Publication 26-CNA-004

Stress Asymmetry in Hard Magnetic Soft Materials

H. Gökçen Güner
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
hguner@andrew.cmu.edu

Francois Barthelat
Department of Mechanical Engineering
University of Colorado

John D. Clayton
Terminal Effects Division
DEVCOM Army Research Laboratory

Carlos Mora-Corral
Departamento de Matemáticas
Universidad Autonóma de Madrid
Madrid, Spain

Noel J. Walkington
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
noelw@andrew.cmu.edu

Kaushik Dayal
Department of Civil and Environmental Engineering
Center for Nonlinear Analysis
Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik.Dayal@cmu.edu

Abstract: Hard magnetic soft materials – soft polymers embedded with hard magnetic particles – are modeled using continuum magnetomechanical formulations in which the deformation and the magnetization field are the primary kinematic variables. A recent question in such formulations is whether the Cauchy stress is symmetric, which is directly related to frame invariance and angular momentum balance. This note discusses energetically equivalent formulations, related by a change of variables between referential and current descriptions of the magnetization, and shows that they generally yield different Cauchy stresses, including a change in their symmetry. Specifically, the formulation based on a referential magnetization produces a symmetric Cauchy stress, while that based on a current magnetization generally yields an asymmetric Cauchy stress. We highlight that when the internal variable (magnetization field) is at the energy-minimizing equilibrium configuration, the divergences of these stresses are the same, and both stresses are symmetric.

Get the paper in its entirety as  26-CNA-004.pdf

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