A brief history of logarithmic strain measures in nonlinear elasticity

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Robert J. Martin ◽  
Ingo Münch ◽  
Bernhard Eidel ◽  
Patrizio Neff
Keyword(s):  
Nonlinear Elasticity ◽  
Logarithmic Strain ◽  
History Of ◽  
Strain Measures

scholarly journals A Riemannian approach to strain measures in nonlinear elasticity

2014 ◽  
Vol 342 (4) ◽  
pp. 254-257 ◽  
Author(s):  
Patrizio Neff ◽  
Bernhard Eidel ◽  
Frank Osterbrink ◽  
Robert Martin
Keyword(s):  
Nonlinear Elasticity ◽  
Strain Measures

scholarly journals Geometry of Logarithmic Strain Measures in Solid Mechanics

2016 ◽  
Vol 222 (2) ◽  
pp. 507-572 ◽  
Author(s):  
Patrizio Neff ◽  
Bernhard Eidel ◽  
Robert J. Martin
Keyword(s):  
Solid Mechanics ◽  
Logarithmic Strain ◽  
Strain Measures

scholarly journals Evaluation of Strains and Thicknesses of Pipe Elbows on the Basis of Expressions Resulting from the Eudirective for the Case of Large and Small Deformations

2017 ◽  
Vol 22 (4) ◽  
pp. 1113-1127
Author(s):  
Z. Śloderbach
Keyword(s):  
Wall Thickness ◽  
Large Deformations ◽  
Engineering Practice ◽  
Logarithmic Strain ◽  
Eu Directive ◽  
Maximum Value ◽  
Relative Strain ◽  
Strain Measures ◽  
Small Deformations ◽  
The Eu

Abstract The relations to calculate the maximum value of strains in processes of bending tubes on benders, in stretched layers of tubes, are presented in this work on the basis of the EU-Directive concerning production of pressure equipment. It has been shown that for large deformations that occur during bending of the pipes on knees, logarithmic strain measures (real) and relative strain measures give different values of strain but equal wall thicknesses in the bending zone. Logarithmic measures are frequently used in engineering practice and are valid for large and small deformations. Reverse expressions were also derived to calculate the required initial wall thickness of the tube to be bent, in order to obtain the desired wall thickness of the knee after bending.

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