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A general and widely tunable method for the generation of Representative Volume Elements ( RVEs ) for cellular materials based on distance and level set functions is presented. The approach is based on random tessellations constructed from random inclusion packings. A general methodology to obtain arbitraryshaped tessellations to produce disordered foams is presented and illustrated. These tessellations can degenerate either in classical Voronoï tessellations potentially additively weighted depending on properties of the initial inclusion packing used, or in Laguerre tessellations through a simple modification of the formulation. A versatile approach to control the particular morphology of the obtained foam is introduced. Specific local features such as concave triangular Plateau borders and non-constant thickness heterogeneous coatings can be built from the tessellation in a straightforward way and are tuned by a small set of parameters with a clear morphological interpretation.

This contribution presents a new framework for the computational homogenization of the mechanical properties of textile reinforced composites. A critical point in such computational procedures is the definition and discretization of realistic representative volume elements (RVEs). A geometrically-based weave generator has been developed to produce realistic geometrical configurations of the reinforcing textile. This generator takes into account the contact conditions between the yarns in the reinforcement by means of an iterative scheme, accommodating the tension in the yarns in an implicit manner. The shape of the cross sections of the yarns can also be adapted as a function of the contact conditions using a level set-based post-processor. This allows a seamless transition towards an extended finite element (XFE) scheme, in which the obtained reinforcement geometry is subsequently exploited to derive the mechanical properties of the composite system using computational homogenization.

This paper presents an automated approach to build computationally Representative Volume Elements (RVE) of open-foam cellular materials, enabling the study of the effects of the microstructural features on their macroscopic behavior. The approach strongly relies on the use of distance and level set functions. The methodology is based on the extraction of random tessellations from inclusion packings following predetermined statistical packing distribution criteria. With the help of simple recombination operations on the distance fields, the tessellations are made to degenerate in Laguerre tessellations. Predetermined morphological characteristics like strut cross-section variation based on commercially available materials are applied on the RVE to ensure the extraction of closely matching models using simple surface extraction tools, and a detailed morphology quantification of the resulting RVEs is provided by comparing them with experimental observations. The extracted RVE surface is then treated with smoothening criteria before obtaining a 3D tetrahedralized model. This model can then be exported for multi-scale simulations to assess the effects of microstructural features by an upscaling methodology. The approach is illustrated by the simulation of a compression test on an RVE incorporating plasticity with geometrically non-linear behavior.