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Data Driven Computing and Machine Learning in Engineering 2019

 
  • Sep 11, 2019

Data Driven Computing and Machine Learning in Engineering 2019 was held at Shanghai, China on September 09-11, 2019. I gave an oral presentation, A Manifold Learning Approach for Multiscale Phase Field Evolution for Fracture, with three groupmates and my master advisor Prof Yongxing Shen.

Pictures

Oral presentation

Group photo

Abstract

  • Title: A Manifold Learning Approach for Multiscale Phase Field Evolution for Fracture

  • Abstract: The multi-scale fracture simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. In this paper we propose a new computational strategy for solving multiscale fracture problem efficiently through homogenization in a FE2-like [1] framework. To take into account the phase field induced by fracture at the microstructure level, the Representative Volume Element (RVE), which consists of an elastic matrix and inclusions (fiber), is endowed. We randomly place an initial crack in the RVE in order to represent the possible microscopic crack paths. The crack is described by the regularized variational theory of fracture, or so-called phase field approach, which is able to predict crack nucleation, propagation and branching without extra criteria [3]. Then the RVE response is homogenized and upscaled to the macroscale as a phase field constitutive model previously developed by the authors [2], which is then used in a framework of a phase field modeling of propagating fracture. This computational scheme for solving multiscale fracture problems can be inefficient and inflexible because the phase field method requires an unpredictable number of iterations. In this paper we consider an alternative route that adopts techniques well known in the machine learning community in order to extract the manifold that contains the inputs to the RVE, namely the initial crack path and the load. Then output data, which is the evolved phase fields, can be interpolated accurately with minimum online computation. In particular, the locally linear embedding is chosen in this work for the local phase field evolution for fracture of heterogeneous microstructures. We construct a manifold which can efficiently and accurately interpolate micro crack evolution laws with given microstructures. In this paper, we perform a manifold learning approach based on the use of LLE technique [6]. Locally linear embedding (LLE) [6], a particular example of kernel principal component analysis (kernel PCA) [4,5,7], is an unsupervised learning algorithm that computes low-dimensional, topology-preserving embeddings of high-dimensional data points. The offline procedure consists of two stages: (1) dataset construction with the phase field analysis for the RVE. (2) data manifold construction with the LLE. The online interpolation procedure then readily delivers the phase field evolution. In the presentation, an accuracy check between FEM results and manifold interpolation is provided.

  • Keywords: Multiscale simulation, Manifold learning, Locally linear embedding, Phase field for fracture, Computational homogenization

  • References:
    1. Feyel, F., Cailletaud, G., École nationale supérieure des mines (Paris)., & ENSMP MAT. (1998). Application du calcul parallèle aux modèles à grand nombre de variables internes.
    2. Cheng, C., Shen, Y. (2018). A micromechanics-based phase field approach to fracture. In: The Third International Conference on Damage Mechanics, The Chinese Society of Theoretical and Applied Mechanics.
    3. Shen, Y., Mollaali, M., Li, Y., Ma, W., Jiang, J. Implementation Details for the Phase Field Approached to Fracture. Journal of Shanghai Jiao Tong University (Science), 23(1), 166-174.
    4. Scholkopf, B., Smola, A., Muller, KR. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10(5), 1299-1319.
    5. Scholkopf, B., Smola, A., Muller, KR. (1999). Kernel principal component analysis. In: Advances in kernel methods: support vector learning. MIT Press, Cambridge, pp, 327-352.
    6. Roweis, ST., Saul, LK. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323-2326.
    7. Zimmer, VA., Lekadir, K., Hooendoorn, C., Frangi, AF., Piella, G. (2015). A framework for optimal kernel-based manifold embedding of medical image data. Computerized Medical Imaging and Graphics, 41, 93-107.
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