J.A. Hernández

TL;DR: In this article, a model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented, where the reduced set of empirical shape functions is obtained using a partitioned version of the Proper Orthogonal Decomposition (POD).

TL;DR: In this article, a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (hyper-reduction), of nonlinear parameterized finite element (FE) models is presented.

TL;DR: In this article, the contact constraints are formulated on a so-called contact domain, which is interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies.

TL;DR: In this article, the authors propose a reduced order modeling (ROM) approach to solve multiscale fracture problems through a FE2 approach, where a domain separation strategy is proposed as a first technique for model order reduction: unconventionally, the low-dimension space is spanned by a basis in terms of fluctuating strains, as primitive kinematic variables, instead of the conventional formulation in terms displacement fluctuations.

TL;DR: In this article, the authors describe the numerical aspects of the developed contact domain method for large deformation frictional contact problems and demonstrate the performance of this method on static and dynamic contact problems in the context of large deformations.