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

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 a...

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Bibliographic Details
Published in:Latin American journal of solids and structures 2010, Vol.7 (4), p.391-411
Main Authors: Pereira, Carlos E. L., Bittencourt, Marco L.
Format: Article
Language:English
Subjects:
ENGINEERING, CIVIL
ENGINEERING, MECHANICAL
Finite Elements
Hyperelasticity
MECHANICS
Nonlinear Elasticity
Topological Derivative
Topological Optimization
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Summary: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.
ISSN:1679-7825
1679-7825
DOI:10.1590/S1679-78252010000400002