Cellular materials, especially foams, are widely used in several applications because of their special mechanical, electrical and thermal properties. Their properties are determined by three factors: bulk material properties, cell topology and shape as well as relative density. The bulk material properties include the mechanical, thermal and electrical properties of the matrix. The cell topology determines if the foam exhibits stretch or bending dominated behaviour. The relative density corresponds to the foaming degree. It is defined by the cell edge length and cell wall thickness. Especially for the linear elastic properties there are many different modelling approaches. In general, these methods can be divided into two groups namely direct modelling, e.g. analytical and finite element models and constitutive modelling, e.g. models which are generated through homogenization methods. This paper presents an overview of the different modelling methods for foams. Furthermore, sensitivity studies are presented which enable the comparison of the models with regard to the estimation of the elastic properties, show the limits of those models and enable the investigation of the influence of the above mentioned factors on the elastic properties. Selected models are validated with experimental data of a low density foam regarding the Young’s modulus.
In this research study, a methodology is introduced for generating finite element simulation models for low density closed cell foams based on computed tomography (CT) measurement results. Creating this kind of simulation models can be very expensive with regard to modelling and computational effort. Hence, a combined modelling technique based on CT data and Voronoi diagrams is developed that minimizes this effort, but nevertheless, generates simulation models with a realistic microstructure. In this article, the generation of simulation models using this modelling method and the necessary adaptation of the models concerning microstructural features to consider, for example, anisotropic properties of the foam, are described. Furthermore, simulations are performed to investigate the mechanical performance of the foam models and to compare the results with several analytical models and experimental data. Finally, conclusions regarding the applicability and possible further extensions of the model are provided.
The non-linear material behaviour of low density polypropylene foams is investigated under several quasi-static loading conditions with a combined modelling technique based on computed tomography data and Voronoi diagrams. A simulation methodology for determining the linear elastic properties is introduced in Hössinger-Kalteis et al. (2021). In this paper, the methodology is extended regarding the material model, where additionally the non-linear region is considered. The model takes into account property determining microstructural features like orientation-dependent cell wall thicknesses and anisotropic cell shapes. Thus, the anisotropic material behaviour under tension and compression load is estimated for extrusion foams with different densities utilizing the microstructural simulation model. Based on the characterized behaviour under tension and compression, constitutive models are generated. These are implemented in bending test simulations due to lower computational effort. The simulation results are validated with experimental results, which shows that the model gives satisfactory results.
Nowadays, there are several methods to obtain simulation models for foams which consider important microstructural features. This research study presents a method to obtain low density foam models directly from computed tomography (CT) data. Finite element meshes are created from CT measurement results of a polypropylene extrusion foam with two different densities. Sensitivity studies with regard to the tension behaviour are performed with the microstructural models. The study shows that the tension behaviour highly depends on the examined area of the foam because the microstructure and density vary through the foam. Furthermore, the simulation results are validated with experimental results. The validation shows that the tension behaviour of the investigated foams characterised by the simulation approach is in good agreement with the experimentally observed behaviour and that specific microstructural characteristics (e.g. anisotropic cell shapes) are captured in the model.
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