期刊
COMPUTATIONAL MECHANICS
卷 59, 期 3, 页码 483-505出版社
SPRINGER
DOI: 10.1007/s00466-016-1358-z
关键词
Computational homogenization; Boundary conditions; Multi-physics; Tangent operator
资金
- F.R.S-F.N.R.S. [PDR T.1015.14]
- Fond de la Recherche Scientifique de Belgique (FRS-FNRS)
This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.
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