Axi-Symmetric Finite Elements for Viscoelastic Analysis

Viscoelastic materials like solid propellant grains exhibit material properties, which are timedependent and incompressible in nature. The displacement based finite elements fails to solve structural problem having incompressible materials. The basic reason is Poisson's ratio approaches 0.5 for such materials. Which makes the constitutive relation between stress and strain very stiff there by the stiffness matrix becomes very stiff which yields very poor displacement results and predicted stresses and strains are unreliable. This phenomenon is known as volumetric locking. To overcome this difficulty special formulations are needed to address such materials. There are many methods available in literature like Hybrid-stress displacement formulation, B-Bar method and Herrmann formulation etc. This project is proposed to develop 8-noded quadrilateral, 9-noded quadrilateral and 6 noded triangular axisymmetric finite elements based on Herrmann formulation to overcome the difficulty of incompressible materials. The developed elements will be studied for its applicability for the ranges of Poisson's ratio and for distortion sensitiveness.