RVE computations with error control and adaptivity: The power of duality. (English) Zbl 1161.74046
Summary: The goal of computational homogenization is to obtain the macro-scale response, normally in terms of macro-scale stress for given macro-scale deformation, via RVE-computations. In this paper we investigate, in a systematic manner, the effects of Dirichlet and Neumann boundary conditions on the RVE. Adaptive computations are carried out to control the error in the macro-scale stress tensor. This requires the corresponding dual solutions. As a new result, it is shown how the dual solutions can be conveniently used in computing the algorithmic tangent stiffness tensor, thereby demonstrating the “power of duality”.
MSC:
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74E30 | Composite and mixture properties |
Keywords:
Dirichlet boundary conditions; Neumann boundary conditions; macro-scale stress tensor; algorithmic tangent stiffness tensorReferences:
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