Force response of a magnetoactive elastomer: the effect of surface roughness of the sample
DOI:
https://doi.org/10.7242/1999-6691/2026.19.3.27Keywords:
magnetoactive elastomer, magnetostriction, magnetoelasticity, roughness of the surface, finite-element method, package FEniCSxAbstract
The article investigates the action of the force exerted by the end wall of a cylindrical sample made of a magnetoactive elastomer (MAE) and subjected to a uniform axial field on the quiescent plate of the measuring cell, i.e., the magnetostriction effect under isometric conditions. Unlike the idealization accepted by default in the majority of experiment interpretations, the end wall of the sample is assumed to be non-flat: it represents a periodic sequence of $n$ concentric humps with hemispherical tops from which a horizontal plane cuts off the segments of height $\delta$. By varying $\delta$ it is possible to continuously change the nature of contact between the sample and the plate from the point contact to the full contact, while varying $n$ changes the depth of the surface relief. The problem is solved in the framework of continuum magnetoelasticity by the finite-element method; the force is evaluated as a finite-difference derivative of the full energy of the system with respect to the end wall shift. It is shown that, provided the surface is rough, the measured force is always underestimated in comparison with its value for the perfectly flat end wall. Notably, the magnitude of this force reduction is determined not only by the fraction of contact area but also by the characteristic scale of the surface roughness: at a fixed percentage of the contact area, the reduction of the size of the humps brings the force closer to the “flat” limit. The consequences of the sample compression prior to its magnetization are analyzed from the viewpoint of enlarging the contact area in order that the results of measurements approach the “flat” limit. It is found that moderate compression is rather effective for increasing the measurement accuracy, whereas strong compression has an ill-effect on the accuracy. The data obtained with numerical modeling have been used to work out recommendations for the proper implementation of isometric magnetomechanical experiments on MAEs.
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