Zusammenfassung
This paper addresses the mechanical and numerical modeling of materials with microstructure in the nonlinear range. One intended application is the simluation of fiber reinforced concrete (cement), a material which allows to design very thin structures. The properties of this composite depend on the one hand on the material layout, e.g. the properties of its components, the fiber length, content, coating and orientation (length scale µm) and on the other hand on the structural layout, e.g. ply thickness (length scale cm). This gives an idea of the physically intrinsic scales appearing: A ”microscale”, the scale of material heterogeneity and a ”macroscale” related to the structural dimensions. The post critical behaviour of such a composite is driven by the accumulation of the failure mechanisms on the microscale. This can be fiber or matrix cracking, debonding between the fibers in a filament, or between fiber and matrix. Those failure mechanisms, taking place on the microscale, are incorporated in the macroscopic formulation using the variational multiscale method (VMM), introduced under this name by Hughes et al. [9]. A central point of the presented scheme for an efficient solution of the discrete problem is the locality assumption for the small scale part of the solution, leading to decoupled problems on the micro scale. One focus of the presentation is the description of the material behaviour of composites on the microscale whereby two potential and well-known approaches will be presented. For applications with smeared failure of the matrix material we use an isotropic gradient enhanced damage model. In addition, the numerical model comprises conventional interface elements which account for interfacial failure between the particular material components. The second approach constitutes the utilization of the extended finite-element method (X-FEM) [13] to model discrete failure of the matrix material as well as of the particular interfaces.
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