Daniele Rosato

Modeling and computational analysis of materials exhibiting intrinsic magnetomechanical coupling

This paper is concerned with the development of a finite element model for fully-coupled magnetomechanical boundary value problems, which allows the implementation of nonlinear, anisotropic and hysteretic material models. The formulation is based on a vector-valued magnetic potential and a small strain setting. The derivation of the numerical algorithm is considered in detail. In order to test its implementation the case of piezomagnetism is considered, for which a thermodynamically-consistent formulation is presented. The results of the finite element analysis that have been obtained for two different boundary value problems, which involve the mechanical and magnetic loading of an elastic matrix material with a transversely isotropic piezomagnetic inclusion, are discussed.

A rate-dependent incremental variational formulation of ferroelectricity

The paper presents continuous and discrete variational formulations for the treatment of the non-linear response of piezoceramics under electrical loading. The point of departure is a general internal variable formulation that determines the hysteretic response of the material as a generalized standard medium in terms of an energy storage and a rate-dependent dissipation function. Consistent with this type of standard dissipative continua, we develop an incremental variational formulation of the coupled electromechanical boundary value problem. We specify the variational formulation for a setting based on a smooth rate-dependent dissipation function which governs the hysteretic response. Such a formulation allows us to reproduce the dielectric and butterfly hysteresis responses characteristic of the ferroelectric materials together with their rate-dependency and to account for macroscopically non-uniform distribution of the polarization in the specimen. An important aspect is the numerical implementation of the coupled problem. The discretization of the two-field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of benchmark problems.