Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Richard A. Regueiro

Second Advisor

Ronald Y. S. Pak

Third Advisor

John A. Evans

Fourth Advisor

Franck Vernerey

Fifth Advisor

Jeong-Hoon Song

Abstract

This study stands as an attempt to consider the micro-structure of materials in a continuum framework by the aid of micromorphic continuum theory in the sense of Eringen. Since classical continuum mechanics do not account for the micro-structural characteristics of materials, they cannot be used to address the macroscopic mechanical response of all micro-structured materials. In the "representative volume element (RVE)" based methods, classical continuum mechanics may be applied to analyze mechanical deformation and stresses of materials at the relevant micro-structural length-scale (such as grains of a polycrystalline metal, or sand, or metal matrix composite, etc), but when applying standard homogenization methods, such lower length scale effects get smeared out at the continuum scale. The micromorphic continuum theory provides the ability to incorporate the micro-structural effects into the macroscopic mechanical behavior. Therefore, the micromorphic continuum is a tool for a higher resolution multi-scale material modeling through capturing the material's micro-structural physics via bridging to the direct numerical simulations (DNS) at the lower length scale. In the micromorphic continuum theory of Eringen, the fundamental assumption is that the material is made of "micro-elements" in such a way that the classical continuum mechanics balance equations and thermodynamics are valid within a micro-element. Note that micro-elements represent the material's micro-structure in a micromorphic continuum. The micro-element deformation with respect to the centroid of a macroscopic continuum point is governed by an independent micro-deformation tensor χ which adds 9 additional degrees of freedom to the continuum model. The micromorphic additional degrees of freedom represent micro-stretch, micro-shear, and micro-rotation of the micro-elements. The macroscopic deformation (macro-element deformation) in the micromorphic continuum is handled through the deformation gradient tensor F. If the hypothesis of micromorphic continuum works, in a multi-scale modeling framework, assuming proper constitutive models can be formulated, and material parameters calibrated, micromorphic continuum theory may fill the gap between the RVE-micro-structural-length-scale models and the macroscopic continuum scale. The advantage of using micromorphic continuum is that it provides a chance of linking the macroscopic model to the lower length scale simulations (DNS) and reducing the computational cost by switching from DNS to the macro-scale finite element analysis or other numerical methods at the continuum scale. The linking is done through defining the overlap coupling region between the lower length scale analysis and micromorphic continuum to calibrate the material parameters and the micromorphic continuum model degrees of freedom. Therefore, in the framework of multi-scale modeling, micromorphic continuum can be used as a filter on top of the DNS simulations to capture underlying length scale and better inform the macroscopic model. This is done through the direct linking of the micromorphic continuum micro-elements to the material's micro-structure. The focus of this research is mainly on discussing the macroscopic mechanical behavior of micro-structured materials from the perspective of micromorphic continuum. This is done via developing a three dimensional finite strain finite element model for micromorphic elasticity, elastoplasticity and dynamics.

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