Back to Departmental Colloquium: Fall 1999
Departmental Colloquium
Date: Thursday, Dec 9, 1999
Time: 4:15PM
Location: JWB 335
Liliana Borcea
Rice
Title |
On the magneto-elastic properties of elastomer-ferromagnet composites |
Abstract |
Work in collaboration with Oscar Bruno (CalTech). We study the macroscopic, mechanical behavior of composite materials consisting of many rigid, magnetically permeable, spherical inclusions embedded firmly in an isotropic, non-magnetic, continuous matrix. Such composites belong to a class of materials called magneto-rheological (MR) solids. The inclusions in MR solids are typically micron size iron, or iron based alloy (carbonyl-iron, iron-cobalt, etc.) particles. These particles are suspended in a non-magnetic elastomer like rubber, polymer gell, etc. Upon application of a magnetic field, the rheological properties of MR materials are rapidly and reversibly altered. The mechanism responsible for this bulk effect is the induced magnetic interaction between ferromagnetic particles in the composite. We consider the coupled elastic and magnetic problem in MR solids. We give a general framework for calculation of bulk properties of MR solids with randomly distributed ferromagnetic particles in volume fraction $\Phi$. For small volume fractions, we calculate the average stress-strain law in elastomer-ferromagnet composites, correct to order $\Phi^2$, by considering both elastic and magnetic interactions between pairs of particles. We show that, due to induced magnetic interactions, the bulk properties of the composite are altered significantly. Specifically, we show that the average strain depends on the elastic properties of the elastic matrix, the volume fraction $\Phi$ and the external magnetic field H _0. The average strain depends on the surface tractions, as well. However, this dependence is not a simple one, as in the problem of pure elasticity. We show that, for a free boundary (no surface tractions), magnetic interactions in the composite cause the material to self-deform. Depending on the softness of the matrix, the volume fraction and the strength of the external magnetic field, this deformation can be quite significant, as high as 10%. Furthermore, the deformation consists of an overall compression, although the average strain in the direction of the external magnetic field is different than the strain in directions orthogonal to H _0. We also show that, for nonzero surface tractions, the response of the composite depends strongly on the strength of the external magnetic field. |
Mathematical Biology
Data Science and Machine Learning