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Title: Finite Element Formulation of Internally Balanced Blatz Ko Material Model
Authors: Hadoush, Ashraf
Keywords: Hypereleacticty;internal balance;finite element
Issue Date: 28-Jun-2020
Publisher: Hashemite University
Citation: A. hadoush (2020), Finite Element Formulation of Internally Balanced Blatz Ko Material Model, JJMIE, vol.14:2, 215-221.
Series/Report no.: Jordan Journal of Mechanical and Industrial Engineering;
Abstract: Material constitutive models often include internal variables in order to capture realistic mechanical effects such as viscosity. Recent work for compressible hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. The finite element formulation for this new treatment is developed, however, the implementation sheds light on a special form of constitutive model. In particular, the material model is a function of the first and third invariants of new quantities derived from the counterparts of the multiplicative decomposition. These new quantities are defined in analogy to the right Cauchy Green tensor. This work demonstrates the required treatment for a special material model that is formulated using the second and third principal invariants of these new derived quantities. Mainly, the treatment simplifies the internal balance equation that emerges from the variational treatment. This facilitates the linearization procedure of this new formulation for internally balanced compressible hyperelastic material. The present work permits the future use of more complicated internally balanced hyperelastic models.
Description: In this work a finite element treatment is demonstrated for a material model based on new theory that applies argument of variation to both counterparts of deformation gradient multiplicative decomposition. The use of Cayley Hamilton equation facilitates significantly the implementation of internally balanced material model. The response of the material model is examined in uniaxial loading and simple shear. The internally balanced theory retrieves the conventional hyperelastic theory in the special limiting case. The uniaxial stress for internally balanced material has a stiffer response compared with hyperelastic uniaxial stress up to significant value of stretching when it reaches maximum value then it shows softening behavior. For simple shear, the internally balanced shear stress shows softer response and reaches an asymptotic value in contrast with unbounded increases of hyperelastic shear stress. The presented treatment complements previous formulation [21] and it allows the use of complicated material models.
ISSN: 1995-6665
Appears in Collections:Engineering and Technology Faculty

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