From c9cdb2c28d8e7b46814b8e8d5b8f6c0b7c878e0c Mon Sep 17 00:00:00 2001 From: kumiori Date: Tue, 3 Dec 2024 14:19:11 +0100 Subject: [PATCH] fixing bib --- paper/paper.bib | 124 ++++++++++++++++++++++++++++++++---------------- 1 file changed, 83 insertions(+), 41 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 5ce62dc..affab1c 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -18,18 +18,21 @@ @article{SICSIC volume = {63}, year = {2014}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022509613001786}, - bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2013.09.003}} + bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2013.09.003} + } @article{bazant, abstract = {We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated following a variational approach based on the principles of irreversibility, stability and energy balance. Applied to a monotonically increasing traction test of a one-dimensional bar, we consider the homogeneous response where both the strain and the damage fields are uniform in space. In the case of a softening behavior, we show that the homogeneous state of the bar at a given time is stable provided that the length of the bar is less than a state dependent critical value and unstable otherwise. However, we also show that bifurcations can appear even if the homogeneous state is stable. All these results are obtained in a closed form. Finally, we propose a practical method to identify the two constitutive functions. This method is based on the measure of the homogeneous response in a situation where this response is stable without possibility of bifurcation, and on a procedure which gives the opportunity to detect its loss of stability. All the theoretical analyses are illustrated by examples.}, author = {Zden\v{e}k P. Ba\v{z}ant}, doi = {10.1061/(ASCE)0733-9399(1988)114:12(2013)}, journal = {Journal of Engineering Mechanics}, - title = {{Stable States and Paths of Stmuctures with Plasticity or Damage}}, + title = {{Stable States and Paths of Stmuctures with Plasticity or Damage} + }, volume = {114}, year = {1988}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S002250961100055X}, - bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2011.03.010}} + bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2011.03.010} + } @book{bourdin:2008-the-variational, abstract = {We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated following a variational approach based on the principles of irreversibility, stability and energy balance. Applied to a monotonically increasing traction test of a one-dimensional bar, we consider the homogeneous response where both the strain and the damage fields are uniform in space. In the case of a softening behavior, we show that the homogeneous state of the bar at a given time is stable provided that the length of the bar is less than a state dependent critical value and unstable otherwise. However, we also show that bifurcations can appear even if the homogeneous state is stable. All these results are obtained in a closed form. Finally, we propose a practical method to identify the two constitutive functions. This method is based on the measure of the homogeneous response in a situation where this response is stable without possibility of bifurcation, and on a procedure which gives the opportunity to detect its loss of stability. All the theoretical analyses are illustrated by examples.}, @@ -44,7 +47,8 @@ @book{bourdin:2008-the-variational title = {The variational approach to fracture}, volume = {91}, year = {2008}, - bdsk-url-1 = {https://doi.org/10.1007/978-1-4020-6395-4}} + bdsk-url-1 = {https://doi.org/10.1007/978-1-4020-6395-4} + } @article{PETRYK, abstract = {Second-order rate constitutive equations are formulated for a time-independent elastic-plastic material, obeying the normality flow rule with a smooth yield surface. Under specified regularity restrictions imposed on the involved fields, the regular second-order rate boundary value problem with quasistatic accelerations as unknowns is posed. It is shown that every solution of this generally non-linear rate problem is governed by a variational principle and that the corresponding functional reaches a strict absolute minimum, provided the solution satisfies a sufficient uniqueness condition. With the same incrementally linear comparison solid, Hill's exclusion condition rules out not only a first- but also a second-order bifurcation. The criticality of the exclusion condition is discussed and conditions are indicated under which a second-order bifurcation becomes possible, while the first-order rate problem is still uniquely solvable.