TY - JOUR
T1 - Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag
AU - Epshteyn, Yekaterina
AU - Liu, Chun
AU - Mizuno, Masashi
N1 - Funding Information:
∗Received by the editors June 3, 2019; accepted for publication (in revised form) March 1, 2021; published electronically May 25, 2021. https://doi.org/10.1137/19M1265855 Funding: The work of the first author was partially supported by National Science Foundation grant DMS-1905463. The work of the first and third authors was partially supported by Simons Foundation grant 415673. The work of the second author was partially supported by National Science Foundation grants DMS-1759535 and DMS-1759536. The work of the third author was partially supported by JSPS KAKENHI grant 18K13446. †Department of Mathematics, University of Utah, Salt Lake City, UT 84112 USA (epshteyn@math.utah.edu). ‡Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616 USA (cliu124@iit.edu). §Department of Mathematics, College of Science and Technology, Nihon University, Tokyo 101-8308, Japan (mizuno@math.cst.nihon-u.ac.jp).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics
PY - 2021
Y1 - 2021
N2 - Most technologically useful materials are polycrystalline microstructures composed of myriad small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this work, we propose a model for the evolution of the grain boundary network with dynamic boundary conditions at the triple junctions, with triple junctions drag, and with dynamic lattice misorientations. Using the energetic variational approach, we derive system of geometric differential equations to describe motion of such grain boundaries. Next, we relax the curvature effect of the grain boundaries to isolate the effect of the dynamics of lattice misorientations and triple junctions drag, and we establish local well-posedness result for the considered model.
AB - Most technologically useful materials are polycrystalline microstructures composed of myriad small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this work, we propose a model for the evolution of the grain boundary network with dynamic boundary conditions at the triple junctions, with triple junctions drag, and with dynamic lattice misorientations. Using the energetic variational approach, we derive system of geometric differential equations to describe motion of such grain boundaries. Next, we relax the curvature effect of the grain boundaries to isolate the effect of the dynamics of lattice misorientations and triple junctions drag, and we establish local well-posedness result for the considered model.
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U2 - 10.1137/19M1265855
DO - 10.1137/19M1265855
M3 - Article
AN - SCOPUS:85107462576
SN - 0036-1410
VL - 53
SP - 3072
EP - 3097
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 3
ER -