Multi-scale response sensitivity analysis based on direct differentiation method for concrete structures

As traditional composite materials, concrete and reinforced concrete (RC) have been widely used for civil and military purposes. The multi-scale response analysis of concrete structures can be implemented by coupling the finite element and discrete element methods (FEM-DEM). To study the response sensitivities, this paper presents a novel approach by extending the direct differentiation method (DDM) to coupled FEM-DEM multi-scale method. The response and response sensitivity analysis methods are implemented by coupling an existing FEM framework, OpenSees, and DEM software, Yade, based on a client-server (CS) software integration technique. An application example is used to demonstrate the multi-scale response sensitivity method presented herein.