A penalty function approach to problems of plastic flow of metals with large surface deformations

1975 ◽  
Vol 10 (3) ◽  
pp. 180-183 ◽  
Author(s):  
O C Zienkiewicz ◽  
P N Godbole
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Plastic Flow ◽  
Penalty Function ◽  
Iterative Solution ◽  
Function Approach ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Penalty Function Approach

An iterative solution permits determination of velocities in plastic flow using a finite element formulation. By updating co-ordinates very large deformation can be followed.

Static Atomistic Simulations of Nanoindentation and Determination of Nanohardness

2005 ◽  
Vol 72 (5) ◽  
pp. 738-743 ◽  
Author(s):  
Yeau-Ren Jeng ◽  
Chung-Ming Tan
Keyword(s):  
Finite Element ◽  
Nonlinear Finite Element ◽  
Deformation Mechanisms ◽  
Finite Element Formulation ◽  
Atomistic Simulations ◽  
Element Formulation ◽  
Indentation Size ◽  
Plastic Deformations ◽  
Nanoindentation Testing

This paper develops a nonlinear finite element formulation to analyze nanoindentation using an atomistic approach, which is conducive to observing the deformation mechanisms associated with the nanoindentation cycle. The simulation results of the current modified finite element formulation indicate that the microscopic plastic deformations of the thin film are caused by instabilities of the crystalline structure, and that the commonly used procedure for estimating the contact area in nanoindentation testing is invalid when the indentation size falls in the nanometer regime.

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