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This research aims to first investigate the potential of machine learning in improving and accelerating elastoplastic material models in the Finite Element Method (FEM). The subsequent objective is to implement the so-called ML-based hybrid material model, validate it, and test its computational performance. This study focuses on the commonly used...
Citations
... After predicting the strain increment, the internal variables and stress state can be updated using Equations (13)(14)(15)(16)(17). To generate the training data, the classical von Mises return mapping algorithm was run on synthetic loading, unloading, and cyclic loading strain paths for random strain magnitudes, strain rates, and material hardening parameters within a specific range. ...
... The inputs and outputs of the model were extracted for the plastic regime. After careful investigation of FNN, LASSO regression [13] and SINDy [14], it was found by Bokil et al. [15] that the sparse nonlinear regression method of SINDy outperformed the others. The algorithm uses ordinary least squared minimization with L2 regularization and zeroes out the coefficients below a specific threshold. ...
Evaluating material models in Finite Element (FE) simulations is computationally expensive. Recently, Machine Learning (ML) techniques have been explored for accelerating elastoplastic algorithms. One such method includes replacing a part of the algorithm with an ML model which is called the “hybrid” approach. One of the most commonly used algorithms for ductile materials is the J2-based von Mises hardening elastoplasticity. To improve the performance of this model, an ML-based hybrid algorithm was sought. In this algorithm, the expensive iterative plastic correction step was replaced with a single-step prediction from a SINDY-inspired sparse nonlinear regression model. As a result, a novel Sparse Identification of Plastic Strain-increment (SIPS) based hybrid von Mises hardening plasticity model was formulated. This SIPS model was trained to predict the plastic strain increment from the trial stress and the unit outward normal to the yield surface at every timestep. The training data comprised loading, unloading and cyclic loading scenarios for randomly sampled numerous hardening parameters. This allowed the hybrid model to be applicable to a wide range of materials. The SIPS-based material model was then programmed in LS-DYNA® via the User Defined Material feature to conduct benchmark FE simulations. The proposed hybrid-SIPS model achieved up to 95% accuracy on standard tests and 3D simulations. Notably, it displayed an average computational cost reduction of 40%. By exploring this approach extensively, it is possible to develop universal and inexpensive hybrid material models.
