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Modeling of visco-hyperelastic behavior of foams

Anani, Y ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1115/IMECE2008-66773
  3. Publisher: 2009
  4. Abstract:
  5. In this paper, a new visco-hyperelastic constitutive law for describing the rate dependent behavior of foams is proposed. The proposed model was based on a phenomenological Zener model: a hyperelastic equilibrium spring, which describes the steady-state, long-term response, parallel to a Maxwell element, which captures the rate-dependency. A nonlinear viscous damper connected in series to a hyperelastic intermediate spring, controls the rate-dependency of the Maxwell element. Therefore, the stress is the sum of equilibrium stress on the equilibrium spring and overstress on the intermediate spring. In hyperelastic theory stress is not calculated directly as in the case of small-strain, linear elastic materials. Instead, stresses are derived from the principle of virtual work using the stored strain energy potential function. In addition, foams are compressible, therefore classic strain energy functions such as the Ogden strain energy function or the Mooney-Rivlin strain energy function are not suitable to describe hyperelastic behavior of foams. So, strain energy functions must include the effect of compressibility. That means the third principal invariant of the deformation gradient tensor F should enter in strain energy functions. For rate-dependent behavior of foams, history integral constitutive law is used. For the equilibrium spring and the intermediate spring, the same strain energy function is employed. In order to use this stain energy function in history integral equation, the kernel function of it is calculated. The effect of compressibility is considered in rate-dependent behavior of foams too. All material constants were obtained from the results of uniaxial tensile tests. Nonlinear regulation was used to find these constants. In these calculations, Average strain rate was employed to find material constants. Copyright © 2008 by ASME
  6. Keywords:
  7. Foams ; Average strain rate ; Compressible materials ; Constitutive law ; Deformation gradient tensors ; Energy functions ; Equilibrium stress ; Hyper elastic ; Hyperelastic behavior ; Hyperelastic theory ; Kernel function ; Large deformation ; Linear elastic material ; Material constant ; Maxwell element ; Nonlinear regulation ; Nonlinear viscous dampers ; Ogden strain energy ; Overstresses ; Principal invariants ; Principle of virtual work ; Rate dependency ; Rate dependent ; Strain energy functions ; Uniaxial tensile test ; Visco-hyperelstic ; Zener model ; Compressibility ; Deformation ; Materials ; Maxwell equations ; Mechanical engineering ; Rate constants ; Strain energy ; Tensile testing ; Strain rate
  8. Source: 2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008, Boston, MA, 31 October 2008 through 6 November 2008 ; Volume 12 , 2009 , Pages 425-433 ; 9780791848739 (ISBN)
  9. URL: https://asmedigitalcollection.asme.org/IMECE/proceedings-abstract/IMECE2008/48739/425/337727