A numerical method is established to solve the problem of minimizing a nonquasiconvex potential energy. Convergence of the method is proved both in the case on its own and in the case when it is combined with a weak boundary condition. Numerical examples are given to show that the method, especially when applied together with a continuation method and some other numerical techniques, is not onl...

OF THE DISSERTATION Controlling the Appearance of Specular Microstructures

It is well known that material chemistry and processing dictate material microstructure and microstructure influences properties and performance of materials. Consequently, quantitative characterization and statistical representation of microstructure are of considerable importance in materials science. Microstructure is essentially a collection of three-dimensional volumes (for example, grains...

We propose a method for high-throughput generation of 3D microstructures using a membrane-mounted microfluidic channel. Utilizing an optofluidic maskless lithography system, photopolymerized 3D microstructures are fabricated in a layer-by-layer fashion with the thickness of each layer controlled by the deformation of the membrane. The combination of low numerical aperture optical systems for ph...

This article presents a new level-cut, inhomogeneous, filtered Poisson random field model for representing two-phase microstructures of statistically inhomogeneous, functionally graded materials with fully penetrable embedded particles. The model involves an inhomogeneous, filtered Poisson random field comprising a sum of deterministic kernel functions that are scaled by random variables and a ...

Microstructures with flexible and stretchable properties display tremendous potential applications including integrated systems, wearable devices and bio-sensor electronics. Hence, it is essential to develop an effective method for fabricating curvilinear and flexural microstructures. Despite significant advances in 2D stretchable inorganic structures, large scale fabrication of unique 3D micro...

Artificial reconstruction of three-dimensional (3D) hydrogel microstructures would greatly contribute to tissue assembly in vitro, and has been widely applied in tissue engineering and drug screening. Recent technological advances in the assembly of functional hydrogel microstructures such as microfluidic, 3D bioprinting, and micromold-based 3D hydrogel fabrication methods have enabled the form...

The microstructures and mechanical properties of cobalt-chromium (Co-Cr) alloys produced by three CAD/CAM-based processing techniques were investigated in comparison with those produced by the traditional casting technique. Four groups of disc- (microstructures) or dumbbell- (mechanical properties) specimens made of Co-Cr alloys were prepared using casting (CS), milling (ML), selective laser me...

Micro/nanoimprinting is a simple and economical way of patterning polymeric structures over large areas. This paper seeks to extend this technique to fabricate three dimensional (3D) metallic microstructures, even in trenches and constrained areas using a flip chip bonder in conjunction with a wire bonder. In this two step process, gold stud bumps were placed first on sputtered metal at appropr...

An efficient full-field method of computing the local and homogenized macroscopic responses of elasto-plastic polycrystalline microstructures based on the fast Fourier transform (FFT) algorithm is presented. This approach takes realistic microstructure images as the input and estimates the mechanical response/properties of polycrystal microstructures under periodic boundary conditions without r...