An adaptive FE²-model for the analysis of the non-linear, thermo-mechanically coupled behavior of fiber-matrix composites

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The analysis of structures with a heterogeneous microstructure, e.g. fiber reinforced concrete or metal composites, requires knowledge of the averaged, effective material parameters. Effective material parameters for heterogeneous composites can be estimated by homogenization processes. The (Finite Element)²- /FE²-method allows for a simultaneous numerical homogenization during the calculation of the overall structure. Therefore, a representative volume element is attached to each integration point of the overall structure. It captures the nonlinear material behavior and provides information on micromechanical processes. The disadvantage of the FE²-method is the high computational cost. It necessitates a finite element analysis of the microstructure in each integration point. Hence, the definition of the finite element model is required for the numerical homogenization to calculate the effective material parameters for each integration point of the overall structure. The research project aims for reducing the computational effort. For this reason, an adaptive FE²-model shall be developed. The coupled numerical homogenization should only be performed in regions where nonlinear material behavior is expected. The adaptive numerical homogenization method is developed for fiber-matrix composites. Here, shape memory alloy (SMA) fibers are considered as fiber reinforcement. Due to the shape memory effect these fibers are able to prestress the cement based matrix materials. The stress-strain-behavior of SMA is strongly nonlinear and depends on the surrounding temperature. If the temperature is known, the nonlinear material behavior is observed, when the stress is increased beyond a characteristic stress value. The material behavior is linear below this stress. Some matrix materials behave similarly; they show linear behavior as long as the stress is below a characteristic value. If the overall material response is linear, an initial homogenization will lead to the effective material data; a simultaneously performed numerical homogenization is not necessary. The research project aims for the development of an indicator which is able to estimate the regions with linear and nonlinear material behavior of the fiber-matrix-composite. This criterion should be valid for possible nonlinearities of the matrix and the fibers. The change of the material behavior for different temperatures and different fiber orientations needs to be considered. The indicator has to be extended for varying temperatures. For the determination of the temperature the non-steady-state heat problem is solved. The effective heat conductivity of the heterogeneous material is derived by a numerical homogenization as well. The indicator allows for a local application of the FE²-method. The project aims for the development of a simulation tool to analyze SMA-fiber-matrix composites, which accounts also for the ability to prestress matrix materials.