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| Parametrical variational principle and its application to a class of ferro-electric models |
| Revised:October 15, 2004 |
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| DOI：10.7511/jslx20063049 |
| KeyWord:ferro-electrics,parametrical variational principle,quadratic programming,finite element, |
| HUANG Ruo-yu WU Chang-chun |
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| Abstract: |
| For the high complexity of the constitutive models of ferro-electrics,the efficiency and stability of the numerical methods must be paid full attention to when simulating the electro-mechanical behavior of ferro-electrics.The present work introduces the parametrical variational principle into the computation of ferroelectrics.A parametrical variational principle based on the Helmholtz free energy is established for a class of multi-axial phenomeno-logical ferro-electric constitutive models which adopts the basic concepts and theoretical framework of the traditional elasto-plasticity.The variational principle can effectively deal with the difficulty of non-symmetric tangent moduli which appears when the non-associated flow law or the yield-liked switching surface without considering the change of material moduli with domain switching is used.Corresponding parametric quadratic programming algorithm is introduced to present a new numerical scheme with reliable numerical stability.Applying the present numerical scheme on a typical ferro-electric constitutive model,the numerical results of the simulation of the hysteresis loop and the butterfly-shaped loop show the good performance of the present method. |
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