On the magneto-mechanical response of piezomagnetic microbeam with size effects

Abstract

Classical piezomagnetic elasticity theory fails to explain the size-dependent magneto-mechanical behaviour. The extended piezomagnetic elasticity theory incorporating the strain gradient elasticity and flexomagneticity is developed to describe the size effects phenomenon. Compared with the flexomagneticity whose contribution is explicit, the influence mechanism of strain gradient elasticity on the magneto-mechanical response is not clarified. In this paper, we clarify the relation and difference among the extended piezomagnetic elasticity theory considering different strain gradient elasticity. For the relation analysis, according to the orthogonal decomposition of the general strain gradient elasticity, we express the extended piezomagnetic elasticity theory in form of strain gradient tensor and its components of symmetric/anti-symmetric splitting, respectively. By ignoring some strain gradients, the extended piezomagnetic elasticity theory with the general strain gradient elasticity can reduce to that with the reduced strain gradient elasticity. For the difference analysis, we perform the magneto-mechanical analysis of the Terfenol-D/Silicon bilayer microbeam. The flexomagnetic coefficient of Terfenol-D is obtained by fitting deflection solution with experiment results. Then, the size-dependent direct/inverse magneto-mechanical behaviour is revealed. Results reveal that the strain gradient effects and flexomagnetic effects significantly affect the magnetic potential and bending defection when the beam thickness is comparable to the material length-scale parameters. Moreover, compared with the extended piezomagnetic elasticity theory with the reduced strain gradient elasticity, the extended piezomagnetic elasticity theory with the general strain gradient elasticity predicts smaller magnetic potential, bending deflection, and thus can describe the magneto-mechanical behaviour more appropriately.