Abstract

In solid mechanics, data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and accuracy. However, the implementation of machine-learned approaches in material modeling has been modest due to the high-dimensionality of the data space, the significant size of missing data, and limited convergence. This work proposes a framework to hire concepts from polymer science, statistical physics, and continuum mechanics to provide super-constrained machine-learning techniques of reduced-order to partly overcome the existing difficulties. Using a sequential order-reduction, we have simplified the 3D stress–strain tensor mapping problem into a limited number of super-constrained 1D mapping problems. Next, we introduce an assembly of multiple replicated neural network learning agents (L-agents) to systematically classify those mapping problems into a few categories, each of which were described by a distinct agent type. By capturing all loading modes through a simplified set of dispersed experimental data, the proposed hybrid assembly of L-agents provides a new generation of machine-learned approaches that simply outperform most constitutive laws in training speed, and accuracy even in complicated loading scenarios. Interestingly, the physics-based nature of the proposed model avoids the low interpretability of conventional machine-learned models.

Highlights

  • The wide range applications of cross-linked polymers in several industries such as automotive, structural, medical, to name but a few, have made them an attractive area of research

  • The main contributions of this work are to infuse knowledge of physics into the model through certain modeling constraints: namely, (1) by providing a new data-driven model based on physics behind a machine learning process for predicting non-linear mechanical behavior of cross-linked polymers, (2) the first data-driven model that captures inelastic behavior of cross-linked polymers such as Mullins effect and permanent set, (3) a new paradigm with the upgrade-ability of model from hyper-elastic to damage behavior roots from easy transformation from the integration of micro-mechanics to the machine learning process, (4) proposing a new model with better training speed and accuracy compared to several well-known models

  • A physics-informed data-driven constitutive model for cross-linked polymers is developed by embedding neural networks into a multi-scale model

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Summary

Introduction

The wide range applications of cross-linked polymers in several industries such as automotive, structural, medical, to name but a few, have made them an attractive area of research. The main contributions of this work are to infuse knowledge of physics into the model through certain modeling constraints: namely, (1) by providing a new data-driven model based on physics behind a machine learning process for predicting non-linear mechanical behavior of cross-linked polymers, (2) the first data-driven model that captures inelastic behavior of cross-linked polymers such as Mullins effect and permanent set, (3) a new paradigm with the upgrade-ability of model from hyper-elastic to damage behavior roots from easy transformation from the integration of micro-mechanics to the machine learning process, (4) proposing a new model with better training speed and accuracy compared to several well-known models. In the appendix section, we explain frame-independence, polyconvexity, and thermodynamic consistency

Non-Linear Features in Cross-Linked Polymers
Physics-Based Reduction
Continuum Mechanics
Micro-Sphere
Network Decomposition
Implementation to Rubber Inelasticity
Dataset Minimization
Accuracy within Confidence Interval
Damage Prediction and Deformation History
Convergence Outside of the Confidence Interval
Conclusions
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