On the Modelling and Computation of Magneto-Sensitive-Elastomers

磁敏弹性体是一种智能材料，它是由填充有磁活性粒子的类橡胶基基体组成的。由于橡胶类材料的高弹性，这些化合物能够在外加磁场的作用下显著变形，即几何非线性变形。快速响应，可以实现的高水平变形，以及通过改变外部磁场控制这些变形的可能性，使这些材料特别有趣；例如，用于抑制振动和噪声。因此，迫切需要在几何非线性连续体物理的框架内对这类新型材料进行建模研究，并在合适的计算方法领域进行研究，以模拟技术上相关的基准问题。本文的主要目标有三个：(i)讨论和制定磁弹性耦合问题的适当边界条件，特别是正确认识磁场对力学边界条件的影响；（ii）本构方程的简单和现实形式的发展，尊重微观结构特征，包括对椭圆性（或无穷小秩一凸性）条件的仔细分析；最后，最重要的目标是（iii）利用新发展的有限元方法解决相关的非线性边值问题。

Magneto-sensitive-elastomers are smart materials which are composed of a rubber-like basis matrix filled with magneto-active particles. Due to the highly elastic properties of the rubberlike material, these compounds are able to deform significantly, i.e. geometrically non-linearly by the application of external magnetic fields. The rapid response, the high level of deformations that may be achieved, and the possibility of controlling these deformations by varying an external magnetic field, make these materials of special interest; e.g., for vibration and noise suppression. Thus, there is an urgent need for research on this novel material class in terms of modelling within the framework of geometrically nonlinear continuum physics and in the area of suitable computational methods in order to simulate technologically relevant benchmark problems. In this proposal, three main objectives are pursued: (i) the discussion and formulation of appropriate boundary conditions for the coupled magneto-elastic problem, in particular the correct acknowledgement of the influence of the magnetic field on the mechanical boundary conditions; (ii) the development of simple and at the same time realistic forms for the constitutive equations, respecting the microstructural features and including a careful analysis of the ellipticity (or infinitesimal rank-one convexity) condition; and, finally, an objective of utmost importance is (iii) to solve relevant nonlinear boundary value problems by resorting to a newly developed finite element method.