}, @@ -59,14 +63,15 @@ @article{PETRYK volume = {33}, year = {1985}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0022509685900043}, - bdsk-url-2 = {https://doi.org/10.1016/0022-5096(85)90004-3}} + bdsk-url-2 = {https://doi.org/10.1016/0022-5096(85)90004-3} + } @incollection{Quoc2002, author = {Nguyen, Quoc Son}, booktitle = {Continuum thermodynamics: the art and science of modeling matter's behavior}, date-added = {2024-08-02 17:04:28 +0900}, date-modified = {2024-08-02 17:06:32 +0900}, - doi = {10.1007/0-306-46946-4\_26}, + doi = {10.1007/0-306-46946-4}, editor = {G\'erard Maugin and Raymonde Drouot and Fran\c{c}ois Sidoroff}, hal_id = {hal-00112276}, hal_version = {v1}, @@ -76,10 +81,12 @@ @incollection{Quoc2002 title = {Standard dissipative systems and stability analysis}, year = {2000}, bdsk-url-1 = {https://hal.science/hal-00112276}, - bdsk-url-2 = {https://doi.org/10.1007/0-306-46946-4%5C_26}} + bdsk-url-2 = {https://doi.org/10.1007/0-306-46946-4%5C_26} + } @article{Quoc, - abstract = {{This paper addresses stability and bifurcation analysis for common systems of solids in the framework of plasticity, of friction and of fracture mechanics. Although physically different, usual time-independent laws adopted in these domains lead to a certain mathematical similarity concerning the quasi-static behaviour of materials and structures. These mechanical systems can be described practically in the same mathematical manner concerning their quasi-static evolution and in particular concerning the stability of their response. Our objective is to present within this framework a review of principal results of the recent literature on these subjects in relation with some energy-related considerations and with an unified description based upon energy and dissipation analysis.}}, + abstract = {{This paper addresses stability and bifurcation analysis for common systems of solids in the framework of plasticity, of friction and of fracture mechanics. Although physically different, usual time-independent laws adopted in these domains lead to a certain mathematical similarity concerning the quasi-static behaviour of materials and structures. These mechanical systems can be described practically in the same mathematical manner concerning their quasi-static evolution and in particular concerning the stability of their response. Our objective is to present within this framework a review of principal results of the recent literature on these subjects in relation with some energy-related considerations and with an unified description based upon energy and dissipation analysis.} + }, author = {Nguyen, Quoc Son}, date-added = {2024-08-02 17:02:15 +0900}, date-modified = {2024-08-02 17:02:41 +0900}, @@ -92,15 +99,20 @@ @article{Quoc title = {Bifurcation and Stability in Dissipative Media (Plasticity, Friction, Fracture)}, volume = {47}, year = {1994}, - bdsk-url-1 = {https://doi.org/10.1115/1.3111068}} + bdsk-url-1 = {https://doi.org/10.1115/1.3111068} + } @unpublished{camilla, author = {Camilla Zolesi and Corrado Maurini}, date-added = {2024-08-02 16:57:06 +0900}, date-modified = {2024-08-02 16:58:32 +0900}, - journal = {preprint, \url{https://hal.sorbonne-universite.fr/hal-04552309}}, - title = {Stability and crack nucleation in variational phase-field models of fracture: effects of length-scales and stress multi-axiality}} - year = {}} + doi = {10.1016/j.jmps.2024.105802}, + journal = {preprint, \url{https://hal.sorbonne-universite.fr/hal-04552309} + }, + title = {Stability and crack nucleation in variational phase-field models of fracture: effects of length-scales and stress multi-axiality} + } + year = {} + } @article{Pham2013aa, abstract = {Considering a family of gradient-enhanced damage models and taking advantage of its variational formulation, we study the stability of homogeneous states in a full three-dimensional context. We show that gradient terms have a stabilizing effect, but also how those terms induce structural effects. We emphasize the great importance of the type of boundary conditions, the size and the shape of the body on the stability properties of such states.