In this paper we present numerical simulations of soil plasticity using isogeometric
analysis comparing the results to the solutions from conventional finite
element method. Isogeometric analysis is a numerical method that uses nonuniform
rational B-splines (NURBS) as basis functions instead of the Lagrangian
polynomials often used in the finite element method. These functions
have a higher-order of continuity, making it possible to represent complex
geometries exactly. After a brief outline of the theory behind the isogeometric
concept, we give a presentation of the constitutive equations, used to simulate
the soil behavior in this work. The paper concludes with numerical examples
in two- and three-dimensions, which assess the accuracy of isogeometric
analysis for simulations of soil behavior. The numerical examples presented
show, that for drained soils, the results from isogeometric analysis are overall
in good agreement with the conventional finite element method in two- and
three-dimensions. Thus isogeometric analysis is a good alternative to conventional
finite element analysis for simulations of soil behavior.
References
[1]
Potts, D.M. and Zdravkovi’c, L. (1999) Finite Element Analysis in Geotechnical Engineering: Theory. Philadelphia University, Philadelphia. https://doi.org/10.1680/feaiget.27534
[2]
Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005) Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement. Computer Methods in Applied Mechanics and Engineering, 194, 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
[3]
Bazilevs, Y., Gohean, J.R. and Hughes, T.J.R. (2009) Patient-Specific Isogeometric Fluid-Structure Interaction Analysis of Thoracic Aortic Blood Flow Due to Implantation of the Jarvik 2000 Left Ventricular Assist Device. Computer Methods in Applied Mechanics and Engineering, 198, 3534-3550. https://doi.org/10.1016/j.cma.2009.04.015
[4]
Benson, D.J., Bazilevs, Y., Hsu, M.C. and Hughes, T.J.R. (2010) Isogeometric Shell Analysis: The Reissner-Mindlin Shell. Computer Methods in Applied Mechanics and Engineering, 199, 276-289. https://doi.org/10.1016/j.cma.2009.05.011
[5]
Irzal, F., Remmers, J.J., Verhoosel, C.V. and Borst, R. (2013) Isogeometric Finite Element Analysis of Poroelasticity. International Journal for Numerical and Analytical Methods in Geomechanics, 37, 1891-1907. https://doi.org/10.1002/nag.2195
[6]
Nguyen, M.N., Bui, T.Q., Yu, T. and Hirose, S. (2014) Isogeometric Analysis for Unsaturated Flow Problems. Computers and Geotechnics, 62, 257-267. https://doi.org/10.1016/j.compgeo.2014.08.003
[7]
Schillinger, D., Evans, J.A., Reali, A., Scott, M.A. and Hughes, T.J. (2013) Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations. Computer Methods in Applied Mechanics and Engineering, 267, 170-232. https://doi.org/10.1016/j.cma.2013.07.017
[8]
Evans, J.A., Bazilevs, Y., Babuska, I. and Hughes, T.J.R. (2009) N-Widths, Sup-Infs, and Optimality Ratios for the K-Version of the Isogeometric Finite Element Method. Computer Methods in Applied Mechanics and Engineering, 198, 1726-1741. https://doi.org/10.1016/j.cma.2009.01.021
[9]
Bazilevs, Y., Calo, V.M., Cottrell, J.A., Evans, J.A., Hughes, T.J.R., Lipton, S., Scott, M.A. and Sederberg, T.W. (2010) Isogeometric Analysis Using T-Spline. Computer Methods in Applied Mechanics and Engineering, 199, 229-263. https://doi.org/10.1016/j.cma.2009.02.036
[10]
Reali, A. and Hughes, T.J.R. (2015) An Introduction to Isogeometric Collocation Methods. In: Beer, G., Ed., Isogeometric Methods for Numerical Simulation, Springer, Berlin, 173-204. https://doi.org/10.1007/978-3-7091-1843-6_4
[11]
Auricchio, F., Veiga, L.B., Hughes, T.J.R., Reali, A. and Sangalli, G. (2010) Isogeometric Collocation Methods. Mathematical Models and Methods in Applied Sciences, 20, 2075-2107. https://doi.org/10.1142/S0218202510004878
[12]
Nguyen, K.D. and Nguyen, H.X. (2017) Isogeometric Analysis of Linear Isotropic and Kinematic Hardening Elastoplasticity. Vietnam Journal of Mechanics, 38.
[13]
Elguedj, T., Bazilevs, Y., Calo, V.M. and Hughes, T.J. (2008) Projection Methods for Nearly Incompress-Ible Linear and Non-Linear Elasticity and Plasticity Using Higher-Order Nurbs Elements. Computer Methods in Applied Mechanics and Engineering, 197, 2732-2762. https://doi.org/10.1016/j.cma.2008.01.012
[14]
Cox, M.G. (1972) The Numerical Evaluation of B-Splines. IMA Journal of Applied Mathematics, 10, 134-149. https://doi.org/10.1093/imamat/10.2.134
[15]
Boor, C. (1972) On Calculating with B-Splines. Journal of Approximation Theory, 6, 50-62. https://doi.org/10.1016/0021-9045(72)90080-9
[16]
Versprille, K.J. (1975) Computer-Aided Design Applications of the Rational B-Splie Approximation. Ph.D. Thesis, Syracuse University, Syracuse.
[17]
Piegl, L.A. and Tiller, W. (1995) The NURBS Book, Monographs in Visual Communication. Springer, Berlin.
[18]
Bathe, K.J. (1996) Finite Element Procedures. Prentice Hall, Englewood Cliffs.
[19]
Hughes, T.J.R. (2012) The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Courier Corporation, North Chelmsford.
[20]
Neto, E.A.D.S., Peric, D. and Owen, D.R.J. (2008) Computational Methods for Plasticity: Theory and Applications. Wiley, Chichester. http://catdir.loc.gov/catdir/toc/ecip0824/2008033260.html https://doi.org/10.1002/9780470694626