Mathematical modeling of three equal collinear cracks in an orthotropic solid
We consider a homogeneous elastic, orthotropic solid containing three equal collinear cracks, loaded in tension by symmetrically distributed normal stresses. Following Guz’s representation theorem and solving Riemann–Hilbert problems we determine the expressions of the complex potentials. Using the...
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| Published in | Meccanica (Milan) Vol. 51; no. 2; pp. 329 - 339 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Springer Netherlands
01.02.2016
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| Abstract | We consider a homogeneous elastic, orthotropic solid containing three equal collinear cracks, loaded in tension by symmetrically distributed normal stresses. Following Guz’s representation theorem and solving Riemann–Hilbert problems we determine the expressions of the complex potentials. Using the asymptotic analysis, we obtain the asymptotic values of the incremental stress and displacement fields. We determine the tangential stresses near the crack tips. Using the maximum tangential stress criterion and numerical computations we study the interaction problem for a Graphite-epoxy fiber reinforced composite material. |
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| AbstractList | We consider a homogeneous elastic, orthotropic solid containing three equal collinear cracks, loaded in tension by symmetrically distributed normal stresses. Following Guz's representation theorem and solving Riemann-Hilbert problems we determine the expressions of the complex potentials. Using the asymptotic analysis, we obtain the asymptotic values of the incremental stress and displacement fields. We determine the tangential stresses near the crack tips. Using the maximum tangential stress criterion and numerical computations we study the interaction problem for a Graphite-epoxy fiber reinforced composite material. |
| Author | Craciun, E. M. Răbâea, A. Marsavina, L. Sadowski, T. |
| Author_xml | – sequence: 1 givenname: T. surname: Sadowski fullname: Sadowski, T. email: t.sadowski@pollub.pl organization: Lublin University of Technology – sequence: 2 givenname: E. M. surname: Craciun fullname: Craciun, E. M. organization: Faculty of Mathematics and Informatics, “Ovidius” University of Constanta – sequence: 3 givenname: A. surname: Răbâea fullname: Răbâea, A. organization: Faculty of Sciences, Technical University of Cluj-Napoca, N.U.C.B.M – sequence: 4 givenname: L. surname: Marsavina fullname: Marsavina, L. organization: Politehnica University of Timisoara |
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| Cites_doi | 10.1007/BF00033702 10.1007/BF00018929 10.1002/zamm.201200293 10.1007/s10778-007-0052-4 10.1016/0167-8442(90)90087-G 10.1016/0020-7225(95)00100-X 10.1016/0020-7225(78)90091-5 10.1016/j.commatsci.2009.06.006 10.1115/1.2789172 10.1007/BF02086728 10.1093/imamat/hxh060 10.1016/j.ijsolstr.2006.10.024 10.1023/A:1007549317153 10.1115/1.3656897 10.1002/(SICI)1521-4001(199812)78:12<855::AID-ZAMM855>3.0.CO;2-0 10.1016/0013-7944(86)90116-5 10.1201/9780203502815 10.1016/S0020-7683(02)00252-4 10.1016/j.commatsci.2009.04.032 10.1007/978-3-540-69633-9 10.1007/978-94-015-8158-5 10.1016/j.commatsci.2008.05.023 10.1115/1.3097344 10.1016/S0020-7683(99)00137-7 |
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| Keywords | Maximum tangential stress criterion Cracks interaction Three equal collinear cracks Riemann–Hilbert problem |
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| References_xml | – volume: 28 start-page: R11 year: 1985 ident: 254_CR29 publication-title: Int J Fract doi: 10.1007/BF00033702 contributor: fullname: M Kachanov – volume: 31 start-page: 233 year: 1986 ident: 254_CR23 publication-title: Int J Fract doi: 10.1007/BF00018929 contributor: fullname: LRF Rose – volume: 94 start-page: 721 issue: 9 year: 2014 ident: 254_CR35 publication-title: Z Angew Math Mech doi: 10.1002/zamm.201200293 contributor: fullname: EM Craciun – volume: 43 start-page: 539 issue: 5 year: 2007 ident: 254_CR28 publication-title: Int Appl Mech doi: 10.1007/s10778-007-0052-4 contributor: fullname: OS Bogdanova – volume: 13 start-page: 193 year: 1990 ident: 254_CR34 publication-title: Theor Appl Fract Mech doi: 10.1016/0167-8442(90)90087-G contributor: fullname: VV Tvardovski – volume: 34 start-page: 363 year: 1996 ident: 254_CR11 publication-title: Int J Eng Sci doi: 10.1016/0020-7225(95)00100-X contributor: fullname: E Soos – volume: 16 start-page: 253 issue: 4 year: 1978 ident: 254_CR33 publication-title: Int J Eng Sci doi: 10.1016/0020-7225(78)90091-5 