Ratel: Extensible, performance-portable solid mechanics#

Ratel is a solid mechanics library and applications based on libCEED and PETSc with support for efficient high-order elements and CUDA and ROCm GPUs.

Solid mechanics simulations provide vital information for many engineering applications, using a large amount of computational resources from workstation to supercomputing scales. The industry standard for implicit analysis uses assembled sparse matrices with low-order elements, typically \(Q_1\) hexahedral and \(P_2\) tetrahedral elements, with the linear systems solved using sparse direct solvers, algebraic multigrid, or multilevel domain decomposition. This approach has two fundamental inefficiencies: poor approximation accuracy per Degree of Freedom (DoF) and high computational and memory cost per DoF due to choice of data structures and algorithms. High-order finite elements implemented in a matrix-free fashion with appropriate preconditioning strategies can overcome these inefficiencies.

For further details on the benefits of high-order, matrix-free finite elements for solid mechanics, see our preprint on arXiv.

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Fig. 1 Ratel badger moving simulation#

Indices and tables#

[AKBP21]

Bilen Emek Abali, Andre Klunker, Emilio Barchiesi, and Luca Placidi. A novel phase-field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable. 2021.

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Hanen Amor, Jean-Jacques Marigo, and Corrado Maurini. Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. Journal of the Mechanics and Physics of Solids, 57(8):1209–1229, 2009.

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[BJ16]

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[BHL+16]

Michael J. Borden, Thomas Joseph Robert Hughes, Chad M. Landis, Amin Anvari, and Isaac J. Lee. A phase-field formulation for fracture in ductile materials: finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Computer Methods in Applied Mechanics and Engineering, 312:130–166, 2016. doi:10.1016/j.cma.2016.09.005.

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[DPA+20]

Denis Davydov, Jean-Paul Pelteret, Daniel Arndt, Martin Kronbichler, and Paul Steinmann. A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid. International Journal for Numerical Methods in Engineering, 121(13):2874–2895, 2020. doi:10.1002/nme.6336.

[dSNEARJ98]

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[KSchluterMuller15]

Charlotte Kuhn, Alexander Schlüter, and Ralf Müller. On degradation functions in phase field fracture models. Computational Materials Science, 108:374–384, 2015.

[MAL02]

Christian Miehe, N Apel, and Matthias Lambrecht. Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials. Computer methods in applied mechanics and engineering, 191(47-48):5383–5425, 2002. doi:10.1016/S0045-7825(02)00438-3.

[MHW10]

Christian Miehe, Martina Hofacker, and Fabian Welschinger. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199(45-48):2765–2778, 2010.

[MWH10]

Christian Miehe, Fabian Welschinger, and Martina Hofacker. Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. International journal for numerical methods in engineering, 83(10):1273–1311, 2010.

[Mli18]

Rabii Mlika. Nitsche method for frictional contact and self-contact: Mathematical and numerical study. phdthesis, Université de Lyon, Jan 2018. URL: https://theses.hal.science/tel-02067118.

[NW99]

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[Ogd97]

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[PDME92]

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[TanneLB+18]

Erwan Tanné, Tianyi Li, Blaise Bourdin, J-J Marigo, and Corrado Maurini. Crack nucleation in variational phase-field models of brittle fracture. Journal of the Mechanics and Physics of Solids, 110:80–99, 2018.