Cellular materials like metal foams are bio-inspired materials which exhibit great potential for application in lightweight construction or as kinetic energy absorber. Such cellular materials show a complex micro-structure which significantly affects the macroscopic global properties. Cellular materials exhibit localised deformation expressed in deformation bands under inelastic strain conditions. Engineering with metal foams requires material models which describe the material behaviour properly even for different load cases. In this work, a new modelling approach has been developed which phenomenologically accounts for microstructural effects by a representative volume element made of several springs. The model is experimentally validated, and its micro-structural motivated parameters are experimentally identified in quasi-static compression tests with unloading cycles. Using digital image correlation, it was possible to connect the micro-structural deformation with the global macroscopic stress-strain behaviour, evaluated locally for the front surface of the specimens.