Skip to main content

Mesomechanics and Multiscale Modelling for Yield Surface

  • Chapter
Computational Plasticity

Part of the book series: Advanced Topics in Science and Technology in China ((ATSTC))

Abstract

Mechanical modelling is an abstraction, a formation of an idea or ideas that may involve the physics of solids with specific geometric configurations. Mathematical models may involve relationship between continuous functions of space and time for describing the homogeneity and/or isotropy of a material or the formation of conservation laws (Meyer, 1985; Tayler, 1986; Besseling and Liessen, 1994). The results based on these models for describing a phenomenon should agree with existing measurements within a specified accuracy and can be used with confidence to predict future observations and events.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aboudi UJ (1989) Micromechanical analysis of composites by the method of cells. Appl. Mech. Rev., 42(7): 193–221.

    Article  Google Scholar 

  • Ashby MF, Evans AG, Fleck NA, Gibson LJ, Hutchinson JW and Wadley HNG (2000) Metal Foams: A Design Guide. Butterworth Heinemann: Oxford.

    Google Scholar 

  • Becker R (2002) Developments and trends in continuum plasticity. Journal of Computer-Aided Materials Design, 9(2): 145–163.

    Article  CAS  Google Scholar 

  • Besseling JE and der Liessen E (1994) Mathematical Modeling of Inelastic Deformation. Chapman & Hall: London.

    Google Scholar 

  • Bhattacharya K and Schlömerkemper A (2004) Transformation yield surface of shape memory alloys. J. Phys. IV France, 115: 155–2.

    Article  CAS  Google Scholar 

  • Bishop JFW and Hill R (1951) A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Philos Mag, 42: 414–27.

    CAS  Google Scholar 

  • Bishop JFW and Hill R (1951) A theoretical derivation of the plastic properties of a polycrystalline face centered metal. Philos Mag, 42: 1298–307.

    CAS  Google Scholar 

  • Bomert M, Herve E, Stolz C, Zaoui A (1994) Self-consistent approaches and strain heterogeneities in two-phase elastoplastic materials. Appl. Mech. Review, 47(1): Part 2, 66–76.

    Article  Google Scholar 

  • Bouvet C, Calloch S and Lexcellent C (2002) Mechanical behavior of a Cu-Al-Be shape memory alloy under multiaxial proportional and nonproportional loadings. J. Eng. Mater. Technol, 124(2): 112–124.

    Article  CAS  Google Scholar 

  • Bouvet C, Calloch S and Lexcellent C (2004) A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and non-proportional loadings. Eur J. of Mech A Solids, 23: 37–61.

    Article  Google Scholar 

  • Buyukozturk O, Nilson AH and State FO (1970) Stress-strain response and fracture of a concrete model in biaxial loading. Journal ACI, 68(8): 590–595.

    Google Scholar 

  • de Buhan P and de Pelice G (1997) A homogenization approach to the ultimate strength of brick masonry. 3∼Mechanics and Physics of Solids, 45 (7): 1085–1104.

    Article  Google Scholar 

  • Caballero A, Carol I and Lopez CM (2007) A 3D meso-mechanical analysis of concrete specimens under biaxial loading. Fatigue and Fracture of Engineering Materials and Structures,30(9): 877–886.

    Article  Google Scholar 

  • Chen SH and Wang ZQ (2009) Micro-scale plasticity mechanics. University of Science and Technology of China Press: Hefei, China.

    Google Scholar 

  • Christeensen RM and Lo KH (1979) Solutions for effective shear properties in three phase sphere and cylinder models, Journal of the Mechanics and Physics of Solids, 27: 315–330.

    Article  Google Scholar 

  • Deshpande VS and Fleck NA (2000) Isotropic constitutive models for metallic foams. J. Mech. Phys. Solids, 48: 1253–283.

    Article  CAS  Google Scholar 

  • Dongare AM, Rajendran AM, Lamattina B, Brenner DW, Zikry MA (2010) Atomic-scale study of plastic-yield criterion in nanocrystalline CU at high strain rates. Metallurgical and Materials Transactions A, 41A(2): 523–31.

    Article  CAS  Google Scholar 

  • Dvorak GJ, Bahei-E1-Din (1997) An inelastic composite materials: Transformation analysis and experiments. In: Continuum Micromechanics, P. Suquet (ed.), Springer: Wien.

