Explicit methods in quasi - static analysis of rubber - like materials

Abstract

Static finite element analysis based on implicit time integration may have con vergence difficulties in presence of complex loading conditions, incompressibility and nonlinear material properties. In such cases, quasi-static analysis with explicit time integration can be utilized. The aim of the thesis is to investigate the accuracy and efficiency of the explicit time integration in the quasi-static analysis of rubber-like materials. Four boundary value problems with varying degree of confinement were analyzed. The first boundary value problem is the uniaxial stretch of a plate with a circular hole and free lateral surfaces. The second boundary problem has the same geometry and loading of the first problem with an additional confinement due to constrained lateral surfaces. These problems are regarded as lightly constrained ones. The third problem is the plane strain analysis of a uniaxial stretch of a plate with a central crack. The fourth problem is the analysis of the compression of a disc with contact algorithms. These problems are regarded as highly constrained ones. In the boundary value problems, the effect of rubber density, loading velocity, compressibility of rubber and the magnitude of the applied load are studied. The accuracy of quasi-static solutions is evaluated with respect to static analysis with implicit integration. The quantities indicating transition from quasi-static to dynamic state are determined. The conclusions could be used as a guidance in quasi-static analysis and fatigue life prediction of real applications such as seismic isolators, bearings and engine mounts.