Master

Short Description

In the past decade the commercial utility & demand of fast Fourier transforms (FFT) based computational homogenization has increased in different industrial sectors over FEM based. The objective of the thesis would be to fundamentally understand the numerics & setup of FFT based homogenization methods. These will be demonstrated for different class of microstructures.

Short Description

The objective of the thesis is to setup a framework for generating polycrystalline microstructure and carrying out computational homogenization in a FEM framework. Later, a mean field homogenization scheme using self-consistent method needs to established. In this work, attention will be restricted to an elastic homogenization problem. 

*The thesis work will be jointly supervised by me and Dr. G. M. Karthik (ME, IIT BHU).

Short Description

Asymptotic homogenization method has been largely used for homogenizing periodic microstructures. The objective of the thesis would be to establish the framework for the class of linear problems. These has to be compared & contrast them with other homogenization methods such as full-field & mean-field methods.

Short Description

Application of full-field homogenization methods are computationally expensive whereas mean-field homogenization methods  are limited to ellipsoidal reinforcements. Machine learning packages could be a potential substitute to predict the effective material properties when trained with data based on computational homogenization. The objective of the thesis would be to explore & setup an AI package to predict effective properties for simple microstructures.

Short Description

Viscoelastic constitutive relation in a small strain framework can be represented in differential and integral forms. The objective of the thesis would be to use differential form of the viscoelastic constitutive relations to setup the homogenization framework. Later this will be contrasted with other methods such as correspondence principle and incremental variational principles.

Polymer micro-lens is widely used for automotive & other optical lighting applications. Inspired from semi-conductor industries these are generally fabricated in bulk quantities on a wafer by UV molding process. Warpage in such each optical lens after UV curing degrades the quality of optical assembly & hence decreases the optical quality of lens.