Presentation Details
The Heterogeneous Multiscale Finite Element Method (FE-HMM) for nonlinear problems in solid mechanics
Wednesday, 11 Oct 2017; 11:30 - 11:50 in room 7.31
In Session:
MS13-1: Multiscale Methods for Complex Materials (Show complete Mini Symposium)
Wednesday, 11 Oct 2017; 10:30 - 12:30 in room 7.31
Show complete Session
1st and presenting Author
Andreas Fischer
Heisenberg Group, Institute of Mechanics/Dept Mechanical Engineering
University of Siegen
Siegen, Germany
Heisenberg Group, Institute of Mechanics/Dept Mechanical Engineering
University of Siegen
Siegen, Germany
2nd Author
Ajinkya Gote
Heisenberg Group, Institute of Mechanics/Dept Mechanical Engineering
University of Siegen
Siegen, Germany
Heisenberg Group, Institute of Mechanics/Dept Mechanical Engineering
University of Siegen
Siegen, Germany
3rd Author
Bernhard Eidel
Mechanical Engineering
University of Siegen
Siegen, Germany
Mechanical Engineering
University of Siegen
Siegen, Germany
Micro Abstract:
The present work proposes a nonlinear extension of the FE-HMM for the homogenization of microheterogeneous solids. The advantage of FE-HMM compared with FE$^2$ is the existence of a priori convergence estimates, which allow for optimal strategies in mesh refinements. While these estimates were proved for linear problems so far, we assess their validity for geometrical nonlinearity and hyperelastic constitutive laws. Applications to complex microstructures showcase the performance of the method.