Computational Micro-Macro Analysis of Impact on Strain-Hardening Cementitious Composites (SHCC) Including Microscopic Inertia

Abstract

This paper presents a numerical two-scale framework for the simulation of fiber reinforced concrete under impact loading. The numerical homogenization framework considers the full balance of linear momentum at the microscale. This allows for the study of microscopic inertia effects affecting the macroscale. After describing the ideas of the dynamic framework and the material models applied at the microscale, the experimental behavior of the fiber and the fiber–matrix bond under varying loading rates are discussed. To capture the most important features, a simplified matrix cracking and a strain rate sensitive fiber pullout model are utilized at the microscale. A split Hopkinson tension bar test is used as an example to present the capabilities of the framework to analyze different sources of dynamic behavior measured at the macroscale. The induced loading wave is studied and the influence of structural inertia on the measured signals within the simulation are verified. Further parameter studies allow the analysis of the macroscopic response resulting from the rate dependent fiber pullout as well as the direct study of the microscale inertia. Even though the material models and the microscale discretization used within this study are simplified, the value of the numerical two-scale framework to study material behavior under impact loading is demonstrated.

A general, implicit, finite-strain FE$$^2$$ framework for the simulation of dynamic problems on two scales

“…Again, the two equations are combined by joining the displacements and the Lagrange multipliers into a single matrix, c.f. (58). By solving the resulting system of equations with respect to the required derivatives ∂üD * , we obtain…”

“…A standard experiment to study material behavior under impact loading is therefore replicated, the split Hopkinson tension bar test, see e.g. [11,58]. By releasing a pre-strained steel bar, a loading pulse is transmitted to an aluminum input bar.…”

“…Therefore there is a need for accurate simulations including inertia at the macroand the microscale. In [58] a quite simplified microstructure was considered as RVE. Although a three-dimensional discretization of the RVE was taken into account, the multidimensional character with respect to mechanics was strongly limited by the fact that only one fiber in the direction of the main macroscopic traveling wave direction was taken into account.…”

“…Although a three-dimensional discretization of the RVE was taken into account, the multidimensional character with respect to mechanics was strongly limited by the fact that only one fiber in the direction of the main macroscopic traveling wave direction was taken into account. Therefore, in contrast to [58], here we consider an RVE with multiple fibers to more realistically reflect the three-dimensional nature of microscopic problems in real SHCC. In total, 13 randomly oriented fibers are included representing a more or less isotropic distribution of fiber orientations.…”

“…A split Hopkinson tension test is conducted on a sample of strain-hardening cementitious composite (SHCC). The presented example is an extension of the example published in [58], presenting a more complex, 3D microstructure. The publication [58] is focused on the comparison to experimental results and the understanding of the composite behavior, without going into detail on the developed homogenization framework.…”