}, @@ -113,10 +125,12 @@ @article{Pham2013aa journal = {Journal of Elasticity}, number = {1}, pages = {63--93}, - title = {{Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting}}, + title = {{Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting} + }, volume = {110}, year = {2013}, - bdsk-url-1 = {https://doi.org/10.1007/s10659-012-9382-5}} + bdsk-url-1 = {https://doi.org/10.1007/s10659-012-9382-5} + } @article{MIEHE20102765, abstract = {The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. Following our recent work [C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically-consistent phase field models of fracture: Variational principles and multi-field fe implementations, International Journal for Numerical Methods in Engineering DOI:10.1002/nme.2861] on phase-field-type fracture, we propose in this paper a new variational framework for rate-independent diffusive fracture that bases on the introduction of a local history field. It contains a maximum reference energy obtained in the deformation history, which may be considered as a measure for the maximum tensile strain obtained in history. It is shown that this local variable drives the evolution of the crack phase field. The introduction of the history field provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a new algorithmic treatment of diffusive fracture. Here, we propose an extremely robust operator split scheme that successively updates in a typical time step the history field, the crack phase field and finally the displacement field. A regularization based on a viscous crack resistance that even enhances the robustness of the algorithm may easily be added. The proposed algorithm is considered to be the canonically simple scheme for the treatment of diffusive fracture in elastic solids. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples.}, @@ -133,7 +147,8 @@ @article{MIEHE20102765 volume = {199}, year = {2010}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0045782510001283}, - bdsk-url-2 = {https://doi.org/10.1016/j.cma.2010.04.011}} + bdsk-url-2 = {https://doi.org/10.1016/j.cma.2010.04.011} + } @article{Miehe10, abstract = {Abstract The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase-field. In this paper, we outline a thermodynamically consistent framework for phase-field models of crack propagation in elastic solids, develop incremental variational principles and consider their numerical implementations by multi-field finite element methods. We start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that Γ-converges for vanishing length-scale parameter to a sharp crack topology functional. This functional provides the basis for the definition of suitable convex dissipation functions that govern the evolution of the crack phase-field. Here, we propose alternative rate-independent and viscous over-force models that ensure the local growth of the phase-field. Next, we define an energy storage function whose positive tensile part degrades with increasing phase-field. With these constitutive functionals at hand, we derive the coupled balances of quasi-static stress equilibrium and gradient-type phase-field evolution in the solid from the argument of virtual power. Here, we consider a canonical two-field setting for rate-independent response and a time-regularized three-field formulation with viscous over-force response. It is then shown that these balances follow as the Euler equations of incremental variational principles that govern the multi-field problems. These principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation, including features such as the symmetry of the monolithic tangent matrices. We demonstrate the performance of the proposed phase-field formulations of fracture by means of representative numerical examples. Copyright {\copyright} 2010 John Wiley \& Sons, Ltd.}, @@ -149,7 +164,8 @@ @article{Miehe10 volume = {83}, year = {2010}, bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.2861}, - bdsk-url-2 = {https://doi.org/10.1002/nme.2861}} + bdsk-url-2 = {https://doi.org/10.1002/nme.2861} + } @article{FRANCFORT, abstract = {A variational model of quasistatic crack evolution is proposed. Although close in spirit to Griffith's theory of brittle fracture, the proposed model however frees itself of the usual constraints of that theory : a preexisting crack and a well-defined crack path. In contrast, crack initiation as well as crack path can be quantified, as demonstrated on explicitly computable examples. Furthermore the model lends itself to numerical implementation in more complex settings.