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.

A comprehensive overview is given of the literature on slip transmission criteria for grain boundaries in metals, with a focus on slip system and grain boundary orientation. Much of this extensive literature has been informed by experimental investigations. The use of geometric criteria in continuum crystal plasticity models is discussed. The theoretical framework of Gurtin (2008, J. Mech. Phys. Solids 56, p. 640) is reviewed for the single slip case. This highlights the connections to slip transmission criteria from the literature that are not discussed in the work itself. Different geometric criteria are compared for the single slip case with regard to their prediction of slip transmission. Perspectives on additional criteria, investigated in experiments and used in computational simulations, are given.

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(2016) Computational electro-and magneto-elasticity for quasi-incompressible media immersed in free space. International Journal for Numerical Methods in Engineering, 108(11), pp. 1307-1342.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. This is the peer reviewed version of the following article: Pelteret, J. SUMMARYIn this work a mixed variational formulation to simulate quasi-incompressible electro-or magnetoactive polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media.