Modelling and quasistatic simulation of the stiffness degradation of concrete based on physical measurements
Authors: Ries Jürgen 
Published: May 2019

AIM:
The description of the mechanical properties of concrete is usually done with two pairs of values "stress-strain" within the "elastic area" which are defining the slope (Young's modulus) and the peak value (strength). The post-peak-behaviour (softening) is usually defined only by a theory giving the decreasing curve e.g. exponential softening. Therefore the aim of this project is the metrological recording of the complete stress-strain-curve for the integration into the material model, reproducing the "linear" and the nonlinear area (softening) within the nonlinear simulation exactly.
The quality of simulation results should improve when using physical measured values as input data of the material model.
PROCEDURE:
According to the statistical evaluation of the experimentally determined material parameters (compressive-, bending -, tensile-, splitting tensile strength), the bending strength was identified as the material parameter with the least deviation from the mean value (relative scattering coefficient, the coefficient of variation). This leads to the objective of implementing the electronically recorded measurement data of the carried out deformation controlled 4-point-bending-tests (according to test guideline German committee for reinforced concrete DAfStB) into the material model. The experimentally recorded forces and displacements were linearly converted into normalized stresses and strains according to the rules of statics. The input for the elastic-degrading material model of the steel-fibre-concrete are 20 pairs of values, ​​taken from the measured data of the 4-point bending test.
The material model (smeared cracking method) of the unreinforced fibre concrete and it’s softening is thus based exclusively on experimentally measured data, taken from the 4-point-bending-tests. The theoretical material models available in "Ansys Mechanical", e.g. “Mohr-Coulomb” or “Drucker-Prager”, have not been applied here. The usual input data of the uniaxial tensile- and compressive strength were also not included in the simulation.
When evaluating the 4-point tests, the lowest force-displacement curve is decisive (minimum work performed); this corresponds to the main crack in midspan. In the area of ​​the damage between the load applications, the constant (bending) normal-stress corresponds to the equivalent stress because of the lack of (bending) shear-stress. The (bending) normal-stress together with the plastic strain are the experimental input values of the material model.
CONCLUSION:
Element size and deformation rate have to be minimal for a good quality simulation result. There are deviations between simulation and experiment in the „elastic zone“ and also concerning the peak value (bending strength) because within the simulation all cracks are smeared homogeneously.
Sufficient local and temporal discretization / sufficient small mesh size and deformation speed bring the nonlinear simulation close to the physical reality. The optimum quality of results is achieved with a specific mesh density and a specific deformation speed - too small values, on the other hand, will worsen the quality of results (optimization process). The elastic-degrading/multilinear-elastic simulation using a physically based material model showed no convergence problems.