Gradient plasticity theory with a variable length scale parameter

2005 ◽  
Vol 42 (14) ◽  
pp. 3998-4029 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Scale Parameter ◽  
Plasticity Theory ◽  
Variable Length ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity

A Modified Gradient Plasticity Theory for Micro-Bending and Micro-Torsion Size Effects

2004 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Size Effects ◽  
Scale Parameter ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Non Local ◽  
Material Length Scale ◽  
Material Length

The definition and magnitude of the intrinsic length scale are keys to the development of the theory of plasticity that incorporates size effects. Gradient plasticity theory with a material length scale parameter is successfully in capturing the size dependence of material behavior at the micron scale. However, a fixed value of the material length-scale is not always realistic and that different problems could require different values. Moreover, a linear coupling between the local and non-local terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed. This model assesses the sensitivity of predictions in the way in which the local and non-local parts are coupled. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

Nanoindentation study of plasticity length scale effects in LIGA Ni microelectromechanical systems structures

2003 ◽  
Vol 18 (3) ◽  
pp. 719-728 ◽  
Author(s):  
J. Lou ◽  
P. Shrotriya ◽  
T. Buchheit ◽  
D. Yang ◽  
W. O. Soboyejo
Keyword(s):  
Plastic Deformation ◽  
Strain Gradient ◽  
Indentation Depth ◽  
Microelectromechanical Systems ◽  
Scale Parameter ◽  
Scale Effects ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Cube Corner

This paper presents the results of a nanoindentation study of the effects of strain gradient plasticity on the elastic–plastic deformation of lithographie, galvanoformung, abformung (LIGA) Ni microelectromechanical systems (MEMS) structures plated from sulfamate baths. Both Berkovich and North Star/cube corner indenter tips were used in the study to investigate possible effects of residual indentation depth on the hardness of LIGA Ni MEMS structures between the micro- and nanoscales. A microstructural length scale parameter, , was determined for LIGA nickel films. This is shown to be consistent with a stretch gradient length-scale parameter, ls, of approximately 0.9 μm.

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

2021 ◽  
pp. 107754632110482
Author(s):  
J Ranjan Banerjee ◽  
Stanislav O Papkov ◽  
Thuc P Vo ◽  
Isaac Elishakoff
Keyword(s):  
Free Vibration ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Dynamic Stiffness ◽  
Modified Couple Stress Theory ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Stress Theory ◽  
Modified Couple Stress

Several models within the framework of continuum mechanics have been proposed over the years to solve the free vibration problem of micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified couple stress theories. Many of these models retain the basic features of the Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one or more material scale length parameters to tackle the problem. The work described in this paper deals with the free vibration problems of micro beams based on the dynamic stiffness method, through the implementation of the modified couple stress theory in conjunction with the Timoshenko–Ehrenfest theory. The main advantage of the modified couple stress theory is that unlike other models, it uses only one material length scale parameter to account for the smallness of the structure. The current research is accomplished first by solving the governing differential equations of motion of a Timoshenko–Ehrenfest micro beam in free vibration in closed analytical form. The dynamic stiffness matrix of the beam is then formulated by relating the amplitudes of the forces to those of the corresponding displacements at the ends of the beam. The theory is applied using the Wittrick–Williams algorithm as solution technique to investigate the free vibration characteristics of Timoshenko–Ehrenfest micro beams. Natural frequencies and mode shapes of several examples are presented, and the effects of the length scale parameter on the free vibration characteristics of Timoshenko–Ehrenfest micro beams are demonstrated.

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