Strain and stress relation for non-linear finite element simulations

This paper presents a procedure to determine an element-length dependent strain and stress relation until fracture that is suitable for implementation in finite element models. This material relation is obtained experimentally with an optical measuring system. The strain until fracture is calculated from the measured surface displacements. The stress is derived from the measured force and the cross-sectional area in the necking region. Furthermore, because of the digital nature of the optical measurements, the strain reference length, being a function of the pixel size, is clearly defined. For the numerical simulation the finite element length is equal to this strain reference length. The overall procedure allows a precise numerical simulation of the tensile experiment until the point of fracture without curve fitting or an iterative procedure to adjust the material relation for the chosen mesh size. This precise material relation can improve non-linear numerical simulations.