Integration algorithms of elastoplasticity for ceramic powder compaction

TL;DR

This paper introduces two novel integration algorithms for elastoplasticity modeling of ceramic powder compaction, addressing the limitations of existing gradient-based methods by ensuring accurate and stable numerical solutions.

Contribution

It proposes explicit and implicit ad hoc algorithms tailored for the Bigoni-Piccolroaz yield function, enabling effective elastoplastic analysis of ceramic powders.

Findings

Both algorithms perform accurately compared to exact solutions.

The implicit scheme offers improved stability for complex loading paths.

Explicit scheme provides computational efficiency for simpler problems.

Abstract

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 and Structures, 41, 2855-2878). 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.