Abstract
For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson’s ratio are obtained from the material characteristics of the constituents. Numerical results show that these models capture well the mechanical responses of finite-element simulations for three-dimensional periodic structures of neo-Hookean material with closed cells under large tension. In particular, the mesoscopic models predict the macroscopic stiffening of the structure when the stiffness of the cell-core increases.
Highlights
Cellular solids are the subject of intensive research efforts in biomedical applications, and many foams and sponges designed for cushioning and re-usability can be found in everyday life as well as in several industrial areas, e.g. microelectronics, aerospace and pharmaceutical processes [1,2,3]
In order to capture the independent influence of the cells number on the elastic behaviour of a cellular body under large deformations characteristic to some cellular structures, namely that, for structures made from the same volume of hyperelastic material, the stiffness increases as the number of cells increases while the ratio between the thickness and the length of the walls remains fixed [7,29,35,36], we replace the strain energy function (4.3) with
There is no established continuum model for this type of structures, even though, in principle, this should stand on the shoulders of the existing nonlinear elasticity theory
Summary
Cellular solids are the subject of intensive research efforts in biomedical applications, and many foams and sponges designed for cushioning and re-usability can be found in everyday life as well as in several industrial areas, e.g. microelectronics, aerospace and pharmaceutical processes [1,2,3]. The first microstructure-based model for a cellular solid is due to Gent & Thomas [18] For this model, general isotropic linearly elastic open-cell foams subject to small strain deformations were assumed, and effective Young’s elastic modulus and the Poisson’s ratio were derived from the constitutive equations [19,20]. Hill’s energy functional of hyperelasticity [27] can be used to describe the simple special case of foams where the principal stresses are uncoupled, i.e. depend only upon the stretch ratio in the corresponding principal direction These approaches are based on the Ogden-type strain energy function for incompressible materials [28] extended to the compressible case. The mechanical performance of the mesoscopic models for structures with neo-Hookean components (§4e) is compared with finite-element simulations of three-dimensional structures with periodic, reproducible architecture (§5)
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