A rosette approach for the determination of the compliance matrix

Abstract

The computation of the Young's moduli and Poisson's ratio using finite element analysis is comparatively straight forward in the case of systems with non-orthogonal lattice vectors. However, the corresponding calculation of the shear coupling coefficients and the shear modulus is more demanding and less readily attainable. Yet these are needed in order to determine the compliance matrix, which is essential in order to obtain a complete description of the mechanical properties of a structure in any direction. Based on these considerations, this work aims at providing a general methodology for the computation of the complete compliance matrix for systems with non-orthogonal lattice vectors from measurements of the Young's modulus and Poisson's ratio obtained using a suitable rosette of unit cells. The theoretical framework will be outlined and then applied on an accordion-like honeycomb that does not possess a rectangular unit cell and has potential applications in cellular scaffolding, particularly of heart muscle tissue. For the computation, the values of the Young's moduli and Poisson's ratio from three differently-orientated non-rectangular unit cells were obtained using finite element simulations allowing the determination of the complete compliance matrix. The results were validated by comparison with numerical simulations carried out on another unit cell having a different orientation from the other three.