    Google Scholar 

  • Dvorak GJ (1999) Composite materials: inelastic behavior, damage, fatigue and fracture. In: Research Trends in Solid Mechanics, G.J. Dvorak (ed.). Pergamon: New York.

    Google Scholar 

  • Faria SH, Hutter K, Kirchner N and Wang Y (2010) Continuum Description of Granular Materials. Springer: Berlin.

    Google Scholar 

  • Fish J and Yu Q (2001) Multiscale damage modeling for composite materials: theory and computational framework. Int. J. for Numerical Methods in Engineering, 52: 161–192.

    Article  Google Scholar 

  • Gall K, Sehitoglu H, Maier HI and Jacobus K (1998) Stress-induced Martensitic Phase Transformations in Polycrystalline CuZnAl Shape Memory Alloys under Different Stress States, Met Mat Trans A., 29A: 765–73.

    Article  CAS  Google Scholar 

  • Ghosh S. and Moorthy S (1995) Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method. Comp. Meth. Appl. Mech. Eng., 121: 373–09.

    Article  Google Scholar 

  • Ghosh S., Lee K. and Moorthy S (1995) Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method. Int. J. Solids Struct., 321: 27–2.

    Article  Google Scholar 

  • Ghosh S, Lee K and Moorthy S (1996) Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model. Comp. Meth. Appl. Mech. Engrg., 132: 63–16.

    Article  Google Scholar 

  • Ghosh S, Lee K and Raghavan P (2001) A multilevel computational model for multi-scale damage analysis in composite and porous materials. Inter. J. of Solids and Structures,38: 2335–385.

    Article  Google Scholar 

  • Gibeau E, Laydi MR and Lexcellent C (2010) Determination and transport of phase transformation yield surfaces for shape memory alloys. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 90(7): 595–695.

    Article  Google Scholar 

  • Gibson LJ, Ashby MF, Zhang J and Triantafillou TC (1989) Failure surface for cellular mateerials under multiaxial loads-(1) modelling. Int. J. Mech. Sci., 31: 635–63.

    Article  Google Scholar 

  • Gibson LJ and Ashby MF (1987, 1997) Cellular Solids: Structure and Propertities. Press Syndicate of the University of Cambridge: London.

    Google Scholar 

  • Gibson LJ (2000) Mechanical behavior of metallic foams. Annu. Rev. Mater. Sci., 30: 191–27.

    Article  CAS  Google Scholar 

  • Gioux G, McCormark TM and Gibson LJ (2000) Failure of aluminum foams under multiaxial loads. Int. J. Mech. Sci. 42: 1097–117.

    Article  Google Scholar 

  • Gologanu M et al. (1993) Approximate models for ductile metals containing non-spherical voids-case of asisymmetric prolate ellipsoidal cavities, J. of the Mechanics and Physics of Solids, 41: 1723–1754.

    Article  Google Scholar 

  • Gologanu M, Leblond JB, Perrin G, Devaux J (1997) Recent extensions of Gurson’s Model for porous ductile metals. In: Continuum Micromechanics, P. Suquet (ed.) Springer: Wien, pp 61–130,.

    Google Scholar 

  • Groger R, Racherla V, Bassani JL and Vitek V (2008) Multiscale modeling of plastic deformation of b molybdenum and tungsten: II. Yield Criterion for single crystals based on atomistic studies of glide of 1/2(11) Screw dislocations. Acta Materialia, 56: 5412–5425

    Article  CAS  Google Scholar 

  • Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth, I. Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Tech., 99: 2–15.

    Article  Google Scholar 

  • Hashin Z (1962) The elastic moduli of heterogeneous materials, J. Applied Mech., 29: 143–150.

    Article  CAS  Google Scholar 

  • Hashin Z and Shtrikman S (1964) A variational approach to the theory of the elastic behavlour of multiphase materials, Mech. Phys. Sci., 11(2): 127–41.

    Article  Google Scholar 

  • Hashin Z (1983) Analysis of composite materials—A survey. J. Appl. Mech., 50: 481–05.

    Article  Google Scholar 

  • Hayakawa K and Murakami S (1998) Space damage conjugate force and damage potential of elastic-plastic damage materials. In: Damage Mechanics in Engineering Materials. Edited by Voyiadjis GZ, Ju J-WW and Chaboche J-L, Elsevier.

    Google Scholar 

  • Haythornthwaite RM (1961) Range of yield condition in ideal plasticity. J. Engrg. Mech., 87: 117–33.

    Google Scholar 

  • Hill R (1965) Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids, 13: 89–101.

