From b098ccdd7517d184d93bb4343463725b44429f75 Mon Sep 17 00:00:00 2001 From: Jean-Paul Pelteret Date: Mon, 3 Apr 2017 08:03:30 +0200 Subject: [PATCH] Add citations and funding acknowledgement --- .../README.md | 57 +++++++++++-------- .../README.md | 9 +++ 2 files changed, 42 insertions(+), 24 deletions(-) diff --git a/Quasi_static_Finite_strain_Compressible_Elasticity/README.md b/Quasi_static_Finite_strain_Compressible_Elasticity/README.md index 7da6b78..13c05c6 100644 --- a/Quasi_static_Finite_strain_Compressible_Elasticity/README.md +++ b/Quasi_static_Finite_strain_Compressible_Elasticity/README.md @@ -1,9 +1,9 @@ ## Overview -The Cook membrane (or cantilever) problem is a classic benchmark test for -finite element formulations for solid mechanics. It is typically used to -test for and demonstrate the shear-locking (or locking-free) behaviour of -a finite element ansatz under quasi-incompressible conditions. -As it is so widely referred to in the literature on finite-strain elasticity, +The Cook membrane (or cantilever) problem is a classic benchmark test for +finite element formulations for solid mechanics. It is typically used to +test for and demonstrate the shear-locking (or locking-free) behaviour of +a finite element ansatz under quasi-incompressible conditions. +As it is so widely referred to in the literature on finite-strain elasticity, we reproduce the example here. However, we consider on the compressible case to avoid many of the complexities that arise in `step-44`, which provides an efficient approach to deal with @@ -11,10 +11,10 @@ the quasi-incompressible case. ### A classical approach to solving the cook membrane problem. -In this work we take a classical approach to solving the equations governing -quasi-static finite-strain compressible elasticity, with code based on -`step-44`. The formulation adopted here is that seen in many texts on solid -mechanics and can be used as the starting point for extension into many +In this work we take a classical approach to solving the equations governing +quasi-static finite-strain compressible elasticity, with code based on +`step-44`. The formulation adopted here is that seen in many texts on solid +mechanics and can be used as the starting point for extension into many topics such as material anisotropy, rate dependence or plasticity, or even as a component of multi-physics problems. @@ -26,11 +26,11 @@ is prevented in order to impose plane strain conditions. ![Problem geometry](./doc/problem_setup.png) -Note that we perform a three-dimensional computation as, for this particular -formulation, the two-dimensional case corresponds to neither plane-strain +Note that we perform a three-dimensional computation as, for this particular +formulation, the two-dimensional case corresponds to neither plane-strain nor plane-stress conditions. - + ## Requirements * Version 8.2.1 or greater of `deal.II` @@ -55,29 +55,38 @@ make run ``` +## Reference for this work +If you use this program as a basis for your own work, please consider citing it in your list of references. +The initial version of this work was contributed to the deal.II project by the authors listed in the following citation: +* J-P. V. Pelteret and A. McBride, The deal.II code gallery: Quasi-Static Finite-Strain Compressible Elasticity, 2016. DOI: [10.5281/zenodo.437601](http://doi.org/10.5281/zenodo.437601) + +### Acknowledgements +The support of this work by the European Research Council (ERC) through the Advanced Grant 289049 MOCOPOLY is gratefully acknowledged by the first author. + + ## Recommended Literature * C. Miehe (1994), Aspects of the formulation and finite element implementation of large strain isotropic elasticity International Journal for Numerical Methods in Engineering 37 , 12, 1981-2004. DOI: [10.1002/nme.1620371202](http://doi.org/10.1002/nme.1620371202); * G.A. Holzapfel (2001), Nonlinear Solid Mechanics. A Continuum Approach for Engineering, John Wiley & Sons. ISBN: [978-0-471-82319-3](http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471823198.html); * P. Wriggers (2008), Nonlinear finite element methods, Springer. DOI: [10.1007/978-3-540-71001-1](http://doi.org/10.1007/978-3-540-71001-1); * T.J.R. Hughes (2000), The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover. ISBN: [978-0486411811](http://store.doverpublications.com/0486411818.html) -The derivation of the finite-element problem, namely the definition and -linearisation of the residual and their subsequent discretisation are quite +The derivation of the finite-element problem, namely the definition and +linearisation of the residual and their subsequent discretisation are quite lengthy and involved. Thankfully, the classical approach adopted in this work is -well documented and therefore does not need to be reproduced here. -We refer the reader to, among many other possible texts, Holzapfel (2001) and -Wriggers (2008) for a detailed description of the approach applied in this work. -It amounts to a reduction and slight reworking of `step-44` (accounting for -the removal of the two additional fields used therein). We also refer the reader -to `step-44` for a brief overview of the continuum mechanics and kinematics +well documented and therefore does not need to be reproduced here. +We refer the reader to, among many other possible texts, Holzapfel (2001) and +Wriggers (2008) for a detailed description of the approach applied in this work. +It amounts to a reduction and slight reworking of `step-44` (accounting for +the removal of the two additional fields used therein). We also refer the reader +to `step-44` for a brief overview of the continuum mechanics and kinematics related to solid mechanics. ## Results -These results were produced using the following material properties: -* Shear modulus is 422.5kPa +These results were produced using the following material properties: +* Shear modulus is 422.5kPa * Poisson ratio is 0.3 -The 32x32x1 discretised reference geometry looks as follows: +The 32x32x1 discretised reference geometry looks as follows: ![Problem geometry](./doc/ref_grid.png) @@ -87,7 +96,7 @@ And an example of the displaced solution is given in the next image. Below we briefly document the tip displacement as predicted for different discretisation levels and ansatz for the displacement field. -A direct and, by visual inspection, favourable comparison of the following +A direct and, by visual inspection, favourable comparison of the following results can be made with those found in Miehe (1994). Since the material is compressible, shear-locking is not exhibited by the beam for low-order elements. diff --git a/Quasi_static_Finite_strain_Quasi_incompressible_ViscoElasticity/README.md b/Quasi_static_Finite_strain_Quasi_incompressible_ViscoElasticity/README.md index 50f6ec8..6cd671c 100644 --- a/Quasi_static_Finite_strain_Quasi_incompressible_ViscoElasticity/README.md +++ b/Quasi_static_Finite_strain_Quasi_incompressible_ViscoElasticity/README.md @@ -72,6 +72,15 @@ This program can be run in `2d` or `3d`; this choice can be made by making the appropriate changes in the `main()` function. +## Reference for this work +If you use this program as a basis for your own work, please consider citing it in your list of references. +The initial version of this work was contributed to the deal.II project by the authors listed in the following citation: +* J-P. V. Pelteret, The deal.II code gallery: Quasi-static Finite-Strain Quasi-incompressible Visco-elasticity, 2017. DOI: [10.5281/zenodo.437604](http://doi.org/10.5281/zenodo.437604) + +### Acknowledgements +The support of this work by the European Research Council (ERC) through the Advanced Grant 289049 MOCOPOLY is gratefully acknowledged by the author. + + ## Recommended Literature * C. Miehe (1994), Aspects of the formulation and finite element implementation of large strain isotropic elasticity. International Journal for Numerical Methods in Engineering 37 , 12, 1981-2004. DOI: [10.1002/nme.1620371202](http://doi.org/10.1002/nme.1620371202); * G.A. Holzapfel (2001), Nonlinear Solid Mechanics. A Continuum Approach for Engineering, John Wiley & Sons. ISBN: [978-0-471-82319-3](http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471823198.html); -- 2.39.5