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F.}, month = feb, year = {2020}, keywords = {Dynamic fracture, Boundary integral method, Cohesive zone model, Crack front waves}, pages = {103806} } @article{barras_emergence_2019, title = {Emergence of {Cracklike} {Behavior} of {Frictional} {Rupture}: {The} {Origin} of {Stress} {Drops}}, volume = {9}, shorttitle = {Emergence of {Cracklike} {Behavior} of {Frictional} {Rupture}}, url = {https://link.aps.org/doi/10.1103/PhysRevX.9.041043}, doi = {10.1103/PhysRevX.9.041043}, number = {4}, urldate = {2020-01-06}, journal = {Physical Review X}, author = {Barras, Fabian and Aldam, Michael and Roch, Thibault and Brener, Efim A. and Bouchbinder, Eran and Molinari, Jean-François}, month = nov, year = {2019}, pages = {041043} } @article{brener_unstable_2018, title = {Unstable {Slip} {Pulses} and {Earthquake} {Nucleation} as a {Nonequilibrium} {First}-{Order} {Phase} {Transition}}, volume = {121}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.234302}, doi = {10.1103/PhysRevLett.121.234302}, number = {23}, urldate = {2020-01-20}, journal = {Physical Review Letters}, author = {Brener, Efim A. and Aldam, Michael and Barras, Fabian and Molinari, Jean-François and Bouchbinder, Eran}, month = dec, year = {2018}, pages = {234302} } @article{barras_emergence_2020, title = {The emergence of crack-like behavior of frictional rupture: {Edge} singularity and energy balance}, volume = {531}, issn = {0012-821X}, shorttitle = {The emergence of crack-like behavior of frictional rupture}, url = {http://www.sciencedirect.com/science/article/pii/S0012821X19306703}, doi = {10.1016/j.epsl.2019.115978}, language = {en}, urldate = {2020-03-29}, journal = {Earth and Planetary Science Letters}, author = {Barras, Fabian and Aldam, Michael and Roch, Thibault and Brener, Efim A. and Bouchbinder, Eran and Molinari, Jean-François}, month = feb, year = {2020}, keywords = {rate-and-state friction, cracks, energy partition, frictional rupture}, pages = {115978} } @article{dieterich_modeling_1979, title = {Modeling of rock friction: 1. {Experimental} results and constitutive equations}, volume = {84}, copyright = {This paper is not subject to U.S. copyright. Published in 1979 by the American Geophysical Union.}, issn = {2156-2202}, shorttitle = {Modeling of rock friction}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB084iB05p02161}, doi = {10.1029/JB084iB05p02161}, language = {en}, number = {B5}, urldate = {2019-04-09}, journal = {Journal of Geophysical Research: Solid Earth}, author = {Dieterich, James H.}, year = {1979}, pages = {2161--2168} } @article{ruina_slip_1983, title = {Slip instability and state variable friction laws}, volume = {88}, copyright = {Copyright 1983 by the American Geophysical Union.}, issn = {2156-2202}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB088iB12p10359}, doi = {10.1029/JB088iB12p10359}, language = {en}, number = {B12}, journal = {Journal of Geophysical Research: Solid Earth}, author = {Ruina, Andy}, year = {1983}, pages = {10359--10370} } @article{aldam_critical_2017, title = {Critical {Nucleation} {Length} for {Accelerating} {Frictional} {Slip}}, volume = {44}, copyright = {©2017. American Geophysical Union. All Rights Reserved.}, issn = {1944-8007}, url = {https://agupubs.pericles-prod.literatumonline.com/doi/abs/10.1002/2017GL074939}, doi = {10.1002/2017GL074939}, language = {en}, number = {22}, journal = {Geophysical Research Letters}, author = {Aldam, Michael and Weikamp, Marc and Spatschek, Robert and Brener, Efim A. and Bouchbinder, Eran}, year = {2017}, keywords = {aseismic slip, bimaterial interfaces, earthquake nucleation, finite-size systems, frictional instability, stability analysis}, pages = {11,390--11,398} } @article{ida_cohesive_1972, title = {Cohesive force across the tip of a longitudinal-shear crack and {Griffith}'s specific surface energy}, volume = {77}, copyright = {Copyright 1972 by the American Geophysical Union.