Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN

• URL: http://arxiv.org/abs/2304.06044v2
• Date: Wed, 6 Sep 2023 12:31:38 GMT
• Title: Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN
• Authors: Shahed Rezaei, Ahmad Moeineddin and Ali Harandi
• Abstract summary: We apply physics-informed neural networks to solve the relations for nonlinear, path-dependent material behavior. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides information about the current material state (i.e., free energy, stress, and the evolution of internal variables) under any given loading scenario without requiring initial data. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models. Additionally, strategies are provided to reduce the required order of derivative for obtaining the tangent operator. The trained model can be directly used in any finite element package (or other numerical methods) as a user-defined material model. However, challenges remain in the proper definition of collocation points and in integrating several non-equality constraints that become active or non-active simultaneously. We tested this methodology on rate-independent processes such as the classical von Mises plasticity model with a nonlinear hardening law, as well as local damage models for interface cracking behavior with a nonlinear softening law. In order to demonstrate the applicability of the methodology in handling complex path dependency in a three-dimensional (3D) scenario, we tested the approach using the equations governing a damage model for a three-dimensional interface model. Such models are frequently employed for intergranular fracture at grain boundaries. We have observed a perfect agreement between the results obtained through the proposed methodology and those obtained using the classical approach. Furthermore, the proposed approach requires significantly less effort in terms of implementation and computing time compared to the traditional methods.

Related papers

• Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks [0.0]
  The proposed model architecture is simpler and more efficient compared to existing solutions from the literature. The validation of the approach is carried out by means of surrogate data obtained with the Armstrong-Frederick kinematic hardening model.
  arXiv  Detail & Related papers  (2024-03-04T07:09:54Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics [97.38308257547186]
  Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
  arXiv  Detail & Related papers  (2023-04-27T17:42:24Z)
• Neural Abstractions [72.42530499990028]
  We present a novel method for the safety verification of nonlinear dynamical models that uses neural networks to represent abstractions of their dynamics. We demonstrate that our approach performs comparably to the mature tool Flow* on existing benchmark nonlinear models.
  arXiv  Detail & Related papers  (2023-01-27T12:38:09Z)
• Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling [3.9181541460605116]
  We propose to use data-driven modeling to predict a material's response without using conventional models. The material response is modeled by learning the implicit mappings between loading conditions and the resultant displacement and/or damage fields. We demonstrate the performance of our proposed method for a number of examples, including hyperelastic, anisotropic and brittle materials.
  arXiv  Detail & Related papers  (2022-03-15T19:08:13Z)
• Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations [62.81701992551728]
  We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-02-24T20:46:52Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Automatically Polyconvex Strain Energy Functions using Neural Ordinary Differential Equations [0.0]
  Deep neural networks are able to learn complex material without the constraints of form approximations. N-ODE material model is able to capture synthetic data generated from closedform material models. framework can be used to model a large class of materials.
  arXiv  Detail & Related papers  (2021-10-03T13:11:43Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)
• Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms [6.806310449963198]
  This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local. The proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion-reaction Chafee-Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process.
  arXiv  Detail & Related papers  (2020-02-22T16:27:05Z)
• Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem [0.0]
  We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms.
  arXiv  Detail & Related papers  (2020-01-15T08:20:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.