Integration algorithms of elastoplasticity for ceramic powder compaction

Inelastic deformation of ceramic powders (and of a broad class of rock-like and granular materials), can be described with the yield function proposed by Bigoni and Piccolroaz (2004. Yield criteria for quasibrittle and frictional materials. Int J Solids Struct, 41:2855–78). This yield function is not defined outside the yield locus, so that ‘gradient-based’ integration algorithms of elastoplasticity cannot be directly employed. Therefore, we propose two ad hoc algorithms: (i) an explicit integration scheme based on a forward Euler technique with a ‘centre-of-mass’ return correction and (ii) an implicit integration scheme based on a ‘cutoff-substepping’ return algorithm. Iso-error maps and comparisons of the results provided by the two algorithms with two exact solutions (the compaction of a ceramic powder against a rigid spherical cup and the expansion of a thick spherical shell made up of a green body), show that both the proposed algorithms perform correctly and accurately.