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Mathematical models of irreversible processes of polarization

发布时间: 2009-08-14 09:05 | 【 【打印】【关闭】

SEMINAR

The key laboratory of
Inorganic Functional Materials and Integerated Devices
Shanghai Institute of Ceramics, Chinese Academy of Sciences

中国科学院上海硅酸盐研究所功能材料与集成器件重点实验室
2009年学术讲座


Mathematical models of irreversible processes of polarization

Speaker
Prof. Alexander S. Skaliukh

时间:2009年08月17日(星期一)上午09:30
地点: 4 号楼 14楼 第一会议室

邀请人: 李国荣  研究员
     殷庆瑞  研究员

ABSTRACT: The mathematical model of polarization polycrystalline ferroelectrics materials (ceramics) in strong electric and mechanical fields is constructed. Use of a method of increments allows carrying out integration on time, and the method of finite elements allows doing the integrating on coordinates. For closing of a problem it is necessary introduce constitutive equations. With this purpose there was used various elementary models and approaches, for example, a method of switching of domains, method Preisach, method Jile-Atherton, methods of the mathematical theory of plasticity. The most effective in practical using was method Jile-Atherton which has been developed for ferromagnetic, but has been transferred for ferroelectricity by authors Smith, Hom, Ounaies and others. Essential generalization of this method was its carrying on a three-dimensional case. Theorems of symmetry of instant dielectrics modules are proved. These theorems have allowed the obtained system of constitutive relations in the form of the partial differential equations to reduce to system of the ordinary differential equations. The obtained differential operators are hysteresis’s operators. Therefore for any increments of an electric field, we obtain corresponding increments of full polarization. This constitutive equation close mathematical statement of a problem, and allow calculating any field of residual polarization for any volume and any form of the applying of electric and mechanical loadings.