Genetic programming for interpretable, data-driven continuum damage models.
The damage mechanisms that lead to failure in engineering alloys have been studied extensively, but converting this knowledge into constitutive models that are suitable for engineering-scale analysis remains a challenge. Evolution laws for continuum damage have been developed in the past and have proven effective but suffer from many non-physical assumptions that inhibit the overall accuracy of the model. Further, the assumptions inherent in these existing models prevent them from being applicable to a broad class of materials. At the same time, computational models of fine-scale damage mechanisms continue to advance making it tractable to generate large training data sets through computer simulation. Data-driven machine learning approaches can leverage these data sets to avoid making limiting assumptions, and instead produce models directly from the results of microstructural simulations and/or experiments. Many of these machine learning approaches are rapid and accurate, but they offer little to no insight into the underlying relationships among state variables being discovered. Conversely, genetic programming symbolic regression (GPSR) is a machine learning method that produces analytic expressions relating the state variables, allowing maximal insight and interpretability. To that end, we propose using GPSR as a data-driven method of obtaining microstructurally informed continuum damage models. Data is generated using microstructural simulations of damage evolution, parameterized over microstructural statistics (i.e., pore shape) and nominally applied deformations. Analytic expressions for damage evolution are obtained from the data using GPSR, and these expressions are then utilized within a continuum constitutive model. Overall, this approach is a promising method of automatically obtaining analytic relations describing constitutive phenomena in a material.