Abstract. We derive a new a posteriori error estimator for the Lamé system based on H(div)-conforming elements and equilibrated fluxes. It is shown that the estimator gives rise to an upper bound where the constant is one up to higher order terms. The lower bound is also established using Argyris elements. The reliability and efficiency of the proposed estimator is confirmed by some numerical tests.

No abstract

The main goal of constitutive model calibration in the field of sheet metal forming is to describe the stress and strain relationship for numerical simulation of the production process as accurate as possible. This may be achieved through enlarged reverse-engineering strategies which are based on available classical or even modified experimental investigations. Therefore, coupon tests have to be discretised and the corresponding test setup is simulated by using the desired spatial and temporal discretisation by finite elements. In this respect the most common characterisation procedure for the identification of constitutive properties of sheet metal is the tensile test acc. to DIN EN ISO 6892-1. In this test, the measurement data such as the tension force and the specimen elongation serve as the basis for classical parameter identification. It particularly aims at identifying the yield behaviour, i.e. the yield locus and the hardening curve of the targeted sheet metal material. The goal of the present research is to investigate how the massive amount of data obtained from state-of-the-art full-field measurement via Digital Image Correlation (DIC) can be used to not only simplify the approach in constitutive parameter identification but also to automate and speed up the process in general. Furthermore, the authors believe that a more accurate description of the yield locus should be possible since the transient development of the deformation gradient is known for every measured local material point. For this purpose a concept to compare transient but scalar data from the DIC measurement with the respective data from virtual tests was developed. These so-called hyper-curves represent response curves in an optimization procedure which are evaluated at multiple locations and are extracted from simulation and experimental data. In a first step, the validation of the method which is based on synthetic (i.e. simulated) data generated with the finite element solver LS-DYNA was accomplished. The generated virtual data consists of hyper-curves with the global force as ordinate value and the local true strain in transversal and longitudinal direction as abscissae value. The results of the validation show that the target hyper-curves can be mapped almost identically and thus the parameter identification using the full-field information from simulated data has proven its applicability. Furthermore, the method was applied to data gained from an experimental tensile test of high strength steel CR210IF. To digitise the transient deformation field on the surface of the specimen a gom/aramis optical measurement system (DIC) has been used. Based on the findings of the present work, it can be stated that the proposed full-field calibration (FFC) method delivers an excellent and efficient approach for the identification of the yield curve parameters. However, the identification of yield curve parameters only shows a small range of the many possibilities that the method could provide in the future. Further constitutive parameters such as those describing the anisotropy of the yield locus, i.e. values for the exponents, Lankford parameters and such, can be identified.

No abstract