}, @@ -165,7 +181,8 @@ @article{FRANCFORT volume = {46}, year = {1998}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022509698000349}, - bdsk-url-2 = {https://doi.org/10.1016/S0022-5096(98)00034-9}} + bdsk-url-2 = {https://doi.org/10.1016/S0022-5096(98)00034-9} + } @article{dalcinpazklercosimo2011, author = {Lisandro D. Dalcin and Rodrigo R. Paz and Pablo A. Kler and Alejandro Cosimo}, @@ -176,25 +193,31 @@ @article{dalcinpazklercosimo2011 note = {New Computational Methods and Software Tools}, number = {9}, pages = {1124 - 1139}, - title = {{Parallel distributed computing using Python}}, + title = {{Parallel distributed computing using Python} + }, volume = {34}, year = {2011}, - bdsk-url-1 = {https://doi.org/10.1016/j.advwatres.2011.04.013}} + bdsk-url-1 = {https://doi.org/10.1016/j.advwatres.2011.04.013} + } @article{moreau:hal-01867187, author = {Moreau, Jean Jacques}, date-added = {2024-07-31 15:03:36 +0900}, hal_id = {hal-01867187}, hal_version = {v1}, - journal = {{Comptes rendus hebdomadaires des s{\'e}ances de l'Acad{\'e}mie des sciences}}, + journal = {{Comptes rendus hebdomadaires des s{\'e}ances de l'Acad{\'e}mie des sciences} + }, pages = {238-240}, - publisher = {{Gauthier-Villars}}, - title = {{D{\'e}composition orthogonale d'un espace hilbertien selon deux c{\^o}nes mutuellement polaires}}, + publisher = {{Gauthier-Villars} + }, + title = {{D{\'e}composition orthogonale d'un espace hilbertien selon deux c{\^o}nes mutuellement polaires} + }, pdf = {https://hal.science/hal-01867187/file/D%C3%A9composition_orthogonale_espace_hilbertien_Moreau_CRAS_1962.pdf}, url = {https://hal.science/hal-01867187}, volume = {255}, year = {1962}, - bdsk-url-1 = {https://hal.science/hal-01867187}} + bdsk-url-1 = {https://hal.science/hal-01867187} + } @article{pham:2011-the-issues, abstract = {We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated following a variational approach based on the principles of irreversibility, stability and energy balance. Applied to a monotonically increasing traction test of a one-dimensional bar, we consider the homogeneous response where both the strain and the damage fields are uniform in space. In the case of a softening behavior, we show that the homogeneous state of the bar at a given time is stable provided that the length of the bar is less than a state dependent critical value and unstable otherwise. However, we also show that bifurcations can appear even if the homogeneous state is stable. All these results are obtained in a closed form. Finally, we propose a practical method to identify the two constitutive functions. This method is based on the measure of the homogeneous response in a situation where this response is stable without possibility of bifurcation, and on a procedure which gives the opportunity to detect its loss of stability. All the theoretical analyses are illustrated by examples.}, @@ -210,7 +233,8 @@ @article{pham:2011-the-issues volume = {59}, year = {2011}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S002250961100055X}, - bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2011.03.010}} + bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2011.03.010} + } @article{bourdin:2000-numerical, abstract = {The numerical implementation of the model of brittle fracture developed in Francfort and Marigo (1998. J. Mech. Phys. Solids 46 (8), 1319--1342) is presented. Various computational methods based on variational approximations of the original functional are proposed. They are tested on several antiplanar and planar examples that are beyond the reach of the classical computational tools of fracture mechanics.}, @@ -226,7 +250,8 @@ @article{bourdin:2000-numerical volume = {48}, year = {2000}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022509699000289}, - bdsk-url-2 = {https://doi.org/10.1016/S0022-5096(99)00028-9}} + bdsk-url-2 = {https://doi.org/10.1016/S0022-5096(99)00028-9} + } @article{hernandez:2005-slepc, abstract = {The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETSc and enforces the same programming paradigm.The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations. Therefore, most of the methods offered by the library are projection methods such as Arnoldi or Lanczos, or other methods with similar properties. SLEPc provides basic methods as well as more sophisticated algorithms. It also provides built-in support for spectral transformations such as the shift-and-invert technique. SLEPc is a general library in the sense that it covers standard and generalized eigenvalue problems, both Hermitian and non-Hermitian, with either real or complex arithmetic.SLEPc can be easily applied to real world problems. To illustrate this, several case studies arising from real applications are presented and solved with SLEPc with little programming effort. The addressed problems include a matrix-free standard problem, a complex generalized problem, and a singular value decomposition. The implemented codes exhibit good properties regarding flexibility as well as parallel performance.}, @@ -240,7 +265,8 @@ @article{hernandez:2005-slepc title = {{SLEPc}: A scalable and flexible toolkit for the solution of eigenvalue problems}, volume = {31}, year = {2005}, - bdsk-url-1 = {https://doi.org/10.1145/1089014.1089019}} + bdsk-url-1 = {https://doi.org/10.1145/1089014.1089019} + } @article{marigo:2023-la-mecanique, abstract = {Gradient damage models used in phase-field approaches to brittle fracture are characterised by material softening and instabilities. We present novel numerical techniques for the bifurcation and stability analysis along quasi-static evolution paths as well as practical tools to select stable evolutions. Our approach stems from the variational approach to fracture and the theory of rate-independent irreversible processes whereby a quasi-static evolution is formulated in terms of incremental energy minimisation under unilateral constraints. Focusing on the discrete setting obtained with finite elements techniques, we discuss the links between bifurcation criteria for an evolution and stability of equilibrium states. Key concepts are presented through the analytical solution of a two-degrees-of-freedom model featuring a continuum family of bifurcation branches. We introduce numerical methods to (i) assess (second-order) stability conditions for time-discrete evolutions subject to damage irreversibility, and (ii) to select possible stable evolutions based on an energetic criterion. Our approach is based on the solution of a coupled eigenvalue problem which accounts for the time-discrete irreversibility constraint on damage. Several numerical examples illustrate that this approach allows us to filter out unstable solutions provided by standard (first-order) minimisation algorithms as well as to effectively compute stable evolution paths. We demonstrate our purpose on a multifissuration problem featuring complex fracture patterns, to show how the eigenvalue analysis enables to compute and retrieve morphological properties of emerging cracks.}, @@ -253,7 +279,8 @@ @article{marigo:2023-la-mecanique year = {2023}, bdsk-file-1 = {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}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022509621001010}, - bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2021.104424}} + bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2021.104424} + } @url{Habera:aa, author = {Michal Habera and Andreas Zilian}, @@ -262,7 +289,8 @@ @url{Habera:aa title = {dolfiny: Python wrappers for DOLFINx}, url = {https://github.com/michalhabera/dolfiny}, year = {2024}, - bdsk-url-1 = {https://github.com/michalhabera/dolfiny}} + bdsk-url-1 = {https://github.com/michalhabera/dolfiny} + } @misc{dolfinx2023preprint, author = {Baratta, Igor A. and Dean, Joseph P. and Dokken, J{\o}rgen S. and Habera, Michal and Hale, Jack S. and Richardson, Chris N. and Rognes, Marie E. and Scroggs, Matthew W. and Sime, Nathan and Wells, Garth N.}, @@ -271,19 +299,23 @@ @misc{dolfinx2023preprint doi = {10.5281/zenodo.10447666}, month = dec, publisher = {Zenodo}, - title = {{DOLFINx: The next generation FEniCS problem solving environment}}, + title = {{DOLFINx: The next generation FEniCS problem solving environment} + }, year = 2023, - bdsk-url-1 = {https://doi.org/10.5281/zenodo.10447666}} + bdsk-url-1 = {https://doi.org/10.5281/zenodo.10447666} + } @misc{petsc-web-page, author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown and Peter Brune and Kris Buschelman and Emil~M. Constantinescu and Lisandro Dalcin and Alp Dener and Victor Eijkhout and Jacob Faibussowitsch and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang}, date-added = {2024-03-01 15:59:45 +0100}, date-modified = {2024-03-01 15:59:45 +0100}, - howpublished = {\url{https://petsc.org/}}, + howpublished = {\url{https://petsc.org/} + }, title = {{PETS}c {W}eb page}, url = {https://petsc.org/}, year = {2023}, - bdsk-url-1 = {https://petsc.org/}} + bdsk-url-1 = {https://petsc.org/} + } @techreport{petsc-user-ref, author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown and Peter Brune and Kris Buschelman and Emil Constantinescu and Lisandro Dalcin and Alp Dener and Victor Eijkhout and Jacob Faibussowitsch and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang}, @@ -293,8 +325,10 @@ @techreport{petsc-user-ref institution = {Argonne National Laboratory}, number = {ANL-21/39 - Revision 3.20}, title = {{PETSc/TAO} Users Manual}, + doi = {10.2172/2205494}, year = {2023}, - bdsk-url-1 = {https://doi.org/10.2172/2205494}} + bdsk-url-1 = {https://doi.org/10.2172/2205494} + } @article{leon-baldelli:2021-numerical, abstract = {Gradient damage models used in phase-field approaches to brittle fracture are characterised by material softening and instabilities. We present novel numerical techniques for the bifurcation and stability analysis along quasi-static evolution paths as well as practical tools to select stable evolutions. Our approach stems from the variational approach to fracture and the theory of rate-independent irreversible processes whereby a quasi-static evolution is formulated in terms of incremental energy minimisation under unilateral constraints. Focusing on the discrete setting obtained with finite elements techniques, we discuss the links between bifurcation criteria for an evolution and stability of equilibrium states. Key concepts are presented through the analytical solution of a two-degrees-of-freedom model featuring a continuum family of bifurcation branches. We introduce numerical methods to (i) assess (second-order) stability conditions for time-discrete evolutions subject to damage irreversibility, and (ii) to select possible stable evolutions based on an energetic criterion. Our approach is based on the solution of a coupled eigenvalue problem which accounts for the time-discrete irreversibility constraint on damage. Several numerical examples illustrate that this approach allows us to filter out unstable solutions provided by standard (first-order) minimisation algorithms as well as to effectively compute stable evolution paths. We demonstrate our purpose on a multifissuration problem featuring complex fracture patterns, to show how the eigenvalue analysis enables to compute and retrieve morphological properties of emerging cracks.}, @@ -313,7 +347,8 @@ @article{leon-baldelli:2021-numerical year = {2021}, bdsk-file-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhbxBcAC4ALgAvAC4ALgAvAC4ALgAvAC4ALgAvAC4ALgAvAEwAaQBiAHIAYQByAHkALwBNAG8AYgBpAGwAZQAgAEQAbwBjAHUAbQBlAG4AdABzAC8AYwBvAG0AfgBhAHAAcABsAGUAfgBDAGwAbwB1AGQARABvAGMAcwAvAFAAYQBwAGUAcgBzAC8AbABlAG8DAQBuACAAYgBhAGwAZABlAGwAbABpAC0AMgAwADIAMQAgADIALgBwAGQAZk8RAcwAAAAAAcwAAgAADE1hY2ludG9zaCBIRAAAAAAAAAAAAAAAAAAAAOGUkbtCRAAB/////xhsZZduIGJhbGRlbGxpLTIwMjEgMi5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD/////3xvc9wAAAAAAAAAAAAUABQAACiBjdQAAAAAAAAAAAAAAAAAGUGFwZXJzAAIAXy86VXNlcnM6a3VtaW9yaTM6TGlicmFyeTpNb2JpbGUgRG9jdW1lbnRzOmNvbX5hcHBsZX5DbG91ZERvY3M6UGFwZXJzOmxlb8yBbiBiYWxkZWxsaS0yMDIxIDIucGRmAAAOADQAGQBsAGUAbwMBAG4AIABiAGEAbABkAGUAbABsAGkALQAyADAAMgAxACAAMgAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAXVVzZXJzL2t1bWlvcmkzL0xpYnJhcnkvTW9iaWxlIERvY3VtZW50cy9jb21+YXBwbGV+Q2xvdWREb2NzL1BhcGVycy9sZW/MgW4gYmFsZGVsbGktMjAyMSAyLnBkZgAAEwABLwAAFQACAA///wAAAAgADQAaACQA3wAAAAAAAAIBAAAAAAAAAAUAAAAAAAAAAAAAAAAAAAKv}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022509621001010}, - bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2021.104424}} + bdsk-url-2 = {https://doi.org/10.1016/j.jmps.2021.104424} + } @techreport{balay:2017-petsc, author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Jed Brown and Peter Brune and Kris Buschelman and Lisandro Dalcin and Victor Eijkhout and Dinesh Kaushik and Matthew~G. Knepley and Dave~A. May and Lois Curfman McInnes and William~D. Gropp and Karl Rupp and Patrick Sanan and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang}, @@ -323,7 +358,8 @@ @techreport{balay:2017-petsc number = {ANL-95/11 - Revision 3.8}, title = {PETSc Users Manual}, year = {2017}, - bdsk-file-1 = {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}} + bdsk-file-1 = {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} + } @book{mielke, author = {Mielke, A. and Roub\'{i}\v{c}ek, A.}, @@ -334,7 +370,8 @@ @book{mielke publisher = {Springer New York, NY}, title = {Rate-Independent Systems}, year = {2015}, - bdsk-url-1 = {https://doi.org/10.1016/j.advwatres.2011.04.013}} + bdsk-url-1 = {https://doi.org/10.1016/j.advwatres.2011.04.013} + } @article{pinto-da-costa:2010-cone-constrained, abstract = {Equilibria in mechanics or in transportation models are not always expressed through a system of equations, but sometimes they are characterized by means of complementarity conditions involving a convex cone. This work deals with the analysis of cone-constrained eigenvalue problems. We discuss some theoretical issues like, for instance, the estimation of the maximal number of eigenvalues in a cone-constrained problem. Special attention is paid to the Paretian case. As a short addition to the theoretical part, we introduce and study two algorithms for solving numerically such type of eigenvalue problems.}, @@ -348,23 +385,27 @@ @article{pinto-da-costa:2010-cone-constrained journal = {Computational Optimization and Applications}, number = {1}, pages = {25--57}, - title = {{Cone-constrained eigenvalue problems: theory and algorithms}}, + title = {{Cone-constrained eigenvalue problems: theory and algorithms} + }, volume = {45}, year = {2010}, bdsk-file-1 = {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}, - bdsk-url-1 = {https://doi.org/10.1007/s10589-008-9167-8}} + bdsk-url-1 = {https://doi.org/10.1007/s10589-008-9167-8} + } @book{jorge-nocedal:1999-numerical, author = {Jorge Nocedal, Stephen Wright}, date-added = {2019-11-27 14:27:43 +0100}, date-modified = {2022-08-10 11:03:49 +0200}, - isbn = {0387987932,9780387987934,9780387227429}, + isbn = {0387303030}, publisher = {Springer}, series = {Springer series in operations research}, title = {Numerical optimization}, year = {1999}, + doi = {10.1007/978-0-387-40065-5}, bdsk-file-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxBZLi4vLi4vLi4vLi4vLi4vTGlicmFyeS9Nb2JpbGUgRG9jdW1lbnRzL2NvbX5hcHBsZX5DbG91ZERvY3MvUGFwZXJzL2pvcmdlIG5vY2VkYWwtMTk5OS5wZGZPEQG+AAAAAAG+AAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADhlJG7QkQAAf////8Wam9yZ2Ugbm9jZWRhbC0xOTk5LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA/////9n52YQAAAAAAAAAAAAFAAUAAAogY3UAAAAAAAAAAAAAAAAABlBhcGVycwACAFsvOlVzZXJzOmt1bWlvcmkzOkxpYnJhcnk6TW9iaWxlIERvY3VtZW50czpjb21+YXBwbGV+Q2xvdWREb2NzOlBhcGVyczpqb3JnZSBub2NlZGFsLTE5OTkucGRmAAAOAC4AFgBqAG8AcgBnAGUAIABuAG8AYwBlAGQAYQBsAC0AMQA5ADkAOQAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAWVVzZXJzL2t1bWlvcmkzL0xpYnJhcnkvTW9iaWxlIERvY3VtZW50cy9jb21+YXBwbGV+Q2xvdWREb2NzL1BhcGVycy9qb3JnZSBub2NlZGFsLTE5OTkucGRmAAATAAEvAAAVAAIAD///AAAACAANABoAJACAAAAAAAAAAgEAAAAAAAAABQAAAAAAAAAAAAAAAAAAAkI=}, - bdsk-url-1 = {http://gen.lib.rus.ec/book/index.php?md5=9F2AB259C0C662B59CDA32277F1CA284}} + bdsk-url-1 = {http://gen.lib.rus.ec/book/index.php?md5=9F2AB259C0C662B59CDA32277F1CA284} + } @article{moreau:1962-decomposition, annote = {⟨hal-01867187⟩}, @@ -376,4 +417,5 @@ @article{moreau:1962-decomposition title = {D{\'e}composition orthogonale d'un espace hilbertien selon deux c{\^o}nes mutuellement polaires}, volume = {255}, year = {1962}, - bdsk-file-1 = {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}} + bdsk-file-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxBSLi4vLi4vLi4vLi4vLi4vTGlicmFyeS9Nb2JpbGUgRG9jdW1lbnRzL2NvbX5hcHBsZX5DbG91ZERvY3MvUGFwZXJzL21vcmVhdS0xOTYyLnBkZk8RAaAAAAAAAaAAAgAADE1hY2ludG9zaCBIRAAAAAAAAAAAAAAAAAAAAOGUkbtCRAAB/////w9tb3JlYXUtMTk2Mi5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD/////30kBjQAAAAAAAAAAAAUABQAACiBjdQAAAAAAAAAAAAAAAAAGUGFwZXJzAAIAVC86VXNlcnM6a3VtaW9yaTM6TGlicmFyeTpNb2JpbGUgRG9jdW1lbnRzOmNvbX5hcHBsZX5DbG91ZERvY3M6UGFwZXJzOm1vcmVhdS0xOTYyLnBkZgAOACAADwBtAG8AcgBlAGEAdQAtADEAOQA2ADIALgBwAGQAZgAPABoADABNAGEAYwBpAG4AdABvAHMAaAAgAEgARAASAFJVc2Vycy9rdW1pb3JpMy9MaWJyYXJ5L01vYmlsZSBEb2N1bWVudHMvY29tfmFwcGxlfkNsb3VkRG9jcy9QYXBlcnMvbW9yZWF1LTE5NjIucGRmABMAAS8AABUAAgAP//8AAAAIAA0AGgAkAHkAAAAAAAACAQAAAAAAAAAFAAAAAAAAAAAAAAAAAAACHQ==} + }