Nonuniform transformation field analysis of elastic–viscoplastic composites

Abstract

To exactly describe the macroscopic behaviour of composites with non linear dissipative constituents, it is necessary to take an infinitely large number of internal variables into account. Simplifying assumptions are usually adopted to reduce this number. A new method has been proposed [Michel JC, Suquet P. Nonuniform transformation field analysis. Int J Solids Struct 2003;40:6937–55], based on the transformation fields approach [Dvorak G. Transformation field analysis of inelastic composite materials. Proc Roy Soc Lond A 1992;437:311–27], but not taking transformation fields to be necessarily uniform. The interest of this new method has been shown in the case of composites with elastic–plastic constituents. Here we deal with composites having elastic–viscoplastic and porous elastic–viscoplastic constituents. In the latter case, the viscoplastic strain has a dilatational part.