2D Mathematical Model of Damping in Cellular Materials

Abstract

AbstractMany biological materials may be considered as cellular materials, for example, soft tissues, but also bones, wood, or foam‐like medulla in a bird feather. The cells may be filled with a fluid or just with air, have different size, shape, and wall thickness. Less is known about how the mechanical and morphological parameters of the cellular materials influence their biologically relevant functions. A simple descriptive 2D numerical model of a cellular material based on Voronoi diagrams is presented here which aims prompt investigation how structural parameters influence its physical properties. The preliminary numerical simulations demonstrate that with an increasing wall thickness the energy dissipation increases and with an increasing cell density also an average stress increases. Other interesting results are that an increased dissipation constant of cellular material reduces the stress, and that in hierarchical foams the dissipation takes place mostly in the thick walls. The presented approach allows screening the influence of further material features and structural parameters, such as for example, different kinds of gradients or different properties of biological or biologically inspired cellular materials at different loading conditions. Direct comparison of different real biological structures could be also performed, especially when real experimental measurements are impossible.