Elastic properties of rhombic mesh structures based on computational homogenisation

Flat mesh structures are used in a wide variety of applications. In particular, meshes with a rhombic unit cell are frequently employed due to their simplicity and relative ease of manufacture. This paper studies the in-plane elastic properties of such a structure as a function of the geometrical parameters by means of homogenisation techniques. We compare predicted elastic in-plane properties (i) including only bending mode of the struts, cf. Gibson-Ashby model, (ii) including both bending and stretching modes of the struts, obtained by homogenisation using beam elements and (iii) by homogenisation using beam-spring elements accounting additionally for strut joint deformation, and (iv) numerical results of elastic properties obtained by homogenisation using solid elements. The expressions of the predicted elastic properties are presented in analytical form. The homogenised elastic properties accounting for both bending and stretching matches very well with those from the model including only bending. The axial deformation of struts thus has negligible impact on the overall elastic behaviour. The complex deformation in the strut joint was also captured in the homogenised using beam-spring elements, and the results agree better with the solid element results. It is concluded that a finite-element-based homogenisation approach could serve as a straightforward analytical method to obtain elastic properties of mesh structures. This approach automatically includes all deformation mechanisms as opposed to the classical unit cell analyses of bending beams.