From 35d5f0316476a1b82a129771431cd55e1ca87eab Mon Sep 17 00:00:00 2001 From: Mohamed ZAARAOUI <115699524+ZAARAOUI999@users.noreply.github.com> Date: Mon, 18 Dec 2023 08:37:17 +0100 Subject: [PATCH] Update README.md --- README.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/README.md b/README.md index 2912cb3..e3cd26a 100644 --- a/README.md +++ b/README.md @@ -9,10 +9,10 @@ [![Generic badge](https://img.shields.io/badge/pypi-v0.1.1-.svg)](https://pypi.org/project/hypermat/) [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.8285247.svg)](https://doi.org/10.5281/zenodo.8285247) [![Downloads](https://static.pepy.tech/badge/hypermat/week)](https://pepy.tech/project/hypermat) -HyperMAT is based on the definitions of the second Piola-Kirchhoff stress $\large S$ and the material tangent modulus $\large \hat{C}$ given below: +HyperMAT is based on the definitions of the first Piola-Kirchhoff stress $\large P$ and the tangent modulus $\large \hat{A}$ given below:

- $\large S = 2 \frac{\partial{W}}{\partial{C}}$
$\large \hat{C} = 4 \frac{\partial^2{W}}{\partial{C}^2}$ + $\large P = \frac{\partial{W}}{\partial{F}}$
$\large \hat{A} = \frac{\partial^2{W}}{\partial{F}^2}$

How to use

@@ -33,10 +33,10 @@ F[...,0,2] = 0.5 F[...,2,1] = 0.3 # Get stress tensor -S = umat.jacobian(F) +P = umat.jacobian(F) -# Get material tangent modulus tensor -C = umat.hessian(F) +# Get tangent modulus tensor +A = umat.hessian(F) ``` Sometimes a lucky engineer will have some tension or compression stress-strain test data, or simple shear test data. Processing and applying these data is a critical step to analyze the hyperelastic models. HyperMAT has a calibration module that can help to get the best fitted model parameters. Let's take a look on how are things going on: