Abstract
Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.
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References
Yuan Z P, Zheng Y. A study on yield and flow of orthotropic materials[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(3):247–253. DOI 10.1007/BF02015205
Shi G Y, Voyiadjis G Z. A new free energy for plastic damage analysis[J]. Mechanics Research Communications, 1997, 24(4):377–383.
Lemaitre J. A continuous damage mechanics model for ductile fracture[J]. J Eng Mater Tech, 1985, 107(1):83–89.
Hayakawa K, Murakami S, Liu Y. An irreversible thermodynamics theory for elastic-plastic-damage materials[J]. Eur J Mech A/Solids, 1998, 17(1):13–32.
Voyiadjis G Z, Deliktas B. A coupled anisotropic damage model for the inelastic response of composite materials[J]. Comlput Methods Appl Mech Engrg, 2000, 183(3/4):159–199.
Hutchinson J W. Post-bifurcation behavior in the plastic range[J]. J Mech Phys Solids, 1973, 21(3):163–190.
Hutchinson J W. Plastic buckling[J]. Advances in Appl Mech, 1974, 14:67–141.
Needleman A, Tvergaard V. An analysis of the imperfection sensitivity of square elastic-plastic plates under axial compression[J]. Int J Solids Structure, 1976, 12(3):185–201.
Nguyen Q S. Bifurcation and post-bifurcation analysis in plasticity and brittle fracture[J]. J Mech Phys Solids, 1987, 35(3):303–324.
Nguyen Q S, Triantafyllidis N. Plastic bifurcation and post-bifurcation analysis for generalized standard continua[J]. J Mech Phys Solids, 1989, 37(5):545–566.
Cimetière A, Léger A. Some problems about elastic-plastic post-buckling[J]. Int J Solids Structures, 1996, 30(10):1519–1533.
Pi Y L, Bradford M A. Elasto-plastic buckling and postbuckling of arches subjected to a central load[J]. Computers and Structures, 2003, 81(18/19):1811–1825.
Lemaitre J. A course on damage mechanics[M]. Berlin: Springer-Veriag, 1992.
Chow C L, Wang J. An anisotropic theory of elasticity for continuum damage mechanics[J]. Engg Fract Mesh, 1987, 33(1):3–16.
Sidoroff F. Description of anisotropic damage application to elasticity[C]. In: Proceedings of IUTAM Colloguium, Physical Nonlinearities in Structural Analysis, 1981, 237–240.
Chia C Y. Nonlinear analysis of plates[M]. New York: McGraw-Hill International Book Company, 1980.
Wang C M, Xiang Y, Chakrabarty J. Elastic/plastic buckling of thick plates[J]. International Journal of Solids and Structures, 2001, 38(48/49):8617–8640.
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Contributed by FU Yi-ming
Project supported by the National Natural Science Foundation of China (No. 10572049)
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Tian, Yp., Fu, Ym. Elasto-plastic postbuckling of damaged orthotropic plates. Appl. Math. Mech.-Engl. Ed. 29, 841–853 (2008). https://doi.org/10.1007/s10483-008-0702-y
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DOI: https://doi.org/10.1007/s10483-008-0702-y