Abaqus script to compute Green strain from Nominal strain

Green's strain is sometimes used in large-rotation, small-strain formulations for such problems as shell buckling. It is not available directly as an Abaqus field output nor is the displacement gradient which is commonly used in its calculation.

This script computes and stores Green strain (GE) field output for all odb step frames which include Nominal strain (NE).

1. Continuum Mechanics
2. Abaqus Theory

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From the command line

abaqus python greenStrain.py Job-1.odb [Job-2.odb ...]

Copy the onJobCompletion() method into a local abaqus_v6.env file for automatic execution whenever an Abaqus job completes. Make sure this script is in the working directory or the PYTHONPATH

Green strain is calculated based on the relationships

$${\bf GE} = {1 \over 2} \left( {\bf F} \cdot {\bf F}^T - {\bf I} \right)$$

$${\bf F} \cdot {\bf F}^T - {\bf I} = {\bf V} \cdot {\bf V}^T - {\bf I} = {\bf V} \cdot {\bf V} - {\bf I} $$

$${\bf V} = {\bf NE} + {\bf I}$$

Where

• ${\bf GE}$ is the Green strain tensor in current configuration
• ${\bf F}$ is the displacement gradient tensor
• ${\bf V}$ is the stretch tensor in current configuration
• ${\bf NE}$ is the Nominal strain tensor in current configuration