Three-dimensional modeling and numerical predictions of multimodal nonlinear behavior in damaged concrete blocks

In this paper, the multimodal nonlinear elastic behavior of concrete, which is representative of a consolidated granular material, is modeled numerically. Starting from a local three-dimensional softening law, the initial stiffness properties are re-estimated according to the local strain field. The experiments deal with samples of thermally damaged concrete blocks successively excited around their first three modes of vibration. The geometry of these samples cannot be described by a one-dimensional approximation in these experiments where compressional and shear motions are strongly coupled. Despite this added complexity, the nonlinear behavior for the three modes of vibration of the samples is well captured by the simulations using a single scalar nonlinear parameter appropriately integrated into the elasticity equations. It is shown that without sufficient attention paid to the latter, the conclusions would have brought erroneous statements such as nonlinearity dispersion or strain type dependence.