Polyconvex anisotropic hyperelasticity with neural networks

• URL: http://arxiv.org/abs/2106.14623v1
• Date: Sun, 20 Jun 2021 15:33:31 GMT
• Title: Polyconvex anisotropic hyperelasticity with neural networks
• Authors: Dominik Klein, Mauricio Fern\'andez, Robert J. Martin, Patrizio Neff and Oliver Weeger
• Abstract summary: convex machine learning based models for finite deformations are proposed. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials. The data for the data approach is based on mechanical considerations and does not require additional experimental or simulation capabilities.
• Score: 1.7616042687330642
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. Thus, in particular the second model presents a highly flexible constitutive modeling approach, that leads to a mathematically well-posed problem.

Related papers

• Physically recurrent neural network for rate and path-dependent heterogeneous materials in a finite strain framework [0.0]
  A hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the models used in the full-order micromodel by embedding them in a neural network.
  arXiv  Detail & Related papers  (2024-04-05T12:40:03Z)
• 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)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Modular machine learning-based elastoplasticity: generalization in the context of limited data [0.0]
  We discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data.
  arXiv  Detail & Related papers  (2022-10-15T17:35:23Z)
• Learning Physical Dynamics with Subequivariant Graph Neural Networks [99.41677381754678]
  Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization. Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall.
  arXiv  Detail & Related papers  (2022-10-13T10:00:30Z)
• Calibrating constitutive models with full-field data via physics informed neural networks [0.0]
  We propose a physics-informed deep-learning framework for the discovery of model parameterizations given full-field displacement data. We work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. We demonstrate that informed machine learning is an enabling technology and may shift the paradigm of how full-field experimental data is utilized to calibrate models.
  arXiv  Detail & Related papers  (2022-03-30T18:07:44Z)
• Dynamic multi feature-class Gaussian process models [0.0]
  This study presents a statistical modelling method for automatic learning of shape, pose and intensity features in medical images. A DMFC-GPM is a Gaussian process (GP)-based model with a shared latent space that encodes linear and non-linear variation. The model performance results suggest that this new modelling paradigm is robust, accurate, accessible, and has potential applications.
  arXiv  Detail & Related papers  (2021-12-08T15:12:47Z)
• 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)
• Model-agnostic multi-objective approach for the evolutionary discovery of mathematical models [55.41644538483948]
  In modern data science, it is more interesting to understand the properties of the model, which parts could be replaced to obtain better results. We use multi-objective evolutionary optimization for composite data-driven model learning to obtain the algorithm's desired properties.
  arXiv  Detail & Related papers  (2021-07-07T11:17:09Z)
• Learning Neural Generative Dynamics for Molecular Conformation Generation [89.03173504444415]
  We study how to generate molecule conformations (textiti.e., 3D structures) from a molecular graph. We propose a novel probabilistic framework to generate valid and diverse conformations given a molecular graph.
  arXiv  Detail & Related papers  (2021-02-20T03:17:58Z)

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.