메뉴 건너뛰기




Volumn 89, Issue 2, 2009, Pages 107-122

A new paradigm: The linear isotropic Cosserat model with conformally invariant curvature energy

Author keywords

Conformal transformations; Cosserat model; Microstructure; Polar materials; Solid mechanics; Structured continua; Variational methods

Indexed keywords


EID: 60849091044     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200800156     Document Type: Article
Times cited : (106)

References (36)
  • 1
    • 0028725268 scopus 로고
    • Size effects due to Cosserat elasticity and surface damage in closed-cell polymethacrylimide foam
    • W. B. Anderson and R. S. Lakes, Size effects due to Cosserat elasticity and surface damage in closed-cell polymethacrylimide foam, J. Mat. Sci. 29, 6413-6419 (1994).
    • (1994) J. Mat. Sci , vol.29 , pp. 6413-6419
    • Anderson, W.B.1    Lakes, R.S.2
  • 2
    • 84870754285 scopus 로고
    • Measurement of characteristic length of non local continuum
    • Z. P. Bazant and G. Pijaudier-Cabot, Measurement of characteristic length of non local continuum, ASCE, J. Eng. Mech. 115, 755-767 (1989).
    • (1989) ASCE, J. Eng. Mech , vol.115 , pp. 755-767
    • Bazant, Z.P.1    Pijaudier-Cabot, G.2
  • 3
    • 34548294684 scopus 로고    scopus 로고
    • Analytical derivation of Cosserat moduli via homogenization of heterogeneous elastic materials
    • D. Bigoni and W.J. Drugan, Analytical derivation of Cosserat moduli via homogenization of heterogeneous elastic materials, J. Appl. Mech. 74, 741-753 (2007).
    • (2007) J. Appl. Mech , vol.74 , pp. 741-753
    • Bigoni, D.1    Drugan, W.J.2
  • 5
    • 60849109304 scopus 로고    scopus 로고
    • E. Cosserat and F. Cosserat, Théorie des corps déformables. Librairie Scientifique A. Hermann et Fils (engl. translation by D. Delphenich 2007, pdf available at http://www.mathematik.tu-darmstadt.de/fbereiche/analysis/ pde/staff/neff/patiizio/Cosserat.html), (Paris, 1909).
    • E. Cosserat and F. Cosserat, Théorie des corps déformables. Librairie Scientifique A. Hermann et Fils (engl. translation by D. Delphenich 2007, pdf available at http://www.mathematik.tu-darmstadt.de/fbereiche/analysis/ pde/staff/neff/patiizio/Cosserat.html), (Paris, 1909).
  • 7
    • 60849125826 scopus 로고    scopus 로고
    • S. Forest, Homogenization methods and the mechanics of generalized continua - Part 2, Theoret. Appl. Mech. (Belgrad) 28-29, 113-143(2002).
    • S. Forest, Homogenization methods and the mechanics of generalized continua - Part 2, Theoret. Appl. Mech. (Belgrad) 28-29, 113-143(2002).
  • 9
    • 0038665420 scopus 로고    scopus 로고
    • Couple stresses in crystalline solids: Origins from plastic slip gradients, dislocation core distortions, and three body interatomic potentials
    • K. Garikipati, Couple stresses in crystalline solids: origins from plastic slip gradients, dislocation core distortions, and three body interatomic potentials, J. Mech. Phys. Solids 51(7), 1189-1214 (2003).
    • (2003) J. Mech. Phys. Solids , vol.51 , Issue.7 , pp. 1189-1214
    • Garikipati, K.1
  • 10
    • 17144423311 scopus 로고    scopus 로고
    • Predictions of microtorsional experiments by micropolar plasticity
    • P. Grammenoudis and C. Tsakmakis, Predictions of microtorsional experiments by micropolar plasticity, Proc. Roy. Soc. London A 461, 189-205 (2005).
    • (2005) Proc. Roy. Soc. London A , vol.461 , pp. 189-205
    • Grammenoudis, P.1    Tsakmakis, C.2
  • 11
    • 0015000088 scopus 로고
