Representation of tensor functions using lower-order structural tensor set: three-dimensional theory
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917334125379584 |
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| author | Madadi, Mohammad Zhang, Pu |
| author_facet | Madadi, Mohammad Zhang, Pu |
| contents | The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order structural tensors, which significantly impedes practical engineering applications. Recent advances have introduced a reformulated representation theory that enables the modeling of anisotropic materials using only lower-order structural tensors (i.e., second-order or lower). Building upon the reformulated theory, this work establishes the representations of tensor functions for three-dimensional centrosymmetric point groups. For each point group, we propose a lower-order structural tensor set and derive the representations of tensor functions explicitly. For scalar-valued and second-order symmetric tensor-valued functions, our theory is indeed applicable to all three-dimensional point groups because their representations are determined by the corresponding centrosymmetric groups. The representation theory presented here is broadly applicable for constitutive modeling of anisotropic materials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation of tensor functions using lower-order structural tensor set: three-dimensional theory Madadi, Mohammad Zhang, Pu Representation Theory Materials Science Group Theory The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order structural tensors, which significantly impedes practical engineering applications. Recent advances have introduced a reformulated representation theory that enables the modeling of anisotropic materials using only lower-order structural tensors (i.e., second-order or lower). Building upon the reformulated theory, this work establishes the representations of tensor functions for three-dimensional centrosymmetric point groups. For each point group, we propose a lower-order structural tensor set and derive the representations of tensor functions explicitly. For scalar-valued and second-order symmetric tensor-valued functions, our theory is indeed applicable to all three-dimensional point groups because their representations are determined by the corresponding centrosymmetric groups. The representation theory presented here is broadly applicable for constitutive modeling of anisotropic materials. |
| title | Representation of tensor functions using lower-order structural tensor set: three-dimensional theory |
| topic | Representation Theory Materials Science Group Theory |
| url | https://arxiv.org/abs/2510.14028 |