}, issn = {2156-2202}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB077i020p03796}, doi = {https://doi.org/10.1029/JB077i020p03796}, language = {en}, number = {20}, urldate = {2020-11-27}, journal = {Journal of Geophysical Research (1896-1977)}, author = {Ida, Yoshiaki}, year = {1972}, note = {\_eprint: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JB077i020p03796}, keywords = {Fractures, Seismology}, pages = {3796--3805} } @article{palmer_growth_1973, title = {The growth of slip surfaces in the progressive failure of over-consolidated clay}, volume = {332}, url = {https://royalsocietypublishing.org/doi/10.1098/rspa.1973.0040}, doi = {10.1098/rspa.1973.0040}, number = {1591}, urldate = {2020-11-27}, journal = {Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences}, author = {Palmer, Andrew Clennel and Rice, James Robert and Hill, Robert}, month = apr, year = {1973}, note = {Publisher: Royal Society}, pages = {527--548} } @article{ortiz_finite-deformation_1999, title = {Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis}, volume = {44}, copyright = {Copyright © 1999 John Wiley \& Sons, Ltd.}, issn = {1097-0207}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819990330%2944%3A9%3C1267%3A%3AAID-NME486%3E3.0.CO%3B2-7}, doi = {https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7}, language = {en}, number = {9}, urldate = {2020-11-28}, journal = {International Journal for Numerical Methods in Engineering}, author = {Ortiz, M. and Pandolfi, A.}, year = {1999}, keywords = {cohesive law, crack propagation, dynamic fracture, finite deformations, finite element, three dimensional}, pages = {1267--1282}, } +@article{prakash_frictional_1998, + title = {Frictional {Response} of {Sliding} {Interfaces} {Subjected} to {Time} {Varying} {Normal} {Pressures}}, + volume = {120}, + issn = {0742-4787}, + url = {https://asmedigitalcollection.asme.org/tribology/article/120/1/97/439195/Frictional-Response-of-Sliding-Interfaces}, + doi = {10.1115/1.2834197}, + language = {en}, + number = {1}, + urldate = {2020-11-28}, + journal = {Journal of Tribology}, + author = {Prakash, Vikas}, + month = jan, + year = {1998}, + note = {Publisher: American Society of Mechanical Engineers Digital Collection}, + pages = {97--102} +} + @misc{pybind11, author = {Wenzel Jakob and Jason Rhinelander and Dean Moldovan}, year = {2017}, note = {https://github.com/pybind/pybind11}, title = {pybind11 -- Seamless operability between C++11 and Python} } @misc{qdyn, author= {Luo,Yingdi and Ampuero, Jean Paul and, Galvez, Percy and van den Ende, Martijn and Idini, Benjamin}, year = {2017}, doi = {10.5281/zenodo.322459}, title = {QDYN: a Quasi-DYNamic earthquake simulator} } diff --git a/paper.md b/paper.md index 6cbad5b..258128b 100644 --- a/paper.md +++ b/paper.md @@ -1,73 +1,81 @@ --- title: 'cRacklet: a spectral boundary integral method library for interfacial rupture simulation' tags: - boundary integral - dynamic rupture - elastodynamics - friction - c++ - python authors: - name: Thibault Roch orcid: 0000-0002-2495-8841 affiliation: 1 - name: Fabian Barras orcid: 0000-0003-1109-0200 affiliation: "1, 2" - name: Philippe H Geubelle orcid: 0000-0002-4670-5474 affiliation: 3 - name: Jean-François Molinari orcid: 0000-0002-1728-1844 affiliation: 1 affiliations: - name: Civil Engineering Institute, École Polytechnique Fédérale de Lausanne, Switzerland index: 1 - name: The Njord Centre Department of Physics, Department of Geosciences, University of Oslo, Norway index: 2 - name: Department of Aerospace Engineering of the University of Illinois at Urbana-Champaign, United States of America index: 3 date: 28 November 2020 bibliography: paper.bib --- # Summary The study of dynamically propagating rupture along faults is of prime importance in fields ranging from engineering to geosciences. Numerical simulations of these phenomena are computationally costly and challenging. A fine discretisation in time and space is required to accurately represent singularities and discontinuities near rupture edges but simulations must also involve larger lengthscale such as the propagation length. In addition, the behavior of such interfaces can be highly non-linear thus increasing the problem complexity. Conventional numerical approaches for fracture problem, for instance the use of cohesive elements in finite-element method [@ortiz_finite-deformation_1999], requires to discretize the whole body containing the fault and is consequently computationally expensive. The use of boundary integral method, reducing the dimensionality of the problem, enable to focuss the computational efforts on the fracture plane and allows for a detailed description of the