Announced 9 days in advance of the defense date with CEE Graduate Committee and Institute approval.

School of Civil and Environmental Engineering

Ph.D. Thesis Defense Announcement

Nonlinear Mechanics of Phase Change-Induced Accretion-Ablation

By Satya Prakash Pradhan

Advisor:

Dr. Arash Yavari (CEE)

Committee Members:  Dr. Phanish Suryanarayana (CEE), Dr. Aditya Kumar (CEE), Dr. Francesco Fedele (CEE),
Dr. Hamid Garmestani (MSE)

Date and Time:  March 22, 12:00 PM

Location: SEB 122

A geometric accretion-ablation theory is formulated in this thesis to study the mechanics of deformable bodies subjected to simultaneous addition and removal of material on different portions of their boundaries, all while undergoing large deformations. Using this theory, first the following two problems are studied: (i) A hollow cylindrical bar subjected to finite extension that undergoes simultaneous outer boundary accretion and inner boundary ablation, and (ii) an accreting bar subjected to finite torsion.  These two examples assume constant accretion and ablation velocities. However, in solidification processes common in biological and industrial applications, accretion/ablation velocities are time dependent. Examination of stress fields during solidification is crucial for managing potential mechanical instabilities and damage. Such modeling is vital in manufacturing, where molten materials solidify, causing substantial temperature drops leading to part distortion, loss of geometric tolerance, and high residual stresses. This thesis further contributes by modeling solidification with thermoelastic accretion, aiming to evaluate potential damage and failures like layer delamination and crack formation. The modeling of phase change-induced accretion is a challenging mathematical problem as it involves an evolving domain. The motion of the unknown phase boundary is correlated with the jump in heat flux (the Stefan's condition). Since the body is growing, the reference configuration --crucial for studying stresses and strains --is a priori unknown. The reference configuration is modeled as a time-dependent Riemannian manifold with a metric that explicitly depends on the instantaneous deformation state during attachment. The governing equations --a system of nonlinear partial differential equations over an evolving domain --are analyzed for inward solidification in a spherical container. Extensive parametric studies are conducted to match results with both experimental and numerical studies in the literature.