A nonlinear variational auto‐encoder (NLVAE) is developed to reconstruct the plane strain stress field in a solid with embedded cracks subjected to uniaxial tension, uniaxial compression, and shear loading paths. Latent features are sampled from a skew‐normal distribution, which allows encoding marked variations of the features of the stress field across the load steps. The NLVAE is trained and tested based upon stress maps generated with the finite element method (FEM) with cohesive zone elements (CZEs). The NLVAE successfully captures stress concentrations that develop across the loading steps as a result of crack propagation, especially when enhanced disentanglement is emphasized during training. Some latent variables consistently emerge as significant across various microstructure descriptors and loading paths. Correlations observed between the evolution of fabric descriptors and that of their significant stress latent features indicate that the NLVAE can capture important microstructure transitions during the loading process. Crack connectivity, crack eccentricity, and the distribution of zones of highly connected opened cracks versus zones with no cracks are the fabric descriptors that best explain the sequences of latent features that are the most important for the reconstruction of the stress field. Notably, the distributional shape, tail behavior, and symmetry of microstructure descriptor distributions have more influence on the stress field than basic measures of central tendency and spread.

中文翻译：

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在 2D 实体中通过深度学习解释应力场和裂纹模式


开发了一种非线性变分自动编码器 （NLVAE），用于在受到单轴拉伸、单轴压缩和剪切载荷路径作用的嵌入裂纹的固体中重建平面应变应力场。潜在特征是从偏态正态分布中采样的，这允许对应力场特征在载荷步骤中的显著变化进行编码。NLVAE 是根据有限元法 （FEM） 生成的应力图和内聚区单元 （CZE） 进行训练和测试的。NLVAE 成功地捕获了由于裂纹扩展而在加载步骤中产生的应力集中，尤其是在训练过程中强调增强的解缠时。一些潜在变量在各种微观结构描述符和加载路径中始终表现出显著性。观察到的织物描述符的演变与其重要的应力潜在特征的演变之间的相关性表明，NLVAE 可以捕捉加载过程中重要的微观结构转变。裂纹连通性、裂纹偏心度以及高度连通的开放裂纹区域与无裂纹区域的分布是最能解释潜在特征序列的织物描述符，这些特征对于应力场的重建最为重要。值得注意的是，与集中趋势和扩散的基本测量相比，微观结构描述符分布的分布形状、尾部行为和对称性对应力场的影响更大。