Browsing by Author "Rosato, Daniele"

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Open Access
On the formulation and numerical implementation of dissipative electro-mechanics at large strains
(2010) Rosato, Daniele; Miehe, Christian (Prof. Dr.-Ing. habil.)
In recent years an increasing interest in functional materials such as erroelectric polymers and ceramics has been shown. For those materials, viscous effects or electric polarizations cause hysteresis phenomena accompanied with possibly large remanent strains and rotations. In this work aspects of the formulation and numerical implementation of dissipative electro-mechanics at large strains are outlined. In particular continuous and discrete variational formulations for the treatment of the non-linear dissipative response of electro-mechanical solids are developed and these formulations are adapted to the modeling of the hysteretic material response of piezoceramics and ferroelectric polymers 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, an incremental variational formulation of the coupled electro-mechanical boundary-value-problem is developed. The variational formulation for a setting based on a smooth rate-dependent dissipation function which governs the hysteretic response is specified. Further, the geometric nature of dissipative electro-mechanics is underlined. 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 and very compact format. Further, constitutive assumptions which account for specific problems arising in the geometric nonlinear setting are discussed. With regard to the choice of the internal variables entering the constitutive functions, a critical point are the kinematic assumptions. Here, the multiplicative decomposition of the local deformation gradient into reversible and remanent parts as well as the introduction of a remanent metric are discussed. 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 together with large attained deformations. The performance of the proposed methods is demonstrated by means of a spectrum of benchmark problems which eventually show large deformations.