A Scaled Boundary Finite Element Formulation for Solving Plane-Strain Viscoelastic Problems

Abstract

A new scaled boundary finite element formulation is developed to solve plane-strain viscoelastic problems. In this method, the integral form of linear viscoelasticity constitutive equation and Prony series definition of viscoelastic properties are used to expand scaled boundary finite element formulation. According to the new formulation, a step-by-step solution process is introduced. The explicit scheme is used for transient analysis; however, results are acceptable for either small or large time increments. Several examples with various geometry, material properties, and loading conditions have been solved, and the efficiency of the new formulation is verified against FEM. In these examples, elements with different shapes (quadrilateral and polygon), orders (linear and quadratic), and densities are studied. The new formulation also showed promising performance in analyzing nearly incompressible materials. The proposed development will introduce SBFEM as a privileged alternative for FEM in computational biomechanics. The scaled boundary finite element formulation for plane-stress viscoelastic problems is also presented in the appendix.

Seyed Sadjad Abedi-Shahri

PhD in Biomechanics | Adjunct Lecturer

My research interests include Numerical Methods in Biomechanics, Scientific Computation, and Computational Geometry.