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JuliaFEM / JuliaFEM.jl

The JuliaFEM software library is a framework that allows for the distributed processing of large Finite Element Models across clusters of computers using simple programming models. It is designed to scale up from single servers to thousands of machines, each offering local computation and storage.
http://juliafem.github.io/JuliaFEM.jl/latest/
MIT License
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Contact Mechanics #21

Open TeroFrondelius opened 9 years ago

TeroFrondelius commented 9 years ago

This looks a relevant paper: http://onlinelibrary.wiley.com/doi/10.1002/gamm.201410004/pdf

TeroFrondelius commented 9 years ago

Very interesting publication of the topic: https://books.google.fi/books?id=o5vEuHwKOGkC&lpg=PA107&ots=S5E-LPKeBo&dq=parallel%20fem%20mortar%20contact%20algorithms&pg=PP1#v=onepage&q&f=false

ahojukka5 commented 8 years ago

Let's start to implement this. In short:

  1. create contact segmentation
  2. calculate mortar matrices
  3. solve variational inequality

Here's a proposal for a road map, with some references.

Tie contact in 2d and 3d

Objective: Tie contact of several bodies in 2d and 3d.

Contact using small sliding theory

Objective: To have contact solver for 2d and 3d. This requires solving a variational inequality e14f6e63b46bcb1d63f3868cb199473e see https://en.wikipedia.org/wiki/Variational_inequality

It seems that a good approach to solve variational inequalities is to use so called primal-dual active set strategy, which has equivalent convergence properties to semismooth Newton method. We should expect superlinear convergence.

Finite sliding contact

Objective: To extend contact from small sliding to finite sliding theory. In finite deformation contact, contact force depends from displacement and requires linearization. Hopefully this can be done using ForwardDiff. Also use of higher order interpolation on contact interfaces is known be be difficult problem.

Improved performance + rest of stuff

Objective: Static condensation of slave side nodes is important if using iterative solvers. We could also consider other specific things like self-contact and friction models.

References

Cichosz, T., and M. Bischoff. Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers. Computer Methods in Applied Mechanics and Engineering 200.9 (2011): 1317-1332.

Dias, A. P. C., A. L. Serpa, and M. L. Bittencourt. High-order mortar-based element applied to nonlinear analysis of structural contact mechanics. Computer Methods in Applied Mechanics and Engineering 294 (2015): 19-55.

Fischer, Kathrin A., and Peter Wriggers. "Mortar based frictional contact formulation for higher order interpolations using the moving friction cone." Computer methods in applied mechanics and engineering 195.37 (2006): 5020-5036.

Gitterle, Markus, et al. Finite deformation frictional mortar contact using a semi‐smooth Newton method with consistent linearization. International Journal for Numerical Methods in Engineering 84.5 (2010): 543-571.

Hüeber, Stefan, and Barbara I. Wohlmuth. A primal–dual active set strategy for non-linear multibody contact problems. Computer Methods in Applied Mechanics and Engineering 194.27 (2005): 3147-3166.

Moradi, Abbas, Saeed Adibnazari, and Mohsen Safajuy. Numerical Modeling of Fretting Fatigue Crack Propagation based on a Combined XFEM and Mortar Contact Approach.

Páczelt, I., and Z. Mróz. Solution of wear problems for monotonic and periodic sliding with p-version of finite element method. Computer Methods in Applied Mechanics and Engineering 249 (2012): 75-103.

Popp, Alexander. Mortar methods for computational contact mechanics and general interface problems. Diss. Technische Universität München, 2012.

Popp, A., and W. A. Wall. Dual mortar methods for computational contact mechanics–overview and recent developments. GAMM‐Mitteilungen 37.1 (2014): 66-84.

Popp, Alexander, Michael W. Gee, and Wolfgang A. Wall. A finite deformation mortar contact formulation using a primal–dual active set strategy. International Journal for Numerical Methods in Engineering 79.11 (2009): 1354-1391.

Popp, Alexander, et al. A dual mortar approach for 3D finite deformation contact with consistent linearization. International Journal for Numerical Methods in Engineering 83.11 (2010): 1428-1465.

Popp, A., et al. Dual quadratic mortar finite element methods for 3D finite deformation contact. SIAM Journal on Scientific Computing 34.4 (2012): B421-B446.

Popp, Alexander, et al. Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach. Computer Methods in Applied Mechanics and Engineering 264 (2013): 67-80.

Puso, Michael A., and Tod A. Laursen. A mortar segment-to-segment contact method for large deformation solid mechanics. Computer methods in applied mechanics and engineering 193.6 (2004): 601-629.

Sitzmann, Saskia, Kai Willner, and Barbara I. Wohlmuth. A dual Lagrange method for contact problems with regularized frictional contact conditions: Modelling micro slip. Computer Methods in Applied Mechanics and Engineering 285 (2015): 468-487.

Yang, Bin, and Tod A. Laursen. A large deformation mortar formulation of self contact with finite sliding. Computer Methods in Applied Mechanics and Engineering 197.6 (2008): 756-772.

Yang, Bin, Tod A. Laursen, and Xiaonong Meng. Two dimensional mortar contact methods for large deformation frictional sliding. International Journal for Numerical Methods in Engineering 62.9 (2005): 1183-1225.

ahojukka5 commented 8 years ago

index

ahojukka5 commented 8 years ago

2d tie contact: https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/notebooks/2015-11-23-2d-tie-contact.ipynb

ahojukka5 commented 8 years ago

3d tie contact seems to be working "almost". 2015-12-14-divided-block-results

ahojukka5 commented 8 years ago

3d tie contact is now working.

2015-12-17-superblock

Very well studied block .. :) the accurate solutions for unit cube under 100 unit of traction force in z direction + symmetric boundary conditions in corner is (1/36, 1/36, -1/9) (E=900, nu=0.25).

ahojukka5 commented 8 years ago

2dcontact

2d frictionless contact working. This should be trivial to extend to 3d.

ahojukka5 commented 8 years ago

hertz2 beam ironing

ahojukka5 commented 8 years ago

Some verifications: Hertzian contact problem modelled using symmetry:

hertzian_1_symmetry_results

Symmetry boundary condition is disturbing results but I haven't figured out yet how to deal with it properly. Anyway contact pressure seems to be close to analytical and is smooth like expected in Mortar contact.

Here's another one without symmetry boundary condition:

mesh_contact

mesh_contact_closer

herzian_2_deformed

hertzian_2_pressure

Models are typically converging in 5-10 iterations. Because active sets are updated during the solution of global system we should have superlinear convergence before correct contact set is found and after that quadratic convergence if using full Newton method. So it shoudn't take much more iterations even when using geometrically nonlinear analysis.

ahojukka5 commented 8 years ago

Frictionless finite sliding. (Click png to see video.)

curved_interface_049

ahojukka5 commented 8 years ago

sliding 0000

Another one. This is done using ForwardDiff, looks that it's doing a good job of taking care all the cumbersome linearizations! Click png to see video.

ahojukka5 commented 8 years ago

beams 0400

TeroFrondelius commented 7 years ago

@ahojukka5 is this issue up to date?

ahojukka5 commented 7 years ago

I think we should split this into smaller issues or we never finish this.

TeroFrondelius commented 7 years ago

I propose you will do the split and reference this issue. After creating those new issues let's close this one.