4], an effcient MultiGrid solver simulating a 3D heterogeneous material through the solution the elastic equations has been built. The effciency has been validated as the computing time and allocated memory remains small compared to traditional numerical methods. Based on this, the aim of the current work is to extend the model with the phase fi eld method for brittle fracture. Following the algorithmic framework proposed in [1, 2], the extension from the current MultiGrid fi nite diff erence model at each incremental step is direct and can be summarized as follows: (1) Split strain tensor: (; d). (2) MultiGrid finite di fference scheme: compute elastic Lame equation according to (; d). (3) Compute history strain energy: H(; d). (4) MultiGrid fi nite di fference scheme: compute phase fi eld function: d(H). The advantage is that steps (2) and (4) can be solved through a MultiGrid fi nite diff erence scheme and are expected to be more efficient compared to the Finite Element scheme in [2]. [1] C Miehe et al. A phase fi eld model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199(45):2765-2778, 2010. [2] T.T Nguyen et al. A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure. Engineering Fracture Mechanics, 139:18-39, 2015. [3] H Bo y et al. Multigrid solution of the 3d stress fi eld in strongly heterogeneous materials. Tribology International, 74:121-129, 2014. [4] H Gu et al. An effi cient multigrid solver for the 3d simulation of composite materials. Computational Material Science, 112PA:230-237, 2016.
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Dates et versions

hal-01350879 , version 1 (02-08-2016)

Identifiants

  • HAL Id : hal-01350879 , version 1

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Hanfeng Gu, Julien Réthoré, Marie-Christine Baietto, Philippe Sainsot, Antonius Lubrecht. MultiGrid fi nite diff erence solver for brittle fracture simulation using phase field method in heterogeneous materials. The 21st European Conference on Fracture, Jun 2016, Catania, Italy. ⟨hal-01350879⟩
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