Topological sensitivity analysis for a two-parameter Mooney-Rivlin hyperelastic constitutive model

Abstract

The Topological Sensitivity Analysis (TSA) is represented by a scalar function, called Topological Derivative (TD), that gives for each point of the domain the sensitivity of a given cost function when an infinitesimal hole is created. Applications to the Laplace, Poisson, Helmoltz, Navier, Stokes and Navier-Stokes equations can be found in the literature. In the present work, an approximated TD expression applied to nonlinear hyperelasticity using the two parameter Mooney-Rivlin constitutive model is obtained by a numerical asymptotic analysis. The cost function is the total potential energy functional. The weak form of state equation is the constraint and the total Lagrangian formulation used. Numerical results of the presented approach are considered for hyperelastic plane problems.

Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel

“…(1) Material parameters of rubber C 10 , C 01 . The constitutive model used in this paper is the Mooney-Rivlin two-parameter model [13]. The model can describe the deformation characteristics of rubber materials in 150%.…”

On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material

“…Different strain energy functions are used to model hyperelastic behavior of these materials and there are numerous efforts in the literature on the derivation and/or fitting of various forms of strainenergy functions, such as works of Mooney (1940), Blatz and Ko (1962), Yeoh (1993), Ogden (1972), Beatty (1987). Presenting precise constitutive model to describe hyperelastic behavior of rubber like material is the subject of a lot of researches in the recent years such as works by Anani and Alizadeh (2011), Bao et al (2003), Silva and Bittencourt (2008), Pereira and Bittencourt (2010), Pascon and Coda (2013), Coelho et al (2014), Santos et al (2015), Tomita et al (2008) and Barforooshi and Mohammadi (2016) As functionally graded rubber is the subject of this study it should be noted that graded rubber like materials were created by Ikeda et al (1998) in the laboratory for the first time, a while after these materials have attracted the attention of investigators for modeling these materials behavior under mechanical and geometrical boundary conditions. Some important and novel researches about analysis of inhomogeneous rubber like materials structures are presented in details by Bilgili (2003Bilgili ( ,2004, Batra (2006), Batra and Bahrami (2009), Rahimi (2015,2016).…”

Predicting the dynamic material constants of Mooney-Rivlin model in broad frequency range for elastomeric components

“…Silva and Bittencourt (2008) used Mooney-Rivlin hyperelastic model in shape optimization of elastomeric media of an engine mount. Pereira and Bittencourt (2010) used the 2 parameter Mooney-Rivlin constitutive model in topological sensitivity analysis. Pearson and Pickering (2001) obtained the constants of Mooney-Rivlin model using axial tensile test and showed that using these constants, the static behavior of the elastomeric material is predicted well.…”