    Article  CAS  Google Scholar 

  • Hodge PG (1959) Plastic Analysis of Structures. McGraw-Hill: New York.

    Google Scholar 

  • Huang W (1999) “Yield” surfaces of shape memory alloys and their applications. Acta Materialia, 47(9): 2769–2776.

    Article  CAS  Google Scholar 

  • Jasiuk I and Ostoja-Strarzewski M eds (1994) Micromechanics of Random Media I. Applied Mechanics Reviews, 47(1): Part 2:Special Supplement.

    Google Scholar 

    Google Scholar 

  • Jasiuk I and Ostoja-Strarzewski M eds (1998) Micromechanics of Random Media II. Int. J. Solids and Structures, 35(19): 2383–2569.

    Google Scholar 

  • Ju J and Tseng K (1996) Effective elastoplastic behavior of two-phase ductile matrix composites: a micromechanical framework. Int. J. Solids Struct., 3329: 4267–291.

    Article  Google Scholar 

  • Kachanov LM (1986) Introduction to Continum Damage Mechanics. Martinus Nijhoff Publishers: Netherlands.

    Google Scholar 

  • Kolupaev VA and Altenbach H (2010) Einige Überlegungen zur Unified Strength Theory von Mao-Hong Yu (Considerations on the Unified Strength Theory due to Mao-Hong Yu), Forschung im Ingenieurwesen (Forsch Ingenieurwes) Springer-Link 29 May 2010 (in German, English Abstract).

    Google Scholar 

  • Kraska M, Doig M, Tikhomirov D, Raabe D and Roters F (2009) Virtual material testing for stamping simulations based on polycrystal plasticity. Comput Mater Sci, 46: 383–92.

    Article  CAS  Google Scholar 

  • Kröner E (1961) On the plastic deformation of polycrystals. Acta Metall, 9: 155–61.

    Article  Google Scholar 

  • Kröner E (1977) Bounds for effective elastic moduli of disordered materials, Mech. Phys Sci, 25(2): 137–55.

    Article  Google Scholar 

  • Ladevdz EC and Fish J (2003) Preface to special issue on multiscale computational mechanics for materials and structure. Computer Methods in Applied Mechanics and Engineering, 192: 28–0.

    Google Scholar 

  • Lemaitre J (1992) A Course on Damage Mechanics. Springer-Verlag.

    Google Scholar 

  • Lexcellent C, Vivet A, Bouvet C, Calloch S and Blanc P (2002) Experimental and numerical determinations of the initial surface of phase transformation under biaxial loading in some polycrystalline shape-memory alloys. J Mech Phys Solids, 50: 2717–735.

    Article  CAS  Google Scholar 

  • Lexcellent C and Blanc P (2004) Phase transformation yield surface determination for some shape memory alloys. Acta Mater 52: 2317–324.

    Article  CAS  Google Scholar 

  • Lexcellent C and Schlömerkemper A (2007) Comparison of several models for the determination of the phase transformation yield surface in shape memory alloys with experimental data. Acta Materialia, 55: 2995–3006.

    Article  CAS  Google Scholar 

  • Li YM and Ishii K (1998a) The evaluation of the elasto-plastic behavior of composite materials under biaxial stress with homogenization method. In: Proc. of the Conference on Computational Engineering and Science, 3: 1023–026.

    Google Scholar 

  • Li YM and Ishii K (1998b) The evaluation of strength for the composite materials. In: Strength Theory: Applications, Developments and Prospects for the 21st Century. Yu MH and Fan SC eds. Science Press: New York, Beijing, 337–42.

    Google Scholar 

  • Li YY, Zheng JL, Cui JZ and Long SY (2010) Iterative multi-scale finite element predicting method for the elasticity mechanical parameters of the concrete with multi-graded rocks. Chinese Journal of Computational Mechanics, 27(1): 115–119 (in Chinese).

    Google Scholar 

  • Li ZX, Sun ZH, Guo L et al. (2007) Multi-objective concurrent approaching of simulating for civil infrastructure. J. of Southeast University (Natural Science Edn.), 37(02):251–260 (in Chinese).

    Google Scholar 

  • Lim TJ and McDowell DL (1999) Mechanical behavior of Ni-Ti shape memory alloys under axial-torsional proportional and nonproportional loading. J Eng Mat and Techn, 121: 9–8.

