Surface magnetoelasticity theory

The boundary surface of a body behaves differently from its bulk. The elastic response of a boundary surface can be studied by the surface elasticity theory. Furthermore, it has been observed experimentally that the strength and direction of magnetization are markedly different between the boundary surface and the bulk. While the surface elasticity theory is well established today to study the mechanical behavior of nanomaterials, a theory to model boundary surface magnetic behavior is missing. The objective of this presentation was to study, from a phenomenological point of view, the magnetomechanical response of materials accounting for boundary surfaces contributions. To do so, the boundary surface of a body is endowed with its own mechanical and magnetic constitutive behavior in the spirit of the surface elasticity theory. The magnetomechanical response of materials is formulated in a thermodynamically consistent manner using both a variational framework and the governing equations of magnetomechanics, namely the Maxwell laws, the balance of linear and angular momentum, the balance of energy and the (in-)balance of entropy. Conceptually speaking, this contribution can be understood as an extension of the surface elasticity theory to the more general case of magnetoelasticity that, however, involves certain additional complexities due to the presence of a surface curl operator, which is not standard.