Abstract
When the interfacial energy is a nonconvex function of orientation, the anisotropic-curvature-flow equation becomes backward parabolic. To overcome the instability thus generated, a regularization of the equation that governs the evolution of the interface is needed. In this paper we develop a regularized theory of curvature flow in three dimensions that incorporates surface diffusion and bulk-surface interactions. The theory is based on a superficial mass balance; configurational forces and couples consistent with superficial force and moment balances; a mechanical version of the second law that includes, via the configurational moments, work that accompanies changes in the curvature of the interface; a constitutive theory whose main ingredient is a positive-definite, isotropic, quadratic dependence of the interfacial energy on the curvature tensor. Two special cases are investigated: (i) the interface is a boundary between bulk phases or grains, and (ii) the interface separates an elastic thin film bonded to a rigid substrate from a vapor phase whose sole action is the deposition of atoms on the surface.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Accepted November 21, 2001¶Published online June 4, 2002
Rights and permissions
About this article
Cite this article
Gurtin, M., Jabbour, M. Interface Evolution in Three Dimensions¶with Curvature-Dependent Energy¶and Surface Diffusion:¶Interface-Controlled Evolution, Phase Transitions, Epitaxial Growth of Elastic Films. Arch. Rational Mech. Anal. 163, 171–208 (2002). https://doi.org/10.1007/s002050200193
Issue Date:
DOI: https://doi.org/10.1007/s002050200193