Our research introduces a novel approach to mechanical simulations by embedding physical laws directly into generative adversarial networks (GANs). This framework integrates physics into the GAN architecture, where the generator produces predictions, and the discriminator evaluates these predictions against data, providing continuous feedback for improvement. Specifically, the generator is guided by physical constraints, while the discriminator utilizes the closest strain–stress data to assess the authenticity of the generator’s output. This combined approach connects machine learning methods with computational mechanics simulations, establishing a new formalism that uses data-driven mechanics and deep learning to simulate and predict mechanical behaviors.
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Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger equation. By incorporating a model order reduction technique based on calculations with a reduced set of Fourier modes, the computational cost of this algorithm can be reduced. It has been shown that the accuracy of this model order reduction technique strongly depends on the choice of Fourier modes by considering a geometrically adapted rather than a fixed sampling pattern to define the reduced set of Fourier modes. Since it is difficult to define a geometrically adapted sampling pattern for complex microstructures, a strain-based sampling pattern was additionally introduced. While this strain-based sampling pattern has the advantage of its adaptability, it also leads to even more accurate simulation results.
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Our research focuses on data-driven computational mechanics, which replaces traditional phenomenological models with datasets in the strain-stress space. This method formulates mechanical problems as optimization tasks, where the closest points in the strain-stress dataset are used to satisfy equilibrium and compatibility conditions. By removing the need for explicit constitutive equations, material behavior can be described directly from the data.
We have extended this approach to include inelastic material behavior by incorporating tangent space representations, enabling the accurate modeling of path-dependent effects such as plasticity. To address the complexity of inelastic problems, we employ data reduction techniques, including the transformation of datasets into Haigh-Westergaard coordinates. This transformation reduces the dimensionality of the data while preserving essential information about material responses. Additionally, we divide the dataset into subsets representing different material behaviors, with transition rules mapping between these subsets. This structured approach enhances the ability to model behaviors such as elasto-plasticity with isotropic hardening.
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Last update: Dec 17, 2024