Mathematical Modeling and Design

Abstract

For the design of functionally gradient materials (FGMs), necessary material properties, such as thermal-expansion-coefficient and Young's modulus in the specific region, are optimized by controlling the distribution profiles of composition and microstructures, as well as micropores in the materials. For this purpose, our research team employs the inverse design procedure in which both the basic material combination and the optimum profile of the composition and microstructures are determined with respect to the objective structural shape and the thermomechanical boundary conditions. Figure 1 shows the inverse design procedure for FGM, in which the final structure to be developed, as well as the boundary conditions, are specified first. After the fabrication method and an allowable material combination are selected from the FGM database, the estimation rules for the material properties of the intermediate compositions are determined based upon the micro-structure. Then, the temperature distribution and the thermal-stress distribution are calculated with the assumed profiles of the distribution functions for the constituents. Other possible combinations and different profiles are also investigated until the optimum is obtained.

Stress Reduction of 3D Printed Compliance‐Tailored Multilayers

“…[1][2][3][4][5][6] With the advent of various technologies to synthesize and process materials in 3D, gradations in composition, structure, and properties may now be practically engineered over a wide range of length scales ranging from nanometers to meters. [3,5,7] Such grading, either continuous or in ever-finer, discrete steps, across an interface and between two dissimilar materials, has been used to redistribute thermal stresses, [8] thereby limiting the stresses at critical locations and thus suppressing the onset of permanent (plastic) deformation, damage, or cracking. [9][10][11] Grading of composition is particularly beneficial at mechanical interfaces between dissimilar materials, where stress and strain jumps naturally arise due to mismatch in elastic properties.…”

Modelling adhesive contact problems involving a layered elastic solid and cylindrical indenter using Lennard Jones potential

“…Graded materials are designed so that their physical and mechanical properties vary continuously or discretely throughout their depth [1]. As a result, these materials can be used to redistribute thermal stresses [2] and reduce stress concentrations which can help minimise the local driving force for crack growth [3] and lead to an increased susceptibility to damage through wear.…”

Investigation on the Effect of Crack Length on Mechanical Properties of Functionally Graded Materials

“…Several review articles have been written on FGMs, covering applications [1], processing [2], modelling [3,4] and fracture mechanics [5,6]. Wiliamson et al [7] studied the influence of the creep phenomenon on the residual stress of the Al 2 O 3 /Ni FGMs by finite element analysis.…”