A recursion formula for the integer power of a symmetric second-order tensor and its application to computational plasticity
DOI:
https://doi.org/10.23998/rm.137537Avainsanat:
toisen kertaluvun tensori, rekursiokaava, Cayley-Hamilton yhälö, Rankinen murtoehtoAbstrakti
In this paper, a recursion formula is given for the integer power of a second-order tensor in 3D Euclidean space. It can be used in constitutive modelling for approximating failure or yield surfaces with corners, and it is demonstrated for the case of Rankine failure criterion. Removing corners provides clear advantages in computational plasticity. We discuss the consequences of the approximation errors for failure analyses of brittle and quasi-brittle
materials.
Lähdeviitteet
A.J. Abbo, A.V. Lyamin, S.W. Sloan, and J.P. Hambleton. A C2 continuous approximation to the Mohr–Coulomb yield surface. International Journal of Solids and Structures, 48(21):3001–3010, 2011. ISSN 0020-7683. doi:https://doi.org/10.1016/j.ijsolstr.2011.06.021.
D. P. Adhikary, C. T. Jayasundara, R. K. Podgorney, and A. H. Wilkins. A robust return-map algorithm for general multisurface plasticity. International Journal for Numerical Methods in Engineering, 109(2):218–234, 2017. doi:https://doi.org/10.1002/nme.5284.
W.F. Chen and D.J. Han. Plasticity for Structural Engineers. Springer-Verlag, 1988.
G.A. Holzapfel. Nonlinear Solid Mechanics - A Continuum Approach for Engineering. John Wiley & Sons, 2000.
M. Itskov. Tensor Algebra and Tensor Analysis for Engineers. With Applications to Continuum Mechanics. Springer, 4th edition, 2015.
W. T. Koiter. Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface. Quarterly of Applied Mathematics, 11:350–354, 1953. doi:https://doi.org/10.1090/QAM/59769.
W.T. Koiter. General theorems for elasto-plastic solids. In I.N. Sneddon and R. Hill, editors, Progress in Solid Mechanics, pages 165–211. North-Holland Publishing Company, 1960.
J. Lubliner. Plasticity Theory. Pearson Education, Inc., 1990.
L.E. Malvern. Introduction to the Mechanics of a Continuous Medium. Prentice Hall, Englewood Cliffs, New Jersey, 1969.
N.S. Ottosen and M. Ristinmaa. Corners in plasticity–Koiter’s theory revisited. International Journal of Solids and Structures, 33(25):3697–3721, 1996. ISSN 0020-7683. doi:https://doi.org/10.1016/0020-7683(95)00207-3.
T. Saksala and R. Kouhia. A damage-plasticity model for brittle materials based on a smooth approximation of Rankine type of failure criterion. Rakenteiden Mekaniikka, 56(4):136–145, 2023. doi:https://doi.org/10.23998/rm.137249.
J.C. Simo and T.J.R. Hughes. Computational Inelasticity. Springer, New York, 1 edition, 1998.
S. W. Sloan and J. R. Booker. Removal of singularities in Tresca and Mohr–Coulomb yield functions. Communications in Applied Numerical Methods, 2(2):173–179, 1986. doi:https://doi.org/10.1002/cnm.1630020208.
S.K. Suryasentana and G.T. Houlsby. A convex modular modelling (CMM) framework for developing thermodynamically consistent constitutive models. Computers and Geotechnics, 142, 2022. doi:https://doi.org/10.1016/j.compgeo.2021.104506
C. Truesdell and W. Noll. The Non-linear Field Theories of Mechanics. Springer, 3. edition, 2004.
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Copyright (c) 2023 Reijo Kouhia, Timo Saksala
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