Nonlinear theory of magnetoelasticity

At Tufts University, Professor Luis Dorfmann studies mathematical models of material behavior and the biomechanics of soft materials in the Department of Civil and Environmental Engineering. Much of Dorfmann’s work with frequent collaborator Professor Ray W. Ogden of the University of Glasgow has focused on magnetoelasticity: the change in magnetic properties that occurs when mechanical stress is placed on a material.

In 2004, Dorfmann and Ogden published a seminal paper combining the theory of electromagnetism with the field of nonlinear mechanics. They proposed using a magnetic field to induce and control large deformations in soft magneto-sensitive materials – an innovation with potential applications in soft robotics, MRI technology, and more. The pair continued to conduct research in related fields, publishing highly-cited papers over the years on nonlinear electroelasticity, a constitutive model for the Mullins effect, and magnetoelastic modeling of elastomers. 

This year, the Royal Society of London invited Dorfmann and Ogden to produce a review paper on the subject of the nonlinear theory of magnetoelasticity. Published in the October 2023 edition of the journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, the paper summarizes the history of the field and prominent discoveries in it, and addresses the role of the Maxwell stress tensor. The Maxwell stress tensor stands for the interaction between mechanical momentum and electromagnetic forces. While the Maxwell stress tensor is important in modeling magnetoactive devices, its use can be controversial in the field of magnetoelasticity. In their review paper, Dorfmann and Ogden paid particular attention to the role of the Maxwell stress.

For more than 350 years, the Royal Society has published scientific articles in publications like the Philosophical Transactions. The journal Proceedings of the Royal Society of London launched in 1831 before splitting into Proceedings of the Royal Society A and B in 1905. Proceedings A publishes leading research in the chemical computational, Earth, engineering, mathematical, and physical sciences.

Learn more in The nonlinear theory of magnetoelasticity and the role of the Maxwell stress: a review, by Luis Dorfmann and Ray W. Ogden.