We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.
Virginia Tech（弗吉尼亚理工大学）；Princeton University（普林斯顿大学）
Constitutive models are widely used for modeling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar-turbulent transition. However, traditional constitutive models based on partial differential equations (PDEs) often lack robustness and are too rigid to accommodate diverse calibration datasets. We propose a frame-independent, nonlocal constitutive model based on a vector-cloud n…
Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses
Lehigh University（理海大学）；Sandia National Laboratories（桑迪亚国家实验室）；Global Engineering and Materials, Inc.（全球工程与材料公司）；Worcester Polytechnic Institute（伍斯特理工学院）
Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；MIT BCS（麻省理工学院脑与认知科学系）；Center for Brains, Minds and Machines（脑、心智与机器中心）；Tsinghua University（清华大学）；Shanghai Qi Zhi Institute（上海期智研究院）；UMass Amherst（马萨诸塞大学阿默斯特分校）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Columbia University（哥伦比亚大学）
The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual and often biased nature of the commonly adopted calibration and validation processes, thus slowing down data collections, hampering the progress towards discovering new physics, increasing expenses and possibly leading to misinterpretations of the credibil…
This paper presents a new meta-modeling framework to employ deep reinforcement learning (DRL) to generate mechanical constitutive models for interfaces. The constitutive models are conceptualized as information flow in directed graphs. The process of writing constitutive models are simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). Thus meta-modeling can be formulated as a Markov decision process with well-defined states, actions, rules, objective functions, and rewards. By using neura…
Delft University of Technology（代尔夫特理工大学）；ETH Zürich（苏黎世联邦理工学院）
We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress-strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies within the scope of our recent framework for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID) and we denote it as NN-EUCLID. The absence of stress labels is compensated for by leveraging a physics-motivated loss function based on t…
Southern University of Science and Technology（南方科技大学）；Hong Kong University of Science and Technology（香港科技大学）
Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad-hoc without a clear physical explanation. We investigated d…
Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurements
Lehigh University（里海大学）；National Technology and Engineering Solutions of Sandia, LLC（桑迪亚国家技术与工程解决方案有限责任公司）；U.S. Department of Energy（美国能源部）；National Institute of Health（美国国立卫生研究院）
Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials
Sibley School of Mechanical and Aerospace Engineering, Cornell University（科林斯大学机械与航空航天工程学院）；Department of Materials Science and Engineering, Technion - Israel Institute of Technology（技术学院-以色列理工学院材料科学与工程系）；Sandia National Laboratories（桑地亚国家实验室）；Center for Applied Mathematics, Ithaca, NY 14850（应用数学中心）；Pasteur Labs, Brooklyn, NY 11205（帕斯特实验室）
