Date of Award

Spring 1-1-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Richard A. Regueiro

Second Advisor

Franck Vernerey

Third Advisor

Carlos A. Felippa

Fourth Advisor

Ronald Y.S. Pak

Fifth Advisor

Stein Sture

Abstract

A three dimensional micromorphic finite strain linear isotropic elastoplastic model for geomaterials is developed and implemented into a finite element code. First, we present the finite element formulation and implementation for the finite strain elasticity together with various examples to investigate the effects of the additional degrees of freedom, additional elastic moduli, length scale, and boundary conditions on micro-displacement tensor field that are all introduced by the micromorphic continuum. We present some findings and results of the finite element analysis of one dimensional and three dimensional problems. Three dimensional results demonstrate that the micromorphic contribution leads to unpredicted behavior under three dimensional stress states, whereas a one dimensional example presents comparatively clear trends for different cases. Examples also present length scale effects and computational benefits of the formulation by direct finite strain elasticity by providing a comparison with rate form of semi implicit time integration formulation in the Total Lagrangian finite element implementation.

The work, then, is extended to finite strain micromorphic elastoplasticity by using slightly different types of yield criteria. We assume yield functions to be in the form of standard Drucker-Prager yield condition and a similar form of a Drucker-Prager-like yield

function. The effect of elastic length scale is investigated in a one dimensional problem, together with the different yield functions and micro boundary conditions. We also consider a plain strain problem as more advanced geometry compared to the one dimensional example. The results which are obtained by Drucker-Prager-like yield criterion including micromorphic terms for this plain strain problem are presented to compare the effect of different number of additional degrees of freedom and the effect of the boundary conditions on the micro-displacement tensor field as well.

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