Mesh superposition‐based multiscale stress analysis of composites using homogenization theory and re‐localization technique considering fiber location variation

• Published in: International journal for numerical methods in engineering Vol. 123; no. 2; pp. 505 - 529
• Main Authors: Sakata, Sei‐ichiro, Tanimasu, Shin
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.01.2022; Wiley Subscription Services, Inc
• Subjects: Accuracy; fiber composite; Finite element analysis; Finite element method; Homogenization; homogenization method; Mathematical analysis; Mesh generation; mesh superposition method; multiscale stochastic stress analysis; random fiber arrangement; Stress analysis; Stress distribution
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6865

In this article, the accuracy of multiscale stress analysis of heterogeneous materials (unidirectional fiber‐reinforced composite) was improved by considering microscopic geometrical variation using the mesh superposition method. When analyzing the stress distribution in a composite with the finite element method considering the variation of the fiber location, updating the mesh significantly is necessary; however, generating an appropriate mesh for a large geometrical variation is difficult. Therefore, we focused on the mesh superposition method, which can easily generate a numerical FE model, even if the internal structure is complex, because the matrix and inclusion can be expressed by the global mesh and local mesh independently. However, in the original mesh superposition method, the analysis accuracy may be degraded owing to the mesh overlap conditions. Therefore, an improved method was applied to the homogenization theory‐based analysis. In this article, the effectiveness of the proposed approach was discussed by comparing the numerical results of this method with those of conventional mesh superposition method and standard finite element method. From the numerical results, accuracy improvement by the proposed approach for the multiscale stochastic stress analysis is confirmed.