interfacial fields evolution. # Statement of need -`cRacklet` is a C++ library with a Python interface ([@pybind11]) developed as a collaboration between the Computational Solid Mechanics Laboratory at EPFL and the the Department of Aerospace Engineering of the university of Illinois at Urbana-Champaign that implements a spectral formulation of the elastodynamics boundary integral relations between the displacements and the corresponding traction stress acting at a planar interface between two solids. [@geubelle_spectral_1995] , [@breitenfeld_numerical_1998]. The stresses acting on the interfaces are partly computed form of the history of the displacement fields in the Fourrier domain, which are computed efficiently using FFTW3/OPENMP. The presciption of an interfacial behavior allows to solve for the equilibrium at a given time step, and time integration is achieved using an explicit time stepping scheme. cRacklet is aimed at researchers interested in interfacial dynamics, ranging from nucleation problem to dynamic propagation of rupture fronts. +`cRacklet` is a C++ library with a Python interface [@pybind11] developed as a collaboration between the Computational Solid Mechanics Laboratory at EPFL and the the Department of Aerospace Engineering of the university of Illinois at Urbana-Champaign that implements a spectral formulation of the elastodynamics boundary integral relations between the displacements and the corresponding traction stress acting at a planar interface between two homogeneous elastic solids [@geubelle_spectral_1995] , [@breitenfeld_numerical_1998]. The stresses acting on the interfaces are partly computed with a convolution of the interfacial displacements history in the Fourrier domain, computed efficiently with FFTW3/OPENMP. The presciption of an interfacial behavior allows to solve for the equilibrium at a given time step. Time integration is achieved using an explicit time stepping scheme. cRacklet is aimed at researchers interested in interfacial dynamics, ranging from nucleation problem to dynamic propagation of rupture fronts. # Features -cRacklet allows for planar rupture interface simulations loaded in any directions. cRacklet handle the simulation of interfaces bonded between dissimilar elastic solids. Any stress or material heterogeneity along the fracture plane can be resolved using cRacklet. Several interfacial behavior are included in the library, such as: +cRacklet allows for planar rupture interface simulations loaded in any combination of normal traction, in-plane and out-of-plane shear sollicitations. cRacklet handle the simulation of interfaces bonded between dissimilar elastic solids. Any stress or material heterogeneity along the fracture plane can be resolved using cRacklet. Several interfacial behavior are included in the library, such as: -- slip-weakening laws [@ida_cohesive_1972] [@palmer_growth_1973] with the possibility to coupled with standard Coulomb friction law. +- Slip-weakening laws [@ida_cohesive_1972] [@palmer_growth_1973]. This behavior can be coupled with a classical Coulomb friction law or a regularized one [@prakash_frictional_1998] to handle friction emerging from the contact of the two surfaces. -- several formulation of rate and state dependant friction laws [@dieterich_modeling_1979], [@ruina_slip_1983], [@aldam_critical_2017] +- Rate and state dependant friction laws. Original formulations by [@dieterich_modeling_1979] and [@ruina_slip_1983]. N-shape formulation proposed in [@aldam_critical_2017] Existing softwares dealing with interfacial rupture are based on a simplified formulation, known as the quasi-dynamic approximation [@qdyn]. We are not aware of any public software package including the implementation of the full elastodynamics equations using the so-called boundary integral spectral method. +# Performance + +Comparison with Akantu? + +# Example + +Add a nice figure with interesting behavior... (Space time diagram of something...) + # Publications The following publications have been made possible with cRacklet: - @barras_study_2014 - @barras_interplay_2017 - @brener_unstable_2018 - @barras_emergence_2019 - @barras_emergence_2020 - @fekak_crack_2020 # Acknowledgements We acknowledge the financial support of the Swiss National Science Foundation (grants #162569 and ...) # References