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#
Indices and tables#
Halphen B. and Q. S. Nguyen. Sur les materiaux standard generalises. Journal de Mécanique, 14:39–63, 1975.
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.
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.
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.
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.
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.
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.
Lee E.H. Elastic-plastic deformation at finite strains. Journal of Applied Mechanics, 36(1):65–76, 1969. doi:10.21236/ad0678483.
M.E. Gurtin, E. Fried, and L. Anand. The mechanics and thermodynamics of continua. Cambridge University Press, 2010. doi:10.1017/CBO9780511762956.
Gerhard Holzapfel. Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester New York, 2000. ISBN 978-0-471-82319-3.
Simo J.C. and Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering, 48(1):101–118, 1985. doi:10.1016/0045-7825(85)90070-2.
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.
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.
Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer-Verlag, New York, 1999.
Raymond W Ogden. Non-linear elastic deformations. Courier Dover Publications, 1997.
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.