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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[AMM09]

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[BHL+16]

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[DPA+20]

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[MFPCL16]

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[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]

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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.