Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers

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• 作者：Ravi Kiran (1)
  Kapil Khandelwal (1)
  
  1. Department of Civil and Environmental Engineering and Earth Sciences ; University of Notre Dame ; Notre Dame ; IN ; 46556 ; USA
  
• 关键词：Hyper ; dual numbers ; Anisotropic hyperelastic models ; Automatic implementation ; Finite difference methods ; Constitutive modeling
• 刊名：Computational Mechanics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：55
• 期：1
• 页码：229-248
• 全文大小：1,247 KB
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• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

The main aim of this paper is to automate the implementation of finite strain anisotropic hyperelastic models into a general finite element framework. The automation presented in this paper enables the end-user to implement a hyperelastic model by programming its Helmholtz free energy function alone. The automation is achieved by employing hyper-dual number system to evaluate analytical quality derivatives. New perturbation techniques are introduced and are employed to extend the hyper-dual numbers system to evaluate tensor derivatives. The capability of the proposed automation scheme is demonstrated by implementing five finite strain anisotropic hyperelastic models. The merits and demerits of the proposed automation scheme are compared to an automation scheme based on the central difference method.