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J. Gager:
"Modeling and Simulation Concepts for Advanced Braided Composites";
VDI Verlag GmbH, Düsseldorf, 2014, ISBN: 978-3-18-333818-4; 117 S.

The present thesis focuses on the development of an efficient modeling and simulation concept of braided and woven composites in the framework of the Finite Element Method

Due to the hierarchical nature of such textiles, a detailed representation of the underlying architecture and constituents' behavior is necessary to accurately predict their mechanical response.

To characterize the mechanical behavior of braided textiles in the perspective of material induced nonlinearities, a numerical approach based on homogenization of a periodic unit cell is applied. The common strategy found in the literature, namely continuum element based modeling of such unit cells, suffers from vast computational requirements which puts its economic application with nonlinear simulations into question. To circumvent this drawback, a modeling approach is proposed by which all constituents are discretized with Finite Elements of shell type only, which are connected using surface based couplings. The application of structural elements leads to a pronounced decrease in degrees of freedom without coarsening the discretization. Thus, the simulation time is drastically reduced, retaining accurate results at the same time. Moreover, the surface based coupling allows to incorporate cohesive behavior between the constituents to simulation intraply delamination phenomena.

In order to assess the predictive capabilities of the proposed approach, a verification study is conducted based on linear elastic assumptions comparing the proposed unit cell with a continuum element based one. In this context, the numerical efficiency of the shell element based approach is highlighted. Based on such linear elastic assump­ tions, the influence of the braiding angle on the elastic properties is investigated as well.

The achieved computational efficiency allows for the simulation of multilayer laminates by modeling the individual layers. This ability is used for studying the influence of different layer stacking and offset schemes on the homogenized elastic properties. Moreover, interlaminar delamination, i.e. delamination between two textile layers, due to in-plane loading is investigated as well.

A major motivation for the development of the present strategy is the possibility of efficient numerical characterization of textile composites taking into account nonlinear constituents behavior. To this end, the shell elements are equipped with an already available elasto-plasto-damage model based on continuum damage mechanics and multi-surface plasticity. By means of this set-up, the nonlinear response of different braids and weaves is predicted and compared with corresponding experimental results.

To apply these mesoscopic results at the structural level accounting for the material nonlinearities, a concept based on energy dissipation assessment is proposed. The concept relies on the evolution of the dissipated energies with respect to proportional loading paths in stress and strain space, respectively, at the unit cell level. This data is precomputed for the investigated textile, stored in a database for later usage. In a second step, it is used during post-processing of linear elastic macroscale simulation results to assess the acting loading state and predict the evolution of the material nonlinearities like damage and plasticity. In this way, various macroscopic structures featuring the same textile plies can be efficiently evaluated beyond the linear elastic regime, requiring only linear elastic simulations at the structural scale. Hence, a computationally efficient evaluation accounting for nonlinear phenomena is achieved. The concept is demonstrated by means of an generic nacelle structure made of a Twill weave carbon/ epoxy laminate.

The proposed modeling strategy proves itself as a viable approach to simulate the linear and nonlinear behavior of braided as well as woven composites. In combination with the energy dissipation concept, large scale composite structures can be efficiently a.ssessed beyond the elastic regime without conducting time and resource intensive nonlinear simulations of such structures. This helps to push the numerical evaluation of composites further and supports designing lightweight and safe parts.