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Constitutive Modeling of Magnetostrictive Materials


Constitutive Modelling of Smart Materials

  1. Srinivasan Gopalakrishnan

Published Online: 15 SEP 2009

DOI: 10.1002/9780470061626.shm061

Encyclopedia of Structural Health Monitoring

Encyclopedia of Structural Health Monitoring

How to Cite

Gopalakrishnan, S. 2009. Constitutive Modeling of Magnetostrictive Materials. Encyclopedia of Structural Health Monitoring. .

Author Information

  1. Indian Institute of Science, Department of Aerospace Engineering, Bangalore, India

Publication History

  1. Published Online: 15 SEP 2009


The constitutive model for a magnetostrictive material is presented in this article. An example of a magnetostrictive material is Terfenol-D. Like the piezoelectric material, this material has two constitutive laws, one of which is the sensing law and the other the actuation law, both of which are highly coupled and nonlinear. For the purpose of analysis, the constitutive laws can be characterized as coupled or uncoupled and linear or nonlinear. The coupled model is studied without assuming any explicit direct relationship with the magnetic field. In the linear-coupled model, which is assumed to preserve the magnetic flux line continuity, the elastic modulus, the permeability, and magnetoelastic constant are assumed as constant. In the nonlinear-coupled model, the nonlinearity is decoupled and solved separately for the magnetic domain and the mechanical domain using two nonlinear curves, namely, the stress versus strain curve and the magnetic flux density versus magnetic field curve. This is performed by two different methods. In the first, the magnetic flux density is computed iteratively, while in the second, the artificial neural network is used, wherein the trained network gives the necessary strain and magnetic flux density for a given magnetic field and stress level. The effect of nonlinearity is demonstrated on a simple magnetostrictive rod.


  • magnetostrictive materials;
  • Terfenol-D;
  • magnetic flux density;
  • magnetostriction and constitutive laws