Hierarchical Tensor Decomposition of Module Partition for the Mechanical Simulation

Abstract

The mechanical simulation experiment can provide guidelines for the structural design of materials, but the module partition of mechanical simulation experiments is still in its infancy. A mechanical simulation contour, e.g., strain and stress contour, has hierarchical characteristics. By analyzing the contour at different layers, the physical properties of the structure material can be improved. Current state-of-the-art methods cannot distinguish between simulation strain contours, as well as sparsely distributed spots of strain (stress concentrations) from simulation strain contour images, resulting in simulation data that does not accurately reflect real strain contours. In this paper, a Hierarchical Tensor Decomposition (HTD) method is proposed to extract hierarchical contours and stress concentrations from the simulation strain contours and then improve the mechanical simulation. HTD decomposes a tensor into three classes of components: the multi-smooth layers, the sparse spots layer, and the noise layer. The number of multismooth layers is determined by the scree plot, which is the difference between the smooth layers and the sparse spots layer. The proposed method is validated by several numerical examples, which demonstrate its effectiveness and efficiency. A further benefit of the module partition is the improvement of the mechanical structural properties.