This poster was presented at the IUTAM Symposium on Data-driven mechanics, taking place in Paris, France in Octoboer 2022. It shows a proof-of-concept for a new application of Data-Driven Computational Mechanics (DDCM): using it as a new type of adaptive refinement for linear elastic FEM simulations.
DDCM is a new paradigm to solve mechanical problems without using a constitutive law. A mechanical problem can be formulated with a set of equations originating from physical principles, such as balance of momentum, and from the geometry of deformation: the compatibility equations. To lose the system in the classical paradigm, a constitutive law, linking stress and strain, is employed. In Data-Driven Mechanics, a set of strain-stress datapoints replaces the constitutive law. No model is assumed, the points are used directly and thus no modeling bias or simplification is introduced.
However, some materials (e.g. metals) can be convincingly described as linear and elastic in the small strain regime. Since DDCM is computationally intensive, it makes sense to use only when and where necessary.