Analytical elastoplastic model for stress and strain of the equivalent representative volume element and material testing application

Highlights: • An elastoplastic load–displacement model was proposed for various specimen types to describe the relations among the material constitutive parameters, geometric dimensions, displacement, and load. • An analytical elastoplastic model for the equivalent stress and strain of the representative volume element at median point is derived based on the energy density equivalence and dimensional analysis. • A data processing method to obtain the equivalent stress–strain curves in real time for various specimen types is proposed and verified. For unidirectional loaded specimens consisting of isotropic-homogeneous ductile materials, an analytical elastoplastic model for the equivalent stress and strain of the representative volume element at the median point were derived based on energy density equivalence and dimensional analysis. Then, a data processing method for various specimen types was proposed to obtain the equivalent stress–strain in real time without presetting the constitutive parameters. Finite element analyses of six specimen types and experiments with four selected specimen types were conducted to verify the method. The results show that the stress–strain curves obtained using this method were consistent with the preset stress–strain curves in the finite element analysis and with the standard tensile results. Using the proposed model and relevant data processing method to obtain the stress–strain curves is effective and, with the theoretical basis, could promote the application of non-tradition and small specimens for obtaining the material mechanical properties.