Numerical manifold computational homogenization for hydro-dynamic analysis of discontinuous heterogeneous porous media

In this paper, a mixed two-scale numerical manifold computational homogenization model is presented for dynamic analysis and wave propagation of the discontinuous heterogeneous porous media based on the first-order homogenization theory. Instead of the conventional version which neglects microscopic dynamics, the extended Hill–Mandel lemma is employed to incorporate the microscale dynamic effects. Microscale and macroscale Initial Boundary Value Problems (IBVPs) are solved simultaneously using the Numerical Manifold Method (NMM) with the information conveyed between different scales. The microscale IBVP is solved under Linear Boundary Conditions (LBCs) and Periodic Boundary Conditions (PBCs) that are defined with macroscale solid displacement, fluid pressure and their first-order gradients. The discontinuous macroscale IBVP is solved iteratively using the Newton method with the macroscale internal forces and Jacobian determined by solving the microscale IBVPs. A stick–slip contact model is implemented using an augmented Lagrange multiplier method to impose frictional contact conditions along the macroscale discontinuities. Through various numerical simulations, the presented two-scale NMM is shown to be able to effectively and accurately capture the fully dynamic and wave propagation responses of the discontinuous heterogeneous porous media under the fluid injection and impact loading condition. •A two-scale numerical manifold computational homogenization model is presented.•Micro dynamics is considered using the extended Hill-Mandel lemma.•Macro contact is modeled with an augmented Lagrange multiplier method.•Wave propagation in discontinuous heterogeneous porous media is modeled.