    • Existence theorems in micropolar elastostatics
    • D. Iesan, Existence theorems in micropolar elastostatics, Int. J. Eng. Sci. 9, 59-78 (1971).
    • (1971) Int. J. Eng. Sci , vol.9 , pp. 59-78
    • Iesan, D.1
  • 12
    • 0029244248 scopus 로고
    • On the equilibrium theory of microstretch elastic solids
    • D. Iesan and A. Pompei, On the equilibrium theory of microstretch elastic solids, Int. J. Eng. Sci. 33, 399-410 (1995).
    • (1995) Int. J. Eng. Sci , vol.33 , pp. 399-410
    • Iesan, D.1    Pompei, A.2
  • 13
    • 60849126779 scopus 로고    scopus 로고
    • J. Jeong and P. Neff, Existence, uniqueness and stability in linear Cosserat elasticity for weakest curvature conditions. Preprint 2550, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/preprints.html, (Math. Mech. Solids, DOI:10.1177/1081286508093581, 2008).
    • J. Jeong and P. Neff, Existence, uniqueness and stability in linear Cosserat elasticity for weakest curvature conditions. Preprint 2550, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/preprints.html, (Math. Mech. Solids, DOI:10.1177/1081286508093581, 2008).
  • 14
    • 60849083044 scopus 로고    scopus 로고
    • A numerical study for linear isotropic cosserat elasticity with conformally invariant curvature. Preprint 2558, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/ preprints.html
    • submitted
    • J. Jeong, H. Ramezani, I. Munch, and P. Neff, A numerical study for linear isotropic cosserat elasticity with conformally invariant curvature. Preprint 2558, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/ preprints.html, (submitted, 2009).
    • (2009)
    • Jeong, J.1    Ramezani, H.2    Munch, I.3    Neff, P.4
  • 15
    • 0001954361 scopus 로고
    • Couple stresses in the theory of elasticity I, II
    • W. T. Koiter, Couple stresses in the theory of elasticity I, II, Proc. Kon. Ned. Akad. Wetenschap B 67, 17-44 (1964).
    • (1964) Proc. Kon. Ned. Akad. Wetenschap B , vol.67 , pp. 17-44
    • Koiter, W.T.1
  • 16
    • 0001087913 scopus 로고
    • Advances in negative Poisson's ratio materials
    • R. S. Lakes, Advances in negative Poisson's ratio materials, Adv. Mater. 5(4), 293-296 (1993).
    • (1993) Adv. Mater , vol.5 , Issue.4 , pp. 293-296
    • Lakes, R.S.1
  • 17
    • 0029400462 scopus 로고
    • On the torsional properties of single osteons
    • R. S. Lakes, On the torsional properties of single osteons, J. Biomech. 25, 1409-1410 (1995).
    • (1995) J. Biomech , vol.25 , pp. 1409-1410
    • Lakes, R.S.1
  • 18
    • 33751114709 scopus 로고    scopus 로고
    • Lie-point symmetries and conservation laws in microstretch and micromorphic elasticity
    • M. Lazar and C. Anastassiadis, Lie-point symmetries and conservation laws in microstretch and micromorphic elasticity, Int. J. Eng. Sci. 44, 1571-1582 (2006).
    • (2006) Int. J. Eng. Sci , vol.44 , pp. 1571-1582
    • Lazar, M.1    Anastassiadis, C.2
  • 19
    • 38949148212 scopus 로고    scopus 로고
    • Is incompressible elasticity a conformal field theory?
    • M. Lazar and C. Anastassiadis, Is incompressible elasticity a conformal field theory? C. R. Mecanique 336, 163-169 (2008).
    • (2008) C. R. Mecanique , vol.336 , pp. 163-169
    • Lazar, M.1    Anastassiadis, C.2
  • 20
    • 65349098961 scopus 로고    scopus 로고
    • P. M. Mariano and G. Modica, Ground states in complex bodies (ESAIM: COCV, DOI: 10.1051/cocv:2008036, 2008).
    • P. M. Mariano and G. Modica, Ground states in complex bodies (ESAIM: COCV, DOI: 10.1051/cocv:2008036, 2008).
  • 21
    • 33947128429 scopus 로고
    • Effects of couple stresses in linear elasticity
    • R. D. Mindlin and H. F. Tiersten, Effects of couple stresses in linear elasticity, Arch. Rat. Mech. Anal. 11, 415-447 (1962).
    • (1962) Arch. Rat. Mech. Anal , vol.11 , pp. 415-447
    • Mindlin, R.D.1    Tiersten, H.F.2
  • 22
    • 33751399160 scopus 로고    scopus 로고
    • The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric. Preprint 2409, http://www3.mathematik.tu-darmstadt.de/fb/mathe/hibliothek/preprints.html
    • P. Neff, The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric. Preprint 2409, http://www3.mathematik.tu-darmstadt.de/fb/mathe/hibliothek/preprints.html, Z. Angew. Math. Mech. 86, 892-912 (2006).
    • (2006) Z. Angew. Math. Mech , vol.86 , pp. 892-912
    • Neff, P.1
  • 23
    • 33751038039 scopus 로고    scopus 로고
    • Existence of minimizers for a finite-strain micromorphic elastic solid. Preprint 2318, http://www3.mathematik.tu-darmstadt.de/fb/mathe/ bibliothek/preprints.html
    • P. Neff, Existence of minimizers for a finite-strain micromorphic elastic solid. Preprint 2318, http://www3.mathematik.tu-darmstadt.de/fb/mathe/ bibliothek/preprints.html, Proc. Roy. Soc. Edinb. A 136, 997-1012 (2006).
    • (2006) Proc. Roy. Soc. Edinb. A , vol.136 , pp. 997-1012
    • Neff, P.1
  • 24
    • 38349011472 scopus 로고    scopus 로고
    • A geometrically exact Cosserat shell-model for defective elastic crystals. Justification via τ-convergence
    • P. Neff and K. Chelmiński, A geometrically exact Cosserat shell-model for defective elastic crystals. Justification via τ-convergence, Interfaces and Free Boundaries 9, 455-492 (2007).
    • (2007) Interfaces and Free Boundaries , vol.9 , pp. 455-492
    • Neff, P.1    Chelmiński, K.2
  • 25
    • 34547447078 scopus 로고    scopus 로고
    • Well-posedness of dynamic Cosserat plasticity. Preprint 2412, http://www3.mathematik.tu-darmstadt.de/fb/mathe/ bibliothek/preprints.html
    • P. Neff and K. Chelmiński, Well-posedness of dynamic Cosserat plasticity. Preprint 2412, http://www3.mathematik.tu-darmstadt.de/fb/mathe/ bibliothek/preprints.html, Appl. Math. Optim. 56, 19-35 (2007).
    • (2007) Appl. Math. Optim , vol.56 , pp. 19-35
    • Neff, P.1    Chelmiński, K.2
  • 26
    • 34547308914 scopus 로고    scopus 로고
    • P. Neff, K. Chelmiński, W. Müller, and C. Wieners, A numerical solution method for an infinitesimal elastic-plastic Cosserat model. Preprint 2470, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/ preprints.html, Math. Mod. Meth. Appl. Sci. (M3AS), 17(8), 1211-1239 (2007).
    • P. Neff, K. Chelmiński, W. Müller, and C. Wieners, A numerical solution method for an infinitesimal elastic-plastic Cosserat model. Preprint 2470, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/ preprints.html, Math. Mod. Meth. Appl. Sci. (M3AS), 17(8), 1211-1239 (2007).
  • 27
    • 34250620957 scopus 로고    scopus 로고
    • A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling, existence of minimizers, identification of moduli and computational results
    • P. Neff and S. Forest, A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling, existence of minimizers, identification of moduli and computational results, J. Elasticity 87, 239-276 (2007).
    • (2007) J. Elasticity , vol.87 , pp. 239-276
    • Neff, P.1    Forest, S.2
  • 28
    • 38149022635 scopus 로고    scopus 로고
