5 papers
Existence of thermodynamically consistent solutions for data-driven porous media problems
Ramon Codina, Cristian Guillermo Gebhardt, Michael Ortiz
Data-Driven Computational Mechanics (DDCM) replaces traditional phenomenological constitutive models by directly reformulating boundary-value problems in terms of local material st…
Intrinsic Structure of Elasticity in Hilbert Space
Cristian G. Gebhardt, Johannes Lankeit, Marc C. Steinbach
Mathematical elasticity has a long history and a huge body of literature. Surprisingly, at its heart elasticity exhibits a rich and transparent structure that, to our knowledge, is…
A Data-Driven Computational Framework for Incompressible Flow in Hydraulic Networks
Pedro B. Bazon, Cristian G. Gebhardt, Roberto F. Ausas
The classical procedure for solving hydraulic networks relies on the assumption of constitutive equations, which state the relationship between the pressure gradient and fluxes alo…
Numerical approximation of a PDE-constrained Optimization problem that appears in Data-Driven Computational Mechanics
Pedro B. Bazon, Cristian G. Gebhardt, Gustavo C. Buscaglia +1
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such a…
Formulating and Heuristic Solving of Contact Problems in Hybrid Data-Driven Computational Mechanics
Cristian Guillermo Gebhardt, Senta Lange, Marc Christian Steinbach
In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear…