Abstract: Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.
Abstract: Present study is aimed on the cutting process of circular
cross-section rods where the fracture is used to separate one rod
into two pieces. Incorporating the phenomenological ductile fracture
model into the explicit formulation of finite element method, the
process can be analyzed without the necessity of realizing too many
real experiments which could be expensive in case of repetitive
testing in different conditions. In the present paper, the steel AISI
1045 was examined and the tensile tests of smooth and notched
cylindrical bars were conducted together with biaxial testing of the
notched tube specimens to calibrate material constants of selected
phenomenological ductile fracture models. These were implemented
into the Abaqus/Explicit through user subroutine VUMAT and used
for cutting process simulation. As the calibration process is based
on variables which cannot be obtained directly from experiments,
numerical simulations of fracture tests are inevitable part of the
calibration. Finally, experiments regarding the cutting process were
carried out and predictive capability of selected fracture models is
discussed. Concluding remarks then make the summary of gained
experience both with the calibration and application of particular
ductile fracture criteria.