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.

Fig. 1 Ratel badger moving simulation¶

Contents

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.

[AGDL15]

Marreddy Ambati, Tymofiy Gerasimov, and Laura De Lorenzis. A review on phase-field models of brittle fracture and a new fast hybrid formulation. Computational Mechanics, 55:383–405, 2015.

[AMM09]

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.

[AR09]

Douglas N Arnold and Marie E Rognes. Stability of lagrange elements for the mixed laplacian. Calcolo, 46(4):245–260, 2009. doi:10.1007/s10092-009-0009-6.

[BN75]

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[BJ16]

Hudobivnik B. and Korelc J. Closed-form representation of matrix functions in the formulation of nonlinear material models. Finite Elements in Analysis and Design, 111:19–32, 2016. doi:10.1016/j.finel.2015.12.002.

[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.

[BF12]

Franco Brezzi and Michel Fortin. Mixed and hybrid finite element methods. Volume 15. Springer Science & Business Media, 2012.

[C94]

Miehe C. Aspects of the formulation and finite element implementation of large strain isotropic elasticity. International Journal for Numerical Methods in Engineering, 37(12):1981–2004, 1994. doi:10.1002/nme.1620371202.

[C98]

Miehe C. Comparison of two algorithms for the computation of fourth-order isotropic tensor functions. Computers & Structures, 66(1):37–43, 1998. doi:10.1016/s0045-7949(97)00073-4.

[CB93]

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[Che16]

Alexander Cheng. Poroelasticity. Springer Cham, Chichester New York, 2016. ISBN 978-3-319-25200-1. doi:10.1007/978-3-319-25202-5.

[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]

Perić D. de Souza Neto E.A. and Owen R.J. Continuum modelling and numerical simulation of material damage at finite strains. Archives of Computational Methods in Engineering, 5(311):311–384, 1998. doi:10.1007/BF02905910.

[DCC13]

Boyang Ding, Alexander H.-D. Cheng, and Zhanglong Chen. Fundamental solutions of poroelastodynamics in frequency domain based on wave decomposition. Journal of Applied Mechanics, 80(6):061021, 08 2013. doi:10.1115/1.4023692.

[EH69]

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[EB90]

Adrian Luis Eterovic and Klaus-Jurgen Bathe. A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures. International Journal for Numerical Methods in Engineering, 30(6):1099–1114, 1990.

[FM98]

Gilles A Francfort and J-J Marigo. Revisiting brittle fracture as an energy minimization problem. Journal of the Mechanics and Physics of Solids, 46(8):1319–1342, 1998.

[FMS22]

Johannes Friedlein, Julia Mergheim, and Paul Steinmann. Observations on additive plasticity in the logarithmic strain space at excessive strains. International Journal of Solids and Structures, 239:111416, 2022.

[GOH05]

T. Christian Gasser, Ray W Ogden, and Gerhard A Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of The Royal Society Interface, 3(6):15–35, September 2005. doi:10.1098/rsif.2005.0073.

[GFA10]

M.E. Gurtin, E. Fried, and L. Anand. The mechanics and thermodynamics of continua. Cambridge University Press, 2010. doi:10.1017/CBO9780511762956.

[Hol00]

Gerhard Holzapfel. Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester New York, 2000. ISBN 978-0-471-82319-3.

[ICR24]

Zachariah T. Irwin, John D. Clayton, and Richard A. Regueiro. A large deformation multiphase continuum mechanics model for shock loading of soft porous materials. International Journal for Numerical Methods in Engineering, 125(6):e7411, 2024. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7411, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7411, doi:https://doi.org/10.1002/nme.7411.

[JCRL85]

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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.

[LMW12]

Anders Logg, Kent-Andre Mardal, and Garth Wells. Automated solution of differential equations by the finite element method: The FEniCS book. Volume 84. Springer Science & Business Media, 2012. doi:10.1007/978-3-642-23099-8.

[MFPCL16]

Filipe Marques, Paulo Flores, J. C. Pimenta Claro, and Hamid M. Lankarani. A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dynamics, 86(3):1407–1443, November 2016. doi:10.1007/s11071-016-2999-3.

[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]

Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer-Verlag, New York, 1999.

[NGD+14]

D. R. Nolan, A. L. Gower, M. Destrade, R. W. Ogden, and J. P. McGarry. A robust anisotropic hyperelastic formulation for the modelling of soft tissue. Journal of the Mechanical Behavior of Biomedical Materials, 39:48–60, November 2014. doi:10.1016/j.jmbbm.2014.06.016.

[Ogd97]

Raymond W Ogden. Non-linear elastic deformations. Courier Dover Publications, 1997.

[PDME92]

Owen D.R.J. Peric D. and Honnor M.E. A model for finite strain elasto-plasticity based on logarithmic strains: computational issues. Computer Methods in Applied Mechanics and Engineering, 94(61):35–61, 1992. doi:10.1016/0045-7825(92)90156-e.

[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.

[VDMO13]

Luigi Vergori, Michel Destrade, Patrick McGarry, and Ray W. Ogden. On anisotropic elasticity and questions concerning its finite element implementation. Computational Mechanics, 52(5):1185–1197, November 2013. doi:10.1007/s00466-013-0871-6.

[WA90]

Gustavo Weber and Lallit Anand. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Computer Methods in Applied Mechanics and Engineering, 79(2):173–202, 1990.