Homogenization based topology optimization of fluid-pressure loaded structures using the Biot-Darcy Model

Homogenization method is applied to topology optimization of a weakly coupled two physics problem, where structures are made of periodically perforated material. The microscopic periodic cell is macroscopically modulated, where the design is characterized by the material density and its homogenized Hooke's law at each point of the domain. The coupling is weak because the two physics involved are solved consecutively: first, the coupled fluid is determined using Biot-Darcy's law and second, the fluid-structure problem by solving the linear poro-elasticity system; our aim is to optimize the homogenized formulation of this two-physic problem. This approach permits a computationally low cost of evaluation of load sensitivities using the adjoint-state method. Numerical two-dimensional test cases are presented using the alternate directions algorithm. It is demonstrated how the implementation can address a variety of design problems.