A mechanics-informed artificial neural network approach in data-driven constitutive modeling
A mechanics-informed artificial neural network approach in data-driven constitutive modeling
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DOI：
10.1002/nme.6957
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发表时间：
2022-03-07
影响因子：
2.9
通讯作者：
Farhat, Charbel
中科院分区：
文献类型：
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作者：
As'ad, Faisal;Avery, Philip;Farhat, Charbel
提出了一种基于力学的人工神经网络方法，用于从应变-应力数据中学习复杂、非线性、弹性材料的本构律。该方法具有鲁棒性和准确性，用于训练基于回归的模型，该模型能够捕获高度非线性的应变-应力映射，同时保留了固体力学的一些基本原理。从这个意义上说，它是一种结构保留方法，用于构建数据驱动模型，该模型既具有纯现象学数据驱动回归的形式不可知论优势，又具有机械模型的物理健全性。所提出的方法在网络架构上强制执行理想的数学特性，以保证满足物理约束，如客观性，一致性（保留刚体模式），动态稳定性和材料稳定性，这对于成功利用数值模拟中的所得模型非常重要。事实上，在学习方法中嵌入这样的概念可以降低模型对噪声的敏感性，并提高其对训练域外输入的鲁棒性。通过几个有限元分析实例，强调了所提出的学习方法的优点。该方法在保证多尺度应用的计算可追溯性方面的潜力，通过对编织伞盖系统的超音速充气动力学的非线性、动态、多尺度、流体结构的加速模拟得到了证明。
A mechanics-informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain-stress data is proposed. The approach features a robust and accurate method for training a regression-based model capable of capturing highly nonlinear strain-stress mappings, while preserving some fundamental principles of solid mechanics. In this sense, it is a structure-preserving approach for constructing a data-driven model featuring both the form-agnostic advantage of purely phenomenological data-driven regressions and the physical soundness of mechanistic models. The proposed methodology enforces desirable mathematical properties on the network architecture to guarantee the satisfaction of physical constraints such as objectivity, consistency (preservation of rigid body modes), dynamic stability, and material stability, which are important for successfully exploiting the resulting model in numerical simulations. Indeed, embedding such notions in a learning approach reduces a model's sensitivity to noise and promotes its robustness to inputs outside the training domain. The merits of the proposed learning approach are highlighted using several finite element analysis examples. Its potential for ensuring the computational tractability of multi-scale applications is demonstrated with the acceleration of the nonlinear, dynamic, multi-scale, fluid-structure simulation of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric.