From the theoretical point of view, nonlinear material models for concrete are suitable for failure simulations of concrete structures. This requires an adjustment of a large number of non-physical model parameters to existing experimental results. Hence, a prognosis of the behavior of building components is impossible. Already in the simulation of a simple uniaxial compression test, the cause for the limitations of existing concrete material models becomes obvious. In the load direction, a realistic force-deformation diagram is predicted. However, the corresponding lateral deformations are simplified to a large extent. In the load direction, concrete failure due to compression is suggested, although the failure occurs due to transverse tensile cracks. This contribution provides the so far missing experimental observations to expand and improve the basic assumptions of the plasticity theory for concrete material models. The performed compression tests contain the required multiple un-and reloading steps under various multi-axial stress conditions, and deformations lateral to the direction of the main load are documented carefully. Quasi-continuously measuring fiber optic sensors without a protective coating were preferred to measure strain inside small specimens. The measuring fibres are positioned in the specimen with a brass profile, the influence of which on the concrete properties is described. The available measuring accuracies and special measuring requirements, especially regarding the transverse pressure-sensitive and non-alkali-resistant measuring fibers, are shown. A comparison with the frequently used strain measurement via brush deformation shows that the fiber optic sensors allow strain measurement in triaxial tests in a so far not achievable accuracy. Based on the new insight, the evolution laws for the multiaxial behavior of concrete are developed. With the resulting model approach, the simulation of various multiaxial compression tests becomes possible without the adaption the model parameters to respective test results.