    • P. Neff and I. Münch, Curl bounds Grad on SO(3). Preprint 2455, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/preprints.html, ESAIM: Control, Optimisation and Calculus of Variations, published online (DOI: 10.1051/cocv:2007050, 14(1), 148-159, 2008).
    • P. Neff and I. Münch, Curl bounds Grad on SO(3). Preprint 2455, http://www3.mathematik.tu-darmstadt.de/fb/mathe/bibliothek/preprints.html, ESAIM: Control, Optimisation and Calculus of Variations, published online (DOI: 10.1051/cocv:2007050, 14(1), 148-159, 2008).
  • 29
    • 60849086564 scopus 로고    scopus 로고
    • Numerical approximation of incremental infinitesimal gradient plasticity. Preprint IWRM 08/01, http://www.mathematik. uni-karlsruhe.de/iwrmm/seite/preprints/media
    • P. Neff, A. Sydow, and C. Wieners, Numerical approximation of incremental infinitesimal gradient plasticity. Preprint IWRM 08/01, http://www.mathematik. uni-karlsruhe.de/iwrmm/seite/preprints/media, Int. J. Num. Meth. Eng. 77(3), 414-436 (2009).
    • (2009) Int. J. Num. Meth. Eng , vol.77 , Issue.3 , pp. 414-436
    • Neff, P.1    Sydow, A.2    Wieners, C.3
  • 30
    • 60849116238 scopus 로고    scopus 로고
    • W. Nowacki, Theory of Asymmetric Elasticity, (polish original 1971) (Pergamon Press, Oxford, 1986).
    • W. Nowacki, Theory of Asymmetric Elasticity, (polish original 1971) (Pergamon Press, Oxford, 1986).
  • 31
    • 0036495017 scopus 로고    scopus 로고
    • Localization issues in local and nonlocal continuum approaches to fracture, European
    • R. Pegon, A. R. De Borst, W. Brekelmans, and M. D. Geers, Localization issues in local and nonlocal continuum approaches to fracture, European J. Mech. Solids. 21, 175-189 (2002).
    • (2002) J. Mech. Solids , vol.21 , pp. 175-189
    • Pegon, R.1    De Borst, A.R.2    Brekelmans, W.3    Geers, M.D.4
  • 32
    • 0002640490 scopus 로고
    • A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity
    • P. Steinmann, A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity, Int. J. Solids Struct. 31(8), 1063-1084(1994).
    • (1994) Int. J. Solids Struct , vol.31 , Issue.8 , pp. 1063-1084
    • Steinmann, P.1
  • 33
    • 0015491157 scopus 로고
    • On the mechanics of materials with microstructure
    • R. Stojanovic, On the mechanics of materials with microstructure, Acta Mechanica 15, 261-273 (1972).
    • (1972) Acta Mechanica , vol.15 , pp. 261-273
    • Stojanovic, R.1
  • 34
    • 60849115368 scopus 로고    scopus 로고
    • J. Tambaca and I. Velcic, Existence theorem for nonlinear micropolar elasticity (ESATM:COCV, DOI: 10.1051/cocv:2008065, 2008).
    • J. Tambaca and I. Velcic, Existence theorem for nonlinear micropolar elasticity (ESATM:COCV, DOI: 10.1051/cocv:2008065, 2008).
  • 35
    • 60849126505 scopus 로고    scopus 로고
    • B. Zastrau, Ein Beitrag zur Erweiterung klassischer Invarianzforderungen für die Herleitung einer Direktortheorie, Z. Angew. Math. Mech. 61, T 135-T 137 (1981).
    • B. Zastrau, Ein Beitrag zur Erweiterung klassischer Invarianzforderungen für die Herleitung einer Direktortheorie, Z. Angew. Math. Mech. 61, T 135-T 137 (1981).
  • 36
    • 84984016769 scopus 로고
    • Herleitung einer Direktortheorie für Kontinua mit lokalen Krümmungseigenschaften
    • B. Zastrau and H. Rothert, Herleitung einer Direktortheorie für Kontinua mit lokalen Krümmungseigenschaften, Z. Angew. Math. Mech. 61, 567-581 (1981).
    • (1981) Z. Angew. Math. Mech , vol.61 , pp. 567-581
    • Zastrau, B.1    Rothert, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.