Arbitrarily explicit/implicit computational procedures for modeling phase evolution

Kaushik Mysore Setty, Purdue University

Abstract

Moving boundary value problems are the crossroads of CAD and Analysis. In these class of problems, boundaries and their motion are of primary interest. Computational approaches that track the motion of such boundaries are either explicit or implicit in nature. Both approaches have their share of advantages and challenges that range from difficulties in inferring exact boundary locations, capturing sharp gradients over small boundary regions to the notion of static-phase-compositions in geometry modeling. Since atomic arrangements near the boundary differ from the interior parts of the domain, boundaries are more sensitive to external stimuli and prone to motion. Naturally, it follows that boundaries are associated with more than just geometric connotations of a lower dimensional entity. Nonetheless, from a completely geometric standpoint, boundary motion plainly brings with it changes to shape and topology of the system. Together, these twin geometric-expressions of moving boundaries form the basis of techniques, algorithms and implementations developed in this thesis. The goals of this thesis are two fold. The primary goal is to develop an explicit/implicit computational procedure for tracking moving boundaries that permits transition from explicit to implicit (and vice-versa) with an arbitrary degree of flexibility. A secondary goal is to develop mechanics formulations for boundary phenomena by considering interplay of multiple physical fields that are defined on both bulk and surfaces of solids. Two applications are demonstrated; the first is evolution of secondary phases during phase coarsening, the second is evolution of voids with applications to electromigration failures observed in microelectronic interconnect structures. Below, specific contributions that are a part of the above overall goals are highlighted. A mathematically and representationally unified procedure for explicit tracking of evolving phase geometries is developed. Boundary sets and connectivity points are formally introduced and the static viewpoint of Constructive Solid Geometry (CSG) modeling is expanded in scope to include dynamic interactions between primitives. Topology changing events such as phase coalescence, separation, pinch-off, nucleation and dissolution in heterogeneous systems are naturally allowed. Isogeometric procedures for boundary phenomena are simultaneously developed. Together, the above techniques enable a better integration of CAD and analysis. A Non-Uniform Rational B-Splines (NURBS) based implicit procedure for tracking moving boundaries is also developed: initialization, solution and updating of order parameters based on a NURBS meshless formulation are demonstrated. Procedures to control sharpness of diffuse boundaries are also discussed. To aid the mechanics formulation of moving boundaries in heterogeneous materials, notion of material mapping is introduced and validated as an alternative to other sharp-interface approaches. A novel sharp-interface formulation involving coupled interactions of displacements, surface energy, lattice diffusion and surface diffusion together with energetic arguments that drive the evolution of void boundaries is developed and demonstrated. The energy arguments are extended to include effects of electric fields on void morphologies. Translation of voids, spade shaped void configurations and interactions of arbitrary shaped voids leading to topological changes are demonstrated. A novel diffuse-interface multi-physics formulation for void evolution involving multiple physical fields is also developed and demonstrated through an implicit procedure.

Degree

Ph.D.

Advisors

Subbarayan, Purdue University.

Subject Area

Mechanical engineering|Packaging|Materials science

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