Description
Multiferroic magneto-electric polymer composites are an emerging class of smart materials that exhibit strong magneto-electric coupling, making them promising candidates for a wide variety of multifunctional applications. To enable the characterization, design, and optimization of novel smart composites like these, the associated mathematical models must have the breadth to account for complex coupled physics, e.g., three-dimensional thermo-electro-magneto-elastic (TEME) behavior, finite deformations (i.e., geometric nonlinearities), and nonlinear constitutive response (i.e., material nonlinearities). In this discussion, we present a Lagrangian (reference configuration) approach to modeling TEME behavior in the finite-deformation regime. We illustrate the development of the fundamental laws of large-deformation TEME, explicitly showing the progression from postulated statements to pointwise equations. To enable the development of finite-strain TEME constitutive models, we use the formalism of continuum thermodynamics to derive a catalog of Helmholtz-type free energies and their corresponding state equations. The ramifications of invariance, angular momentum, and material symmetry are then explored. Finally, we establish contact with well-known linear theories, such as piezoelectricity, to illustrate the breadth and overarching nature of the proposed nonlinear framework.
Recommended Citation
Lowe, R. (2014). Linear and nonlinear thermo-electro-magneto elasticity. In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.). Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014 , West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014. https://docs.lib.purdue.edu/ses2014/mss/mmms/33
Linear and nonlinear thermo-electro-magneto elasticity
Multiferroic magneto-electric polymer composites are an emerging class of smart materials that exhibit strong magneto-electric coupling, making them promising candidates for a wide variety of multifunctional applications. To enable the characterization, design, and optimization of novel smart composites like these, the associated mathematical models must have the breadth to account for complex coupled physics, e.g., three-dimensional thermo-electro-magneto-elastic (TEME) behavior, finite deformations (i.e., geometric nonlinearities), and nonlinear constitutive response (i.e., material nonlinearities). In this discussion, we present a Lagrangian (reference configuration) approach to modeling TEME behavior in the finite-deformation regime. We illustrate the development of the fundamental laws of large-deformation TEME, explicitly showing the progression from postulated statements to pointwise equations. To enable the development of finite-strain TEME constitutive models, we use the formalism of continuum thermodynamics to derive a catalog of Helmholtz-type free energies and their corresponding state equations. The ramifications of invariance, angular momentum, and material symmetry are then explored. Finally, we establish contact with well-known linear theories, such as piezoelectricity, to illustrate the breadth and overarching nature of the proposed nonlinear framework.