    Article  CAS  Google Scholar 

  • Lin TH and Ito YM (1965) Theoretical plastic distortion of a polycrystalline aggregate under combined and revered stress. J. Mech. Phys. Solids.,13:103–15.

    Article  CAS  Google Scholar 

  • Lin TH and Ito YM (1966) Theoretical plastic stress-strain relationship of a polycrystal and comparisions with Mises and Tresca plasticity theories. Int. J. Engng. Sci., 4: 543–61.

    Article  Google Scholar 

  • Liu D and Jiang CZ (2008) Plastic limit analysis of circular plates based on twin-shear unified strength theory. Engineering Mechanics, 25(8): 77–84 (in Chinese).

    Google Scholar 

  • Liu TCY, Nilson AH and Slate FO (1972) Biaxial stress-strain relation for concrete, Proc. ASCE, Journal of Structural Division, 98(5): 1025–1034.

    Google Scholar 

  • Liu TCY, Nilson AH and Slate FO (1972) Stress-strain response and fracture of concrete in uniaxial and biaxial compression. Journal ACI, 69(5): 191–195.

    Google Scholar 

  • Liu WK, Qian D and Horstemeyer ME (2004) Preface to special issue on multiple scale methods for nanoscale mechanics and materials. Computer Methods in Applied Mechanics and Engineering, 193: l7–20

    Google Scholar 

  • Lou ZW (1991) Foundation of Damage Mechanics. Xi’an Jiaotong University Press: Xi’an (in Chinese).

    Google Scholar 

  • Lu XZ, Lin XC, Ye LP (2008) Multiscale finite element modeling and its application in structural analysis. Journal of Huazhong University of Science and Technology (Urban Science Edition), 25(4): 76–80 (in Chinese).

    Google Scholar 

  • Lund AC and Schuh CA (2005) Strength asymmetry in nanocrystalline metals under multiaxial loading. Acta Material, 53: 3173–3205.

    Article  CAS  Google Scholar 

  • Ma HF, Chen HQ, Li BK (2004) Progress in concrete meso-mechanics research and comment on. Chinese Journal of Water Resources and Hydropower Research, 2004(2).

    Google Scholar 

  • Ma HF, Chen HQ, Wu JP, Li BK (2008) Study on numerical algorithm of 3D meso-mechanics model of dam concrete. Chinese J. of Computational Mechanics, 25(2): 244–247.

    Google Scholar 

  • McDowell DL (1985) An experimental study of the structure of constitutive equations for nonproportional cyclic plasticity, ASME Journal of Engineering Materials and Technology, 107: 307–315.

    Article  Google Scholar 

  • McDowell DL, Stock SR, Stahl D and Antolovich SD (1988) Biaxial path dependence of deformation substructure of type 304 stainless steel, Metallurgical Transactions, 19: A 1277–1293.

    Google Scholar 

  • McDowell DL, Marin E, and Bertoncelli C (1993) A combined kinematicisotropic hardening theory for porous inelasticity of ductile metals, Int. J. of Damage Mechanics, 2: 137–161.

    Article  CAS  Google Scholar 

  • McDowell DL(1999) Non-associative aspects of multiscale evolutionary phenomena. In: Picu, R.C., Krempl, E. (Eds.), Proceedings 4th International Conference on Constitutive Laws for Engineering Materials, pp 54–57.

    Google Scholar 

  • McDowell DL(2001) Materials design: a useful research focus for inelastic behavior of structural metals. In: Sih GC, Panin VE (Eds.), Special Issue of the Theoretical and Applied Fracture Mechanics, Prospects of Mesomechanics in the 21st Century: Current Thinking on Multiscale Mechanics Problems, vol. 37, pp 245–259.

    Google Scholar 

  • McDowell DL(2007) Simulation-assisted materials design for the concurrent design of materials and products, JOM., 59 (9): 21–25.

    Article  Google Scholar 

  • McDowell DL and Olson GB (2008) Concurrent design of hierarchical materials and structures, Scientific Modeling and Simulation (CMNS), 15(1): 207.

    Article  CAS  Google Scholar 

  • McDowell DL, Choi H-J, Panchal J, Austin R, Allen JK and Mistree F (2007) Plasticity-related microstructure—property relations for materials design, Key Engineering Materials, 340–341: 21–30.

    Article  Google Scholar 

  • McDowell DL (2010) A perspective on trends in multiscale plasticity. Khan International Medal Lecture, Int. J. of Plasticity.

