122 citations · 228 across the 15 of their papers we have counts for
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Atomistic-Continuum Coupling by Homogenization
Aagashram Neelakandan, Karsten Albe, Bernhard Eidel
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessi…
From image data towards microstructure information -- accuracy analysis at the digital core of materials
Bernhard Eidel, Andreas Fischer, Ajinkya Gote
A cornerstone of computational solid mechanics in the context of digital transformation are databases for microstructures obtained from advanced tomography techniques. Uniform disc…
Error Analysis for Quadtree-Type Mesh-Coarsening Algorithms Adapted to Pixelized Heterogeneous Microstructures
Andreas Fischer, Bernhard Eidel
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding…
A Nonlinear Finite Element Heterogeneous Multiscale Method for the Homogenization of Hyperelastic Solids and a Novel Staggered Two-Scale Solution Algorithm
Bernhard Eidel, Andreas Fischer, Ajinkya Gote
In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of…
Convergence and Error Analysis of FE-HMM/FE for Energetically Consistent Micro-Coupling Conditions in Linear Elastic Solids
Andreas Fischer, Bernhard Eidel
A cornerstone of numerical homogenization is the equivalence of the microscopic and the macroscopic energy densities, which is referred to as Hill-Mandel condition. Among these cou…
The Heterogeneous Multiscale Finite Element Method for the Homogenization of Linear Elastic Solids and a Comparison with the FE Method
Bernhard Eidel, Andreas Fischer
The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was intr…