scholarly journals Critical time step for DEM simulations of dynamic systems using a Hertzian contact model

2019 ◽  
Vol 119 (5) ◽  
pp. 432-451 ◽  
Author(s):  
Shane J. Burns ◽  
Petri T. Piiroinen ◽  
Kevin J. Hanley
Keyword(s):  
Dynamic Systems ◽  
Critical Time ◽  
Contact Model ◽  
Hertzian Contact ◽  
Time Step ◽  
Dem Simulations ◽  
Critical Time Step ◽  
Hertzian Contact Model

Small correction required when applying the Hertzian contact model to instrumented indentation data

2001 ◽  
Vol 16 (5) ◽  
pp. 1280-1286 ◽  
Author(s):  
J. L. Hay ◽  
P. J. Wolff
Keyword(s):  
Mechanical Properties ◽  
Contact Model ◽  
Hertzian Contact ◽  
Test Material ◽  
Contact Radius ◽  
Test Surface ◽  
Instrumented Indentation ◽  
Hardness Testing ◽  
Small Correction ◽  
Hertzian Contact Model

Instrumented indentation testing (IIT) is a relatively new form of mechanical testing which significantly expands on the capabilities of traditional hardness testing. In an IIT experiment, an indenter of known mechanical properties is pressed into contact and then withdrawn from a test material. The fundamental measurements during an IIT experiment are the applied load and the resulting penetration of the indenter into the test surface. The Hertzian contact model, or a derivative thereof, is often employed to relate these measurements to interesting mechanical properties of the test material. This article argues for a small correction to the Hertzian contact model when applied to instrumented indentation data. The magnitude of the correction primarily depends on Poisson's ratio of the test material and the contact radius normalized by the radius of the indenter tip. Neglecting this correction can cause significant errors in the calculation of elastic modulus and hardness from instrumented indentation data.

Numerical Simulations of Slider Interaction With Multiple Asperity Using Hertzian Contact Model

1995 ◽  
Vol 117 (4) ◽  
pp. 575-579 ◽  
Author(s):  
Ellis Cha ◽  
D. B. Bogy
Keyword(s):  
Disk Drive ◽  
Contact Model ◽  
Hertzian Contact ◽  
Flying Height ◽  
Radius Of Curvature ◽  
Asperity Contact ◽  
Disk Contact ◽  
Suspension Dynamics ◽  
Magnetic Hard Disk ◽  
Hertzian Contact Model

A numerical simulation of slider-disk contact in a magnetic hard disk drive is studied using the Hertzian contact model. The slider-disk contact is caused by flying height fluctuation due to disk runout for very low flying sliders. The rough disk topography is generated numerically by combining a sinusoidal waviness and a Gaussian roughness. For each asperity contact, the radius of curvature is calculated from the disk topography, and the radius is used to calculate the contact force using the Hertzian contact model. The slider’s response to a single asperity calculated using the Hertzian contact model agrees well with the result obtained using the impulse-momentum based contact model. The simulation results of slider-disk contact including suspension dynamics are calculated with and without friction for a “nano-slider.”

Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

1978 ◽  
Vol 45 (2) ◽  
pp. 371-374 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Transient Analysis ◽  
Critical Time ◽  
Unconditional Stability ◽  
Time Step ◽  
Explicit Finite Element ◽  
New Family ◽  
Critical Time Step ◽  
Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

scholarly journals A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

2007 ◽  
Vol 7 (3) ◽  
pp. 227-238 ◽  
Author(s):  
S.H. Razavi ◽  
A. Abolmaali ◽  
M. Ghassemieh
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Time Integration ◽  
Critical Time ◽  
Linear Acceleration ◽  
Time Step ◽  
Time Integration Method ◽  
Acceleration Method ◽  
The Stability ◽  
Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

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