Variable-order approach to nonlocal elasticity: theoretical formulation, order identification via deep learning, and applications
Variable-order approach to nonlocal elasticity: theoretical formulation, order identification via deep learning, and applications
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DOI：
10.1007/s00466-021-02093-3
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发表时间：
2021-09
影响因子：
4.1
通讯作者：
Sansit Patnaik;M. Jokar;F. Semperlotti
中科院分区：
文献类型：
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作者：
Sansit Patnaik;M. Jokar;F. Semperlotti
本文介绍了变阶连续介质力学理论的建立及其在非局部非均质固体分析中的应用。变阶连续介质理论提供了一种独特的方法来模拟表现出位置相关的非局部行为的固体的响应。该公式还保证了框架不变性，前提是对变量阶数的函数定义施加适当的约束。该研究还提出了一种深度学习方法来识别描述介质行为的变阶分布。这种方法为变阶理论在实际问题中的实际应用提供了一条非常有希望的途径，特别是当微观结构未知且必须从介质的物理响应中推断时。通过数值模拟具有多孔或功能梯度核的非局部梁的静态响应，说明了变阶理论的能力。与完全分解梁几何的三维有限元模型的参考解相比，降阶变分数模型具有良好的精度和显著的计算效率。
This study presents the formulation of the variable-order continuum mechanics theory and its application to the analysis of nonlocal heterogeneous solids. The variable-order continuum theory enables a unique approach to model the response of solids exhibiting position-dependent nonlocal behavior. The formulation also guarantees frame-invariance provided that proper constraints on the functional definition of the variable-order are imposed. The study also presents a deep learning approach to identify the variable-order distribution describing the behavior of the medium. This methodology presents a very promising route for the practical application of the variable-order theory to real-world problems, especially when the microstructure is not knowna prioriand must be inferred from the physical response of the medium. The capabilities of the variable-order theory are illustrated by numerically simulating the static response of nonlocal beams having either a porous or a functionally graded core. The reduced-order variable fractional model shows excellent accuracy and significant computational efficiency when compared with a reference solution produced by a 3D finite element model that fully resolves the beam geometry.