An energy formulation of continuum magneto-electro-elasticity with applications |
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Affiliation: | 1. Graduate School at Shenzhen, Harbin Institute of Technology, Harbin 150001, PR China;2. Centre for Infrastructure Engineering, School of Computing, Engineering and Mathematics, Western Sydney University, Penrith, NSW 2751, Australia |
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Abstract: | We present an energy formulation of continuum electro-elasticity and magneto-electro-elasticity. Based on the principle of minimum free energy, we propose a form of total free energy of the system in three dimensions, and then systematically derive the theories for a hierarchy of materials including dielectric elastomers, piezoelectric ceramics, ferroelectrics, flexoelectric materials, magnetic elastomers, magnetoelectric materials, piezo-electric–magnetic materials among others. The effects of mechanical, electrical and magnetic boundary devices, external charges, polarizations and magnetization are taken into account in formulating the free energy. The linear and nonlinear boundary value problems governing these materials are explicitly derived as the Euler–Lagrange equations of the principle of minimum free energy. Finally, we illustrate the applications of the formulations by presenting solutions to a few simple problems and give an outlook of potential applications. |
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Keywords: | Continuum mechanics Energy formulation Magneto-electro-elastic coupling |
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