有限元法
可塑性
本构方程
人工神经网络
计算机科学
柯西分布
边值问题
稳健性(进化)
应用数学
各向同性
背景(考古学)
数学
数学优化
数学分析
人工智能
结构工程
工程类
物理
基因
热力学
古生物学
生物
化学
量子力学
生物化学
作者
Sijun Niu,Enrui Zhang,Yuri Bazilevs,Vikas Srivastava
标识
DOI:10.1016/j.jmps.2022.105177
摘要
Physics-informed neural networks (PINN) can solve partial differential equations (PDEs) by encoding the mathematical information explicitly into the loss functions. In the context of plasticity, discussions of PINN have only focused on small-strain formulations. We present a framework of finite-strain elasto-plasticity for PINN, considering rate-independent isotropic hardening in this work. Details of the model architecture are discussed, including inputs and outputs of the neural network and the construction of the loss function that incorporates equilibrium equations, boundary conditions and constitutive relations. In addition, the overall architecture can learn the constitutive relations from discrete measurements on a stress–strain curve, hence eliminating the need for modeling hardening law in the formulation. We demonstrate the performance of PINN through a numerical example that includes a multi-step loading and unloading history. Moreover, we assess the performance of PINN in terms of its accuracy and robustness under mesh refinement and as a function of the network architecture design. Displacement, Cauchy stress and accumulated plastic strain fields are compared to the finite element results for the same problem for the purposes of this assessment, which is intended to provide insight and guidance for the future designs of PINN for plasticity and related problems in solid mechanics.
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