A FEM Multiscale Homogenization Procedure using Nanoindentation for High Performance Concrete

High-performance model reduction techniques in computational multiscale homogenization

A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version —that accounts for the elastic/inelastic character of the solution— of the Proper Orthogonal Decomposition (POD). On the other hand, it is shown that the standar...

Characterisation of Asphalt Concrete Using Nanoindentation

In this study, nanoindentation was conducted to extract the load-displacement behaviour and the nanomechanical properties of asphalt concrete across the mastic, matrix, and aggregate phases. Further, the performance of hydrated lime as an additive was assessed across the three phases. The hydrated lime containing samples have greater resistance to deformation in the mastic and matrix phases, in...

High Performance FEM Simulation

Processor technology is still dramatically advancing and promises further enormous improvements in processing data for the next decade. On the other hand, much lower advances in moving data are expected such that the efficiency of many numerical software tools for Partial Differential Equations (PDEs) is restricted by the cost for memory access. In this article, we briefly discuss concepts for ...

Two-Scale FEM for Homogenization Problems

The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale ε " 1 is analyzed. Full elliptic regularity independent of ε is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the ε scale of the solution with work independent of ε and without ana...

Sparse Two-Scale FEM for Homogenization Problems

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale ε 1. Based on a refined two-scale regularity on the solutions, two-scale tensor product FE spaces are introduced and error estimates which are robust (i.e. independent of ε) are given. We show that under additional two-scale regularity ...

Homogenization via p-FEM for Problems