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.
Highlights
The characteristic composition of strain-hardening cementitious composites (SHCC) consisting of fine-grained mineral-bonded matrices in combination with high-performance polymer micro-fibers in a volume content of up to 2 % is defined by a purposeful material design, accounting for the mechanical and physical properties of the cementitious matrix, of the reinforcing fibers and of their interaction, see [1,2]
Due to the limitations imposed by the testing facilities and measuring techniques, the micromechanical experiments assumed displacement rates considerably lower than the crack opening speeds in SHCC subject to tensile impact loading in Hopkinson bar tests [4,26], the latter serving for validation purposes in the numerical study presented in the paper at hand
The two parts were combined in a multiscale simulation of a split Hopkinson tension test on an SHCC specimen
Summary
The characteristic composition of strain-hardening cementitious composites (SHCC) consisting of fine-grained mineral-bonded matrices in combination with high-performance polymer micro-fibers in a volume content of up to 2 % is defined by a purposeful material design, accounting for the mechanical and physical properties of the cementitious matrix, of the reinforcing fibers and of their interaction, see [1,2]. The framework in [6] considers a quasi-static microstructure but applies an additional body force at the macroscale to account for microinertia effects This framework was extended in [16] to account for localizations at the microscale under impact loading. The paper at hand applies the homogenization method to study full sized SHCC specimens under impact loading, while simultaneously including the most relevant microstructural processes as matrix cracks and fiber pullout. To the best of the authors knowledge, this is the first application of a multiscale framework which considers microinertia for a simulation of fiber reinforced concrete to study the dynamic effects arising at the fine scale.
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