Research

The finite element method (FEM) is a common approach that comes with a restrictive computational cost in the case of repetitive simulations, such as optimization, control, real-time monitoring, probabilistic modeling, and uncertainty quantification. This is due to the fact that forward simulations require solving large non-linear equations repeatedly.

The advent of Machine Learning (ML) and AI in recent years has provided an opportunity to construct quick surrogate ML models to replace high fidelity multi-physics models, which have a high computational cost and may not be applicable for high nonlinear equations. PINN differs from other

Our goal is to find techniques to make PINN training less costly, lower the amount of trial-anderror necessary to appropriately tune the hyper-parameters, and at the very least, empirically increase the training process’s robustness. Our current paper is to present a synthesis that incorporates: (i) employing non-dimensionalization and normalization of the physical parameter to address the problem of complex equations, (ii) infusing a broad understanding of the solution field with imprecise knowledge, (iii) using a weighted-sum scheme to enhance optimization algorithms in the context of multi-objective optimization, (IV) exploiting different approaches for weight initialization due to unbalanced gradients causes inaccuracy in optimization.

This work presents a new generation of super-constrained deep-learned hybrid constitutive models that can describe the accumulated effects of the mechanical and environmental damage on elastomer Matrix. The model describes the matrix through a cooperative multi-agents framework where each agent has been defined by a simple deep-learned neural network (NN) which is super-constrained by equations derived from physics, thermodynamics, and continuum mechanics. The use of NN agents within the micro-mechanical models, as opposed to traditional physics-driven modeling methods, provides a new generation of hybrid models that use the interpretability/simplicity of micromechanical models plus the computational speed and adaptability of machine-learned algorithms. While the accuracy of the predictions of the proposed hybrid model still relies heavily on the quality of the data used for training, the model output is already constrained within the region that satisfies our existing knowledge of the matrix behavior.

The model has been constrained at multiple steps; (1) model defined based on strain energy; (2) hiring micro-sphere for 3D to 1D order reduction; (3) using network decomposition to separate different inelastic effects; (4) defining learning agents to represent each 1D subnetwork. Those steps which are required to build a cooperative multi-agents hybrid model and their formulation are outlined in our paper.

proper prediction of the end-life of rubberlike materials has been a subject of significant interest, which comes with major challenges. One major challenge is the large uncertainty observed in the behavior of elastomers induced by intrinsic defects, processing, sample manufacturing, or simply heterogeneous nature of the matrix. Elastomers are often made by highly cross-linked polymer matrix that behave fully elastic with entropic force, which results in a highly non-linear behavior, especially during large deformation and significant hardening observed before failure.

In this contribution, our goal is to carry out three fundamental steps in probabilistic modeling of elastomers, namely (i) Bayesian evaluation of constitutive model’s parameters for hyperelastic behavior of rubber-like materials from distinct experimental data, (ii) Development of confidence bounds for stress– strain curves based on conjugate prior, and (iii) failure probability calculation based on First Order Reliability Method (FORM) and validated against that of Crude Monte Carlo (CMC) simulation to provide a sensitivity analysis on the effect of model parameters on failure probability.