A phenomenological framework of constitutive modelling for incompressible and compressible elasto-plastic solids

A unified framework of constructing phenomenological constitutive models for a broad class of elasto-plastic materials exhibiting either plastical incompressibility (e.g., grey cast iron) or plastical compressibility (e.g., metal foams) is proposed. The constitutive framework also enables the different yielding behaviours under tension and compression as well as differential hardening along different loading paths to be accounted for in a relatively simple manner. The resulting plasticity model does not require the difficult task of experimentally probing the initial yield surface and its subsequent evolution; it is completely determined from a set of as few as two distinctive stress–strain curves measured along the characteristic loading paths for isotropic materials. The predicted yielding behaviours for grey cast iron and metal foams compare favourably with those measured.