| RESEARCH ANNOUNCEMENTS ON “DPK: DEEP NEURAL NETWORK APPROXIMATION OF THE FIRST PIOLA-KIRCHHOFF STRESS” |
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| 作者姓名： | YANG Zhi-jian YUAN Cheng |
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| 作者单位： | School of Mathematics and Statistics,Wuhan University |
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| 基金项目： | Supported by National Key Research and Development Program of China(2020YFA0714200)；;National Nature Science Foundation of China (12125103;12071362)；;Natural Science Foundation of Hubei Province (2021AAA010;2019CFA007)；;Fundamental Research Funds for the Central Universities； |
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| 摘 要： | 1 Introduction and Main Results Consider the first Piola-Kirchhoff stress P defined as1]P(F)=?W(F)/?F,(1.1)where F and W refer to the deformation tensor and strain energy density.Due to the principle of material frame-indifference and the material symmetry,two important constraints should be satisfied by these relations1].
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