Abstract

This paper presents a multiscale concurrent isogeometric design method for the cellular structure composed of the multiple prototype microstructures. Based on the unified-skeleton modeling scheme, the graded microstructures obtained from a same prototype have similar topology and good connectivity between each other. For the different prototypes, the configurations are rearranged and added the thin-wall material in common interfaces. Thus, the geometric features as well as the structural skeletons can have a smooth transition. Through combining the numerical homogenization method with the interpolation technique, the effective properties of graded microstructures can be estimated efficiently. For the multiscale scheme, the allocation of microstructures is optimized by a material distribution-based method while the configurations of prototypes are designed by the isogeometric parameterized level set method. The proposed method inherits the high accuracy and high efficiency of isogeometric analysis and the smooth boundaries and distinct interfaces of level set method. The cellular structure can be freely customized with favorable connectivity.

Abstract

The present work aims to investigate the mechanical properties of the cellular structure based on the Isotruss unit cell by implementing the finite element method (FEM) introducing a representative elementary volume (REV). As an orthotropic cellular structure, the three principal Young's modulus along the longitudinal and transversal directions are evaluated. The influence of the geometrical parameters on the elastic properties is studied in detail. Results reveal that Young's modulus in two transverse directions are almost close, showing a 12% difference. Besides, the proposed unit cell presents the ability to tune the elasticity along with the main directions. It is seen that increasing the angle of helical pitch, increases the longitudinal Young's modulus while decreases the transverse ones that suggest a considerable possibility for optimal designs. As an example, mimicking Young's modulus of the human cortical bone as an orthotropic material is explored and it is seen that the presented cellular structure based on the Isotruss unit cell can successfully fit.