Mechanics of filled cellular materials

• Published in: Mechanics of materials Vol. 97; pp. 26 - 47
• Main Authors: Ongaro, F., De Falco, P., Barbieri, E., Pugno, N.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2016
• Subjects: Cellular; Cellular material; Composite; Computer simulation; Constitutive relationships; Continuums; Estimating; Finite element method; Homogenization; Homogenizing; Linear elasticity; Mathematical models; Parenchyma tissue; Winkler model; Finite element method; Cellular material; Composite; Parenchyma tissue; Winkler model; Linear elasticity
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2016.01.013

•This paper presents a continuum model for composite cellular materials.•Finite element simulations performed on the microstructure and numerical homogenization demonstrate a convergence towards non-micro polarity, in contrast to classical empty materials.•Theoretical homogenization, in its most general setting, confirms that the gradients of micro-rotations disappear in the continuum limit.•The resulting constitutive model remains isotropic, as for the non-filled cellular structures, and reconciles with existing studies where the filling material is absent.•The effective elastic constants are related to the microstructure parameters. The analysis developed to investigate such inuence, reveals that the macroscopic mechanical behavior of the medium is improved by increasing the stiffness of the material that fills the cells.•The model shows estimates for the mechanical properties of parenchyma tissues (carrots, apples and potatoes). The theory provides values for Young moduli reasonably close to the ones measured experimentally for turgid samples. Many natural systems display a peculiar honeycomb structure at the microscale and numerous existing studies assume empty cells. In reality, and certainly for biological tissues, the internal volumes are instead filled with fluids, fibers or other bulk materials. Inspired by these architectures, this paper presents a continuum model for composite cellular materials. A series of closely spaced independent linear-elastic springs approximates the filling material. Firstly, finite element simulations performed on the microstructure and numerical homogenization demonstrate a convergence towards non-micro polarity, in contrast to classical empty materials. Secondly, theoretical homogenization, in its most general setting, confirms that the gradients of micro-rotations disappear in the continuum limit. In addition, the resulting constitutive model remains isotropic, as for the non-filled cellular structures, and reconciles with existing studies where the filling material is absent. Finally, the model is applied for estimating the mechanical properties of parenchyma tissues (carrots, apples and potatoes). The theory provides values for Young moduli reasonably close to the ones measured experimentally for turgid samples.