Data-driven non-linear elasticity: constitutive manifold construction and problem discretization

摘要: The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to need increasingly detailed models as well engineered materials. Data-Driven simulation constitutes potential change paradigm SBES. Standard computational mechanics is based on two very different types equations. first one, axiomatic character, related balance laws (momentum, mass, energy, $$\ldots $$ ), whereas second one consists that scientists have extracted collected, either natural or synthetic, data. Data-driven (or data-intensive) directly linking experimental computers order perform simulations. These simulations will employ laws, universally recognized epistemic, while minimizing explicit, often phenomenological, models. main drawback such an approach large amount required data, some them inaccessible nowadays testing facilities. Such difficulty can be circumvented many cases, and any case alleviated, by considering complex tests, collecting possible then using data-driven inverse generate whole manifold few discussed present work.