Study of efficient homogenization algorithms for nonlinear problems

Okada, Jun-ichi; Washio, Takumi; Hisada, Toshiaki
July 2010
Computational Mechanics;Jul2010, Vol. 46 Issue 2, p247
Academic Journal
A framework for the homogenization of nonlinear problems is discussed with respect to block LU factorization of the micro�macro coupled equation, and based on the relation between the characteristic deformation and the Schur-Complement as the homogenized tangent stiffness. In addition, a couple of approximation methods are introduced to reduce the computational cost, i.e., a simple scheme to reuse the old characteristic deformation and a sophisticated method based on the mode-superposition method developed by our group. Note that these approximation methods satisfy the equilibrium conditions in both scales. Then, using a simplified FE model, the conventional algorithm, a relative algorithm originating from the block LU factorization, and the above-mentioned algorithms with the approximated Schur-Complement are compared and discussed. Finally, a large-scale heart simulation using parallel computation is presented, based on the proposed method.


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