    Google Scholar 

  • Meyer WJ (1985) Concepts of Mathematical Modeling. McGraw-Hill, Singapore.

    Google Scholar 

  • Murakami S, Hayakawa K and Liu Y (1998) Damage evolution and damage surface of elastic-plastic-damage materials under multiaxial loading. Int. Journal of Damage Mechanics, 7(2):103–128.

    Article  CAS  Google Scholar 

  • Novák V and Šittner P (2004) Micromechanics modelling of NiTi polycrystalline aggregates transforming under tension and compression stress. Mat Sci Eng A, 378: 490–498.

    Article  CAS  Google Scholar 

  • Ortiz M (2008) Multiscale modeling of materials: Linking microstructure and macroscopic behavior. Invited Lecture, Seminarios Interuniversitarios de Mecanica y Materiales, Barcelona, Zaragoza, Seville, Spain.

    Google Scholar 

  • Ortiz M (2008) Nonconvex Plasticity and Microstructure. Rodney Hill Prize Plenary Lecture, 22nd International Congress of Theoretical and Applied Mechanics, Adelaide, Australia.

    Google Scholar 

  • Ostoja-Strarzewski M (1993) Micromechanics as a basis of random elastic continuum approximations. Probablistic Engineering Mechanics, 8(2): 107–114.

    Article  Google Scholar 

  • Ostoja-Strarzewski M (1994) Micromechanics as a basis of continuum random fields. Applied Mechanics Reviews (Special Issue: Micromechanics of Random Media), 47(1) Part 2: S221–230.

    Google Scholar 

  • Ostoja-Strarzewski M (1994) Random field models of heterogeneous matrials. Int. J. Solids and Structures, 35(19): 2429–2455..

    Article  Google Scholar 

  • Ottosen NS and Ristinmaa M (2005) The Mechanics of Constitutive Modeling. Elsevier.

    Google Scholar 

  • Picu RC (2003) Foreword to special issue on linking discrete and continuum models. Int. Multiscale Computational Engng, 1(1): vii–viii.

    Article  Google Scholar 

  • Pindera M-J and Aboudi J (1989) Micromechanical investigation of the convexity of yield surfaces of metal matrix composites. In: Advances in Plasticity A.S. Khan and M. Tokuda (eds.), pp 129–132.

    Google Scholar 

  • Raabe D (1998) Computational Materials Science: The Simulation of Materials Microstructures and Properties. Wiley-VCH Verlag: London.

    Google Scholar 

  • Roters F. Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR and Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Materialia, 58(4): 1152–1211.

    Article  CAS  Google Scholar 

  • Sadowski T(2005) Multiscale Modelling of Damage and Fracture Processes in Composite Materials. Springer: Berlin.

    Book  Google Scholar 

  • Save MA and Massonnet CE (1972) Plastic Analysis and Design of Plates, Shells and Disks. North-Holland: Amsterdam.

    Google Scholar 

  • Sawczuk A (1989) Mechanics and Plasticity of Structures. Ellis Horwood: Chichester.

    Google Scholar 

  • Schrefler BA (2009) Multiscale Modelling. In: Zienkiewicz OC and Taylor RL (2009) The Finite Element Method for Solid and Structural Mechanics. Sixth edn. Elsevier, Amsterdam and Elsevier (Singapore) Pte Ltd, pp 547–589.

    Google Scholar 

  • Schuh CA and Lund AC (2003) Atomic basis for the plastic yield criterion of metallic glass. Nature Materials, 2: 499–452.

    Article  CAS  Google Scholar 

  • Sih GC ed (2000) Role of Mechanics for Development of Science and Technology. Proceedings of an Int. Conf. of Role of Mechanics for Development of Science and Technology, held at Xi’an Jiaotong University, China, June Tsinghua University press: Xi’an.

    Google Scholar 

  • Sridhar I and Fleck NA (2000) Yield behaviour of cold compacted composite powders. Acta Materials, 48(13): 3341–3352.

    Article  CAS  Google Scholar 

  • Stronge WJ and Yu TX (1993) Dynamic Models for Structural Plasticity. Springer: Berlin.

    Book  Google Scholar 

  • Sun CT and Vaidya RS (1996) Prediction of composite properties from a representative volume element. Composites Science and Technology, 56(2): 171–179.

    Article  CAS  Google Scholar 

  • Tayler AB (1986) Mathematical Models in Applied Mechanics. Clarendon Press: Oxford.

    Google Scholar 

  • Tailard K, Blanc P, Calloch and Lexcellent (2006) Phase transformation yiels surface of anisotropic shape memory allys. Materials Science and Engineering, A 438–440: 436–440.

    Google Scholar 

  • Theocaris PS (1991) The elliptic paraboloid failure criterion for cellular solids and brittle foams. Acta Mechanica, 89: 93–121.

    Article  Google Scholar 

  • Triantafillou TC, Zhang J et al (1989) Failure surface for cellular Mateerials under multiaxial loads-(2) Comparison of models with experment. Int. J. Mech. Sci., 31(9): 665–678

    Article  Google Scholar 

  • Triantafillou TC and Gibson LJ (1990) Multiaxial failure criteria for brittle foams. Int. J. Mech. Sci., 32(6): 479–496.

    Article  Google Scholar 

  • Voyiadjis GZ, Ju JW and Chaboche JL eds (1998) Damage Mechanics in Engineering Materials, Elsevier.

    Google Scholar 

  • Wu BJ, Li ZX and Tang KK (2007) Multi-scale modeling and damage analyses of large civil structure: multi-scale mechanics from material to structure. Advances in Mechanics, 37(3): 321–336.

    Google Scholar 

  • Yu MH (1961a) General behaviour of isotropic yield function. Res. Report of Xi’an Jiaotong University. Xi’an, China (in Chinese).

    Google Scholar 

  • Yu MH (1961b) Plastic potential and flow rules associated singular yield criterion. Res. Report of Xi’an Jiaotong University. Xi’an, China (in Chinese).

    Google Scholar 

  • Yu MH (1983) Twin shear stress yield criterion. Int. J. of Mech. Science, 25(1): 71–74.

    Article  Google Scholar 

  • Yu MH et al. (1985) Twin shear theory and its generalization. Science in China, Series A,English edition,28 (11): 1174–1183.

    Google Scholar 

  • Yu MH and He LN (1991) A new model and theory on yield and failure of materials under the complex stress state, Mechanical Behaviour of Materials-6, (ICM-6), Jono M and Inoue T (eds.), Pergamon Press: Oxford, 3: 841–846.

    Google Scholar 

  • Yu MH and Zeng WB (1993a) Twin-shear plasticity and mesomechanics. In: Collection of Papers Dedicated to Professor Tung-Hua Lin in Celebration of His 80th Birthday (Wang ZQ, Xu BY and Huang ZP eds. Peking University Press: Beijing (in Chinese).

    Google Scholar 

  • Yu MH and Zeng WB (1993b) Mesomechanical simulation of failure criterion for a composite material. Macro-Meso-micro Mechanical Properties of Materials.

    Google Scholar 

  • Tokuda M and Xu BY eds. Mie Academic Press: Mie, Japan, pp 571–576.

    Google Scholar 

  • Yu MH (2000) Material Model in Mesomechanics and Macromechanics. Plenary lecture. In: Mesomechanics 2000, Tsinghua University Press, pp 239–246.

    Google Scholar 

  • Yu SW and Feng XQ (1997) Damage Mechanics. Tsinghua University Prtess: Beijing.

    Google Scholar 

  • Zeng WB and Wei XY (1998) Computer simulation of failure criteria for concrete. Strength Theory: Applications, Developments and Prospects for the 21st Century. Yu MH and Fan SC eds. Science Press: New York, Beijing, pp 639–642.

    Google Scholar 

  • Zhu H, Sankar BV and Marrey RV (1998) Evaluation of failure criteria for fiber composites using finite element micromechanics Journal of Composite Materials, 32(8): 766–782.

    Article  Google Scholar 

  • Zienkiewicz OC and Taylor RL (2009) The Finite Element Method for Solid and Structural Mechanics. Sixth edn. Elsevier: Amsterdam and Elsevier (Singapore) Pte Ltd.

    Google Scholar 

  • Zohdi TI and Wridggers P (2001) Computational micro-macro material testing. Archives of Computational Methods in Engineering, 8(2): 131–228.

    Article  Google Scholar 

  • Zyczkowski M (1981) Combined Loadings in the Theory of Plasticity. Polish Scientific Publishers: PWN and Nijhoff.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Zhejiang University Press, Hangzhou and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yu, MH., Li, JC. (2012). Mesomechanics and Multiscale Modelling for Yield Surface. In: Computational Plasticity. Advanced Topics in Science and Technology in China. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24590-9_19

Download citation

Publish with us

Policies and ethics