Interspace Minimisation for Optimal Description of Temperature-Dependent Nonlinear Material Behaviour

This paper focuses on optimisation of material parameters to describe the elastoplastic stress–strain relationship in finite element solvers. Two new methods are introduced to minimise the numerical error that occurs in the interspace between the experimental cyclic stress–strain curve and its representation using multilinear interpolation. Specifically, both methods are integrated into a Prandtl operator approach, which can be used to simulate the elastoplastic response of mechanical components subjected to variable thermomechanical loadings. The improvement as compared to standard interpolation is most substantial when the number of yield planes is limited, especially in the case of bilinear stress–strain curves. The innovation of this study is an algorithm that optimises positions of the stress–strain points across the temperature range of interest considering several input temperatures. It is shown that these methods are especially applicable for optimisation of material parameters when the stress–strain curves are available for a range of test temperatures that are needed for simulating thermomechanical fatigue. The improvement in the interpolation using these methods is exhibited for two materials with available experimental results: stainless steel EN 1.4512 and polyamide PA12.