2.2.49. addStrainTensors


Purpose

Add column(s) containing given strains based on given stretches of requested deformation gradient column(s).

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Usage

> addStrainTensors options ASCII table(s) 

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Options

-u / --right
material strains based on right Cauchy--Green deformation, i.e., C and U
-v / --left
spatial strains based on left Cauchy--Green deformation, i.e., B and V
-0 / --logarithmic
calculate logarithmic strain tensor
-1 / --biot
calculate biot strain tensor
-2 / --green
calculate green strain tensor
-f / --defgrad [ ['f'] ]
heading(s) of columns containing deformation tensor values


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Note

the »material stretch tensor« $ \tnsr U $ following from the »right Cauchy–Green deformation tensor«: $ \tnsr C = \tnsr F^\text T\tnsr F = \tnsr U^\text T \tnsr R^\text T \tnsr R\,\tnsr U = \tnsr U^2 = \lambda_i^2\,\vctr u_i \otimes \vctr u_i $ the »spatial stretch tensor« $ \tnsr V $ following from the »left Cauchy–Green deformation tensor«: $ \tnsr B = \tnsr F\,\tnsr F^\text T = \tnsr V \tnsr R \tnsr R^\text T \tnsr V^\text T = \tnsr V^2 = \lambda_i^2\,\vctr v_i \otimes \vctr v_i $
  1. : $ \ln(\lambda_i)\,\vctr n_i \otimes \vctr n_i $ (»material« or »spatial Hencky«)
  2. : $ (\lambda_i-1)\,\vctr u_i \otimes \vctr u_i $ (»material Biot«)
    $ (1-{\lambda_i}^{-1})\,\vctr v_i \otimes \vctr v_i $ (»spatial Biot«)
  3. : $ \frac{1}{2}({\lambda_i}^2-1)\,\vctr u_i \otimes \vctr u_i $ (»material Green«)
    $\frac{1}{2}(1-{\lambda_i}^{-2})\,\vctr v_i \otimes \vctr v_i $ (»spatial Almansi«)

Strain formulas are taken from chapter 2.3 in

A. Bertram
Elasticity and Plasticity of Large Deformations: An Introduction
3rd edition, Springer, 2012
ISBN:9783642246142
Topic revision: r11 - 07 Mar 2019, MartinDiehl


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