Homogenized modeling and micromechanics analysis of thin-walled lattice plate structures for brake discs

Abstract

Periodic cellular structures, especially lattice designs, have potential to improve the cooling performance of brake disk system. In this paper, the method of two scales asymptotic homogenization was used to indicate the effective elastic stiffnesses of lattice plates structures. The arbitrary topology of lattice core cells connected to the back and front plates which are made of generally orthotropic materials, due to use in brake disc design. This starts with the derivation of general shell model with consideration of the set of unit cell problems and then making use of the model to determine the analytical equations and calculate the effective elastic properties of lattice plate concerning the connected back and front plates. The analytical and numerical method allows determining the stiffness properties and the internal forces in the trusses and plates of the lattice. Three types of core-based lattice plates, which are pyramidal, X-type and I-type lattices, have been studied. The I-type lattice is characterized here for the first time with particular attention on the role that the cell trusses and plates plays on the stiffness and strength properties. The lattice designs are finite element characterized and compared with the numerical and experimentally validated pyramidal and X-type lattices under identical conditions. The I-type lattice provides 4% higher strength more than the other lattice types with 9% higher truss fraction coefficient. Results show that the stiffness and yield strength of the lattices depend upon the stress–strain response of the parent alloy of trusses and plates, the truss mass fraction coefficient, the face carriers thickness and the core elements parameters. The study described here is limited to a linear analysis of lattice properties. Geometric nonlinearities, however, have a considerable impact on the effective behavior of a lattice and will be the subject of future studies.