Micromechanical modeling using computational homogenization

Sammanfattning: This thesis addresses micromechanical modeling of materials using computational homogenization. On this topic, theoretical and computational issues are discussed, and numerical investigations of different material systems are performed. The material systems considered are; metal matrix composites, metal sheets with stiff inclusions, metal sheets containing voids, sand with inclusions of gravel and sand with inclusions of clay. A numerical tool suitable when modeling complex micromechanical systems is developed and evaluated. A homogenization technique, using a representative volume element (RVE) is the foundation of the method. To be able to handle large problem sizes a parallel solution scheme is developed. A speedup investigation shows good performance of the implementation. Different boundary conditions acting on the representative volume element are shown to affect the overall response significantly. The numerical tool is in the following work used to solve problems where the behavior of heterogeneous material systems is investigated on a local and on a global scale. Anisotropic effects originating from considering heterogeneous material structures are studied for a material system consisting of a metal matrix containing stiffer inclusions. For plane strain conditions this material system represents a metal matrix composite and for plane stress conditions it is representing a metal sheet with stiff inclusions. A Bauschinger effect as well as anisotropic hardening characteristics is found despite the solely isotropic material models used on the local level. The formability of voided metal sheets is studied using a plane stress assumption. The size dependence of the formability of voided metal sheets is investigated using a nonlocal material model containing a constitutive material length scale. It is found that the formability of the material system is dependent on the nonlocal material model. Changes in the void distribution as well as in local material parameters are also found to have a large influence on the formability. Studies of soil systems, where a bulk of sand is containing inclusions of gravel or clay, are also conducted. The behavior of these systems is examined when altering the inclusion material, the inclusion shape and the bulk material properties. The overall and local responses, obtained for a footing problem, are also investigated for homogeneous sand, a sand-gravel system and a sand-clay system.