Incompatible mode C₁-continuous tetrahedral 4-node 3D user element for Abaqus

This repository contains all the necessary tools to use a tetrahedral incompatible mode C₁-continuous user element in Abaqus that has the following features:

1. Fully compatible with C3D4-meshes
2. Large strain formulation
3. Simple user material interface
4. 4 degrees of freedom (DOF, field value and gradient) at each corner node, i.e.~16 total DOF per scalar field
5. Full 5^th order polynomial shape function
6. Numerical integration exact up to a full 6^th order polynomial

It supplements the article A C1 incompatible mode element formulation for strain gradient elasticity DOI: 10.1007/978-3-030-30406-5_6

Walkthrough

1. Element formulation
2. Mathematica: Shape function derivation and code generation
3. Fortran UEL
4. Abaqus example
5. Visualisation with Paraview

Referencing

Please cite as follows:

@article{GLUEGE20192,
  author = {Gl{\"u}ge, R.},
  editor = {Altenbach, H. and M{\"u}ller, W.H. and Abali, B.E.},
  title = {A C1 Incompatible Mode Element Formulation for Strain Gradient Elasticity},
  booktitle = {Higher Gradient Materials and Related Generalized Continua},
  year = {2019},
  publisher = {Springer International Publishing},
  address = {Cham},
  pages = {95--120},
  isbn = {978-3-030-30406-5},
  doi = {10.1007/978-3-030-30406-5_6},
  url = {https://doi.org/10.1007/978-3-030-30406-5_6}
}