Skip to content

Solving bifurcation problems in elasticity using auto-07p

Notifications You must be signed in to change notification settings

sgangaprasath/autoTutorial

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

17 Commits
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

Elastic instabilities using auto-07p - A tutorial series

Elastic materials are characterised by their ability to undergo local dilation, shear and twist under externally applied load and relax to a neutral configuration when the load is removed. Often when the applied load exceeds a critical value these materials undergo instabilities characterized by a smooth or dramatic change in their morphology. These instabilities are captured by identifying the forces at play and deriving governing equations for the deformation of the material. The deformation field in the material is then related to the internal stress through a constituent relation, Hooke's law being a famous one. These elastic instability problems, as we shall see, are boundary value problems which are notorious to solve even numerically (analytical solutions are available only in isolated instances).

In this set of 4 tutorials we will see how to solve for the deformation field of the material under various active and passive forces and capture the instabilities using auto-07p, a numerical continuation package. The purpose of this tutorial really is to introduce you to the power of auto-07p to approach these problems. Though the documentation is a very good place to start, I realized during my learning process that there are a few important technical gaps that are often not discussed if one were to go from the documentation to implementation.

We begin by introducing the framework here. Please click this link and go over it before you start reading the tutorial problems. The relevant codes used in these tutorials are available here. The problems we will be looking at (and the focus of each example in auto-07p implementation) are

You can find the entire tutorial collection in pdf format here.

Tutorial Cover

About

Solving bifurcation problems in elasticity using auto-07p

Topics

Resources

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published