contributor: fullname: GK Dhawan – volume: 46 start-page: 687 issue: 3 year: 2009 ident: 254_CR24 publication-title: Comput Mater Sci doi: 10.1016/j.commatsci.2009.06.006 contributor: fullname: T Sadowski – volume: 66 start-page: 79 year: 1999 ident: 254_CR17 publication-title: J Appl Mech doi: 10.1115/1.2789172 contributor: fullname: M Valentini – volume: 32 start-page: 813 issue: 10 year: 1996 ident: 254_CR22 publication-title: Int Appl Mech doi: 10.1007/BF02086728 contributor: fullname: AA Kaminskii – volume: 70 start-page: 39 issue: 1 year: 2005 ident: 254_CR14 publication-title: IMA J Appl Math doi: 10.1093/imamat/hxh060 contributor: fullname: EM Craciun – start-page: 68 volume-title: Fracture—an advanced treatise, vol II, mathematical fundamentals year: 1968 ident: 254_CR8 contributor: fullname: GC Sih – volume: 44 start-page: 5437 year: 2007 ident: 254_CR31 publication-title: Int J Solids Struct doi: 10.1016/j.ijsolstr.2006.10.024 contributor: fullname: S Mukherjee – volume-title: Theory of elasticity of aniosotropic elastic body year: 1963 ident: 254_CR5 contributor: fullname: SG Lekhnitski – volume-title: Crack problem in the classical theory of elasticity year: 1969 ident: 254_CR10 contributor: fullname: IN Sneddon – volume: 94 start-page: 137 year: 1998 ident: 254_CR3 publication-title: Int J Fract doi: 10.1023/A:1007549317153 contributor: fullname: EM Craciun – ident: 254_CR20 – volume: 13 start-page: 269 year: 1961 ident: 254_CR26 publication-title: Q J Mech Appl Mech contributor: fullname: CJ Tranter – volume: 85 start-page: 519 year: 1963 ident: 254_CR36 publication-title: ASME J Basic Eng doi: 10.1115/1.3656897 contributor: fullname: F Erdogan – volume-title: Some basic problems of the mathematical theory of elasticity year: 1953 ident: 254_CR4 contributor: fullname: NI Muskhelishvili – volume: 39 start-page: 48434865 year: 2002 ident: 254_CR18 publication-title: Int J Solids Struct contributor: fullname: D Bigoni – ident: 254_CR27 – volume: 78 start-page: 855 issue: 12 year: 1998 ident: 254_CR30 publication-title: Z Angew Math Mech doi: 10.1002/(SICI)1521-4001(199812)78:12<855::AID-ZAMM855>3.0.CO;2-0 contributor: fullname: BD Aggarwala – volume: 23 start-page: 695 issue: 4 year: 1986 ident: 254_CR25 publication-title: Eng Fract Mech doi: 10.1016/0013-7944(86)90116-5 contributor: fullname: RS Dhaliwal – volume-title: Mechanics of elastic composites year: 2003 ident: 254_CR2 doi: 10.1201/9780203502815 contributor: fullname: ND Cristescu – volume: 10 start-page: 435 year: 1980 ident: 254_CR32 publication-title: Rundfunktech Mitt contributor: fullname: RS Dhaliwal – volume: 39 start-page: 3971 year: 2002 ident: 254_CR15 publication-title: Int J Solids Struct doi: 10.1016/S0020-7683(02)00252-4 contributor: fullname: E Radi – volume: 46 start-page: 677 issue: 3 year: 2009 ident: 254_CR13 publication-title: Comput Mater Sci doi: 10.1016/j.commatsci.2009.04.032 contributor: fullname: A Carabineanu – volume-title: Fundamentals of fracture mechanics year: 1974 ident: 254_CR7 contributor: fullname: LM Kachanov – ident: 254_CR9 – volume-title: Fundamentals of the three dimensional theory of stability of deformable bodies year: 1999 ident: 254_CR1 doi: 10.1007/978-3-540-69633-9 contributor: fullname: AN Guz – volume-title: Fracture mechanics. An introduction year: 1993 ident: 254_CR37 doi: 10.1007/978-94-015-8158-5 contributor: fullname: EE Gdoutos – volume: 45 start-page: 684 issue: 3 year: 2009 ident: 254_CR12 publication-title: Comput Mater Sci doi: 10.1016/j.commatsci.2008.05.023 contributor: fullname: N Peride – volume-title: Crack problems in the classical theory of elasticity year: 1969 ident: 254_CR21 contributor: fullname: IN Sneddon – volume: 53 start-page: 117 issue: 5 year: 2000 ident: 254_CR19 publication-title: Appl Mech Rev doi: 10.1115/1.3097344 contributor: fullname: V Petrova – volume-title: Strength and fracture of solids with cracks year: 2002 ident: 254_CR6 contributor: fullname: VV Panasyuk – volume: 37 start-page: 64336478 year: 2000 ident: 254_CR16 publication-title: Int J Solids Struct doi: 10.1016/S0020-7683(99)00137-7 contributor: fullname: A Azhdari |
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| SubjectTerms | Automotive Engineering Civil Engineering Classical Mechanics Computational Micromechanics of Materials Cracks Criteria Displacement Graphite fiber reinforced plastics Graphite-epoxy composites Mathematical models Mechanical Engineering Physics Physics and Astronomy Representations Stresses |
| Title | Mathematical modeling of three equal collinear cracks in an orthotropic solid |
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