Solution of nonlinear nearly incompressible hyperelastic problems by isogeometric analysis method.

This article is devoted to the derivation of formulation and isogeometric solution of nonlinear nearly incompressible elastic problems, known as nearly incompressible hyperelasticity. After problem definition, the governing equations are linearized for employing the Newton-Raphson iteration method. Then, the problem is discretized by using concepts of isogeometric analysis method and its solution algorithm is devised. To demonstrate the performance of the proposed approach, the obtained results are compared with the finite elements solutions. Due to large deformations in this kind of problems, the finite element method requires a relatively large number of elements, as well as the need for remeshing in some problems, that result in a large system of equations with a high computational cost. In the isogeometric analysis method, B-Spline and NURBS (Non-Uniform Rational B-Spline) basis functions provide a good flexibility in modeling of geometry without any need for further remeshing. The examples studied in this article indicate that by using the isogeometric approach good quality results are obtained with a smaller system of equations and less computational cost. Also, influence of different volumetric functions for the nearly incompressible materials is investigated. [ABSTRACT FROM AUTHOR]