Thermomechanics of solids with lower-dimensional energetics: On the importance of surface, interface, and curve structures at the nanoscale. A unifying review

Javili, A., McBride, A. and Steinmann, P. (2013) Thermomechanics of solids with lower-dimensional energetics: On the importance of surface, interface, and curve structures at the nanoscale. A unifying review. Applied Mechanics Reviews, 65(1), 010802. (doi:10.1115/1.4023012)

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Abstract

Surfaces and interfaces can significantly influence the overall response of a solid body. Their behavior is well described by continuum theories that endow the surface and interface with their own energetic structures. Such theories are becoming increasingly important when modeling the response of structures at the nanoscale. The objectives of this review are as follows. The first is to summarize the key contributions in the literature. The second is to unify a select subset of these contributions using a systematic and thermodynamically consistent procedure to derive the governing equations. Contributions from the bulk and the lower-dimensional surface, interface, and curve are accounted for. The governing equations describe the fully nonlinear response (geometric and material). Expressions for the energy and entropy flux vectors, and the admissible constraints on the temperature field, all subject to the restriction of non-negative dissipation, are explored. A particular emphasis is placed on the structure of these relations at the interface. A weak formulation of the governing equations is then presented that serves as the basis for their approximation using the finite element method. Various forms for a Helmholtz energy that describes the fully coupled thermomechanical response of the system are given. They include the contribution from surface tension. The vast majority of the literature on surface elasticity is framed in the infinitesimal deformation setting. The finite deformation stress measures are, thus, linearized and the structure of the resulting stresses discussed. The final objective is to elucidate the theory using a series of numerical example problems.

Item Type:Articles
Additional Information:The support of this work by the European Research Council Advanced Grant MOCOPOLY is gratefully acknowledged. The second author thanks the National Research Foundation of South Africa for their support.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Dr Andrew
Authors: Javili, A., McBride, A., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Applied Mechanics Reviews
Publisher:American Society of Mechanical Engineers (ASME)
ISSN:0003-6900
ISSN (Online):1088-8535

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