Publication 17-CNA-014
Finite element approximation of the fields of bulk and interfacial line defects
Chiqun Zhang
Carnegie Mellon University
Pittsburgh, PA 15213
Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu
Saurabh Puri
Microstructure Engineering
Portland, OR 97208
Abstract: A generalized disclination (g.disclination) theory [AF15] has been recently introduced that goes
beyond treating standard translational and rotational Volterra defects in a continuously distributed
defects approach; it is capable of treating the kinematics and dynamics of terminating
lines of elastic strain and rotation discontinuities. In this work, a numerical method is developed
to solve for the stress and distortion fields of g.disclination systems. Problems of small and
finite deformation theory are considered. The fields of a single disclination, a single dislocation
treated as a disclination dipole, a tilt grain boundary, a misfitting grain boundary with disconnections,
a through twin boundary, a terminating twin boundary, a through grain boundary, a
star disclination/penta-twin, a disclination loop (with twist and wedge segments), and a plate,
a lenticular, and a needle inclusion are approximated. It is demonstrated that while the far-field
topological identity of a dislocation of appropriate strength and a disclination-dipole plus a slip
dislocation comprising a disconnection are the same, the latter microstructure is energetically
favorable. This underscores the complementary importance of all of topology, geometry, and energetics
in understanding defect mechanics. It is established that finite element approximations
of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner,
thus contributing to the study of intricate defect microstructures in the scientific understanding
and predictive design of materials. Our work also represents one systematic way of studying the
interaction of (g.)disclinations and dislocations as topological defects, a subject of considerable
subtlety and conceptual importance [Mer79, AMK17].
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