Accelerating the distance-minimizing method for data-driven elasticity with adaptive hyperparameters

Abstract

Data-driven constitutive modeling in continuum mechanics assumes that abundant material data are available and can effectively replace the constitutive law. To this end, Kirchdoerfer and Ortiz proposed an approach, which is often referred to as the distance-minimizing method. This method contains hyperparameters whose role remains poorly understood to date. Herein, we demonstrate that choosing these hyperparameters equal to the tangent of the constitutive manifold underlying the available material data can substantially reduce the computational cost and improve the accuracy of the distance-minimizing method. As the tangent of the constitutive manifold is typically not known in a data-driven setting, and as it can also change during an iterative solution process, we propose an adaptive strategy that continuously updates the hyperparameters on the basis of an approximate tangent of the hidden constitutive manifold. By several numerical examples we demonstrate that this strategy can substantially reduce the computational cost and at the same time also improve the accuracy of the distance-minimizing method.