Bustamante R, Rajagopal K R
Departamento de Ingeniería Mecánica , Universidad de Chile , Beaucheff 850, Santiago Centro, Santiago, Chile.
Department of Mechanical Engineering , University of Texas A&M , College Station, TX, USA.
Proc Math Phys Eng Sci. 2015 Mar 8;471(2175):20140959. doi: 10.1098/rspa.2014.0959.
Implicit constitutive relations that characterize the response of elastic bodies have greatly enhanced the arsenal available at the disposal of the analyst working in the field of elasticity. This class of models were recently extended to describe electroelastic bodies by the present authors. In this paper, we extend the development of implicit constitutive relations to describe the behaviour of elastic bodies that respond to magnetic stimuli. The models that are developed provide a rational way to describe phenomena that have hitherto not been adequately described by the classical models that are in place. After developing implicit constitutive relations for magnetoelastic bodies undergoing large deformations, we consider the linearization of the models within the context of small displacement gradients. We then use the linearized model to describe experimentally observed phenomena which the classical linearized magnetoelastic models are incapable of doing. We also solve several boundary value problems within the context of the models that are developed: extension and shear of a slab, and radial inflation and extension of a cylinder.
描述弹性体响应的隐式本构关系极大地丰富了弹性领域分析人员可用的方法。最近，本文作者将这类模型扩展到描述电弹性体。在本文中，我们将隐式本构关系的发展扩展到描述对磁刺激有响应的弹性体的行为。所开发的模型提供了一种合理的方式来描述迄今经典模型尚未充分描述的现象。在为经历大变形的磁弹性体建立隐式本构关系之后，我们考虑在小位移梯度的背景下对模型进行线性化。然后，我们使用线性化模型来描述经典线性化磁弹性模型无法描述的实验观察到的现象。我们还在开发的模型框架内解决了几个边值问题：平板的拉伸和剪切，以及圆柱的径向膨胀和拉伸。
