Summary
The constitutive equations of hypoplasticity are of the rate type. They can thus be considered as differential equations. In this paper, we are concerned with the time integration of such equations. The main challenge in time integration is to guarantee that the objectivity of the formulation is preserved by the numerical integrator. Among other possibilities, we discuss in detail a rotation neutralized description of the hypoplastic equations and its integration by projection methods.
In a second part of the paper, we use techniques from the theory of differential equations to analyze the hypoplastic equations without integrating particular trajectories, e.g. specific stress paths. For example, we show that the K 0-line in an oedomentric element test is exponentially attractive, and we compute possible bifurcation points of the hypoplastic equations for a triaxial element test.
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References
Abraham R, Marsden J E (1978) Foundations of Mechanics. Benjamin-Cummings, Reading, Mass.
Bauer E (1992) Zum mechanischen Verhalten granularer Stoffe unter vorwiegend ödometrischer Beanspruchung. Institut für Bodenmechanik und Felsmechanik der Universität Karlsruhe, Karlsruhe
Fellin W, Ostermann A (2002) Int. J. Numer. Anal. Meth. Geomech. 26: 1213–1233
Goldscheider M (1976) Mech. Res. Comm. 3, 463–468
Gurtin M E (1981) An Introduction to Continuum Mechanics. Academic Press, San Diego New York
Hairer E, Lubich C, Wanner G (2002) Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer, Berlin Heidelberg New York
Hairer E, Nørsett S P, Wanner G (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd rev. ed., Springer, Berlin Heidelberg New York
Hairer E, Wanner G (1996) Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. 2nd rev. ed., Springer, Berlin Heidelberg New York
Higham D J (1997) BIT 37: 24–36
Kolymbas D (2000) Introduction to Hypoplasticity. Balkema, Rotterdam
Olver P J (1993) Applications of Lie Groups to Differential Equations. 2nd ed., Springer, Berlin Heidelberg New York
Simo J C, Hughes T J R (1998) Computational Inelasticity. Springer, Berlin Heidelberg New York
Wu W (1997) Int. J. Numer. Anal. Meth. Geomech. 21: 153–174
Wu W (1992) Hypoplastizität als mathematisches Modell zum mechanischen Verhalten granularer Stoffe. Institut für Bodenmechanik und Felsmechanik der Universität Karlsruhe, Karlsruhe
Wu W, Kolymbas D (1990) Mechanics of Materials 9: 245–253
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Fellin, W., Osterman, A. (2003). Objective integration and geometric properties of hypoplasticity. In: Kolymbas, D. (eds) Advanced Mathematical and Computational Geomechanics. