Brittle fracture during folding of rocks : A finite element study
Identifieur interne : 003048 ( PascalFrancis/Curation ); précédent : 003047; suivant : 003049Brittle fracture during folding of rocks : A finite element study
Auteurs : P. J Ger [Allemagne] ; S. M. Schmalholz [Suisse] ; D. W. Schmid [Norvège] ; E. Kuhl [États-Unis]Source :
- Philosophical magazine : (2003. Print) [ 1478-6435 ] ; 2008.
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Abstract
The goal of the present work is the development of a novel computational analysis tool to elaborate folding-induced fracture of geological structures. Discrete failure of brittle rocks is characterised by three sets of governing equations: the bulk problem, the interface problem and the crack problem. The former two sets which define the deformation field are highly nonlinear and strongly coupled. They are solved iteratively within a Hansbo-type finite element setting. The latter set defines the crack kinematics. It is linear and solved in a single post-processing step. To elaborate the features of the computational algorithm, we define a unique benchmark problem of a single, geometrically nonlinear plate, which is subjected to layer-parallel in-plane compression combined with different levels of superposed in-plane shear. The resulting folding, or buckling, induces brittle failure in the tensile regime. By systematically increasing the shear strain at constant compression, we develop crack deviation angle versus shear-to-compression ratio tables. We determine the corresponding damage zones, analyse the folding modes and elaborate the force versus amplification diagrams. The proposed two-field folding-induced fracture algorithm can ultimately be applied to interpret natural folded rocks and understand their evolution, structural development and histology.
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Schmid</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Physics of Geological Processes, University of Oslo</s1><s2>Oslo</s2><s3>NOR</s3><sZ>3 aut.</sZ></inist:fA14><country>Norvège</country></affiliation></author><author><name sortKey="Kuhl, E" sort="Kuhl, E" uniqKey="Kuhl E" first="E." last="Kuhl">E. Kuhl</name><affiliation wicri:level="1"><inist:fA14 i1="04"><s1>Department of Mechanical Engineering, Stanford University</s1><s2>Stanford</s2><s3>USA</s3><sZ>4 aut.</sZ></inist:fA14><country>États-Unis</country></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">09-0126196</idno><date when="2008">2008</date><idno type="stanalyst">PASCAL 09-0126196 INIST</idno><idno type="RBID">Pascal:09-0126196</idno><idno type="wicri:Area/PascalFrancis/Corpus">002F70</idno><idno type="wicri:Area/PascalFrancis/Curation">003048</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Brittle fracture during folding of rocks : A finite element study</title><author><name sortKey="J Ger, P" sort="J Ger, P" uniqKey="J Ger P" first="P." last="J Ger">P. J Ger</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Mechanical Engineering, University of Kaiserslautern</s1><s2>Kaiserslautern</s2><s3>DEU</s3><sZ>1 aut.</sZ></inist:fA14><country>Allemagne</country></affiliation></author><author><name sortKey="Schmalholz, S M" sort="Schmalholz, S M" uniqKey="Schmalholz S" first="S. M." last="Schmalholz">S. M. Schmalholz</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Geological Institute, ETH Zürich</s1><s2>Zürich</s2><s3>CHE</s3><sZ>2 aut.</sZ></inist:fA14><country>Suisse</country></affiliation></author><author><name sortKey="Schmid, D W" sort="Schmid, D W" uniqKey="Schmid D" first="D. W." last="Schmid">D. W. Schmid</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Physics of Geological Processes, University of Oslo</s1><s2>Oslo</s2><s3>NOR</s3><sZ>3 aut.</sZ></inist:fA14><country>Norvège</country></affiliation></author><author><name sortKey="Kuhl, E" sort="Kuhl, E" uniqKey="Kuhl E" first="E." last="Kuhl">E. Kuhl</name><affiliation wicri:level="1"><inist:fA14 i1="04"><s1>Department of Mechanical Engineering, Stanford University</s1><s2>Stanford</s2><s3>USA</s3><sZ>4 aut.</sZ></inist:fA14><country>États-Unis</country></affiliation></author></analytic><series><title level="j" type="main">Philosophical magazine : (2003. Print)</title><title level="j" type="abbreviated">Philos. mag. : (2003, Print)</title><idno type="ISSN">1478-6435</idno><imprint><date when="2008">2008</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Philosophical magazine : (2003. Print)</title><title level="j" type="abbreviated">Philos. mag. : (2003, Print)</title><idno type="ISSN">1478-6435</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithms</term><term>Amplification</term><term>Brittle fracture</term><term>Buckling</term><term>Damage</term><term>Deformation</term><term>Finite element method</term><term>Fractures</term><term>Interface crack</term><term>Iterative methods</term><term>Material processing</term><term>Non linear effect</term><term>Rocks</term><term>Shear</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Rupture fragile</term><term>Méthode élément fini</term><term>Fracture</term><term>Fissure interface</term><term>Déformation</term><term>Effet non linéaire</term><term>Méthode itérative</term><term>Traitement matériau</term><term>Algorithme</term><term>Cisaillement</term><term>Flambage</term><term>Endommagement</term><term>Amplification</term><term>Roche</term><term>6220M</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The goal of the present work is the development of a novel computational analysis tool to elaborate folding-induced fracture of geological structures. Discrete failure of brittle rocks is characterised by three sets of governing equations: the bulk problem, the interface problem and the crack problem. The former two sets which define the deformation field are highly nonlinear and strongly coupled. They are solved iteratively within a Hansbo-type finite element setting. The latter set defines the crack kinematics. It is linear and solved in a single post-processing step. To elaborate the features of the computational algorithm, we define a unique benchmark problem of a single, geometrically nonlinear plate, which is subjected to layer-parallel in-plane compression combined with different levels of superposed in-plane shear. The resulting folding, or buckling, induces brittle failure in the tensile regime. By systematically increasing the shear strain at constant compression, we develop crack deviation angle versus shear-to-compression ratio tables. We determine the corresponding damage zones, analyse the folding modes and elaborate the force versus amplification diagrams. The proposed two-field folding-induced fracture algorithm can ultimately be applied to interpret natural folded rocks and understand their evolution, structural development and histology.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>1478-6435</s0></fA01><fA03 i2="1"><s0>Philos. mag. : (2003, Print)</s0></fA03><fA05><s2>88</s2></fA05><fA06><s2>28-29</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Brittle fracture during folding of rocks : A finite element study</s1></fA08><fA09 i1="01" i2="1" l="ENG"><s1>Instabilities Across The Scales: Part 2</s1></fA09><fA11 i1="01" i2="1"><s1>JÄGER (P.)</s1></fA11><fA11 i1="02" i2="1"><s1>SCHMALHOLZ (S. M.)</s1></fA11><fA11 i1="03" i2="1"><s1>SCHMID (D. W.)</s1></fA11><fA11 i1="04" i2="1"><s1>KUHL (E.)</s1></fA11><fA12 i1="01" i2="1"><s1>SUIKER (Akke S. 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To elaborate the features of the computational algorithm, we define a unique benchmark problem of a single, geometrically nonlinear plate, which is subjected to layer-parallel in-plane compression combined with different levels of superposed in-plane shear. The resulting folding, or buckling, induces brittle failure in the tensile regime. By systematically increasing the shear strain at constant compression, we develop crack deviation angle versus shear-to-compression ratio tables. We determine the corresponding damage zones, analyse the folding modes and elaborate the force versus amplification diagrams. 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