A stress-resultant shell theory based on multiscale homogenization

Journal article, 2013

In this paper we propose a multiscale method based on computational homogenization for simulating the mechanical response of a thin–walled porous structure. Due to the inhomogeneous nature of the porous material in the thickness direction, the length scale of the deformation-field variations in the thickness direction is in the same order of magnitude as in the microstructure. To resolve this issue a higher-order stress-resultant shell formulation (with linear variation of the thickness stretch) based on multiscale homogenization is considered. The microscale is accounted for by calculating the micro-fluctuations from a boundary value problem over the domain of a 3D Representative Volume Element (RVE). The breadth and width of the RVE are determined by the representative microstructure of the porous material, whereas in the thickness direction of the shell the RVE completely resolves the microscopic variation. As a result the macroscopic stress resultants are obtained as volume averages through the entire thickness of the shell. The nested solution scheme is quite computationally demanding and it should only be applied where it is needed. The paper is concluded by a couple of numerical examples that illustrate the method and support the arguments put forward in the paper. Comparison is made to a 2D plane strain reference solution with complete resolution of the microstructure over the domain. Also a 3D case is considered, showing the significance of resolving the microscopic fluctuations.