A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

•Two-scale homogenization was integrated with phase-field fracture in porous media.•Generalized formulation for quadrilateral element-based homogenization was developed.•Microscopic heterogeneity was considered in fracture modeling for porous media.•Microscopic pore structure influences fracture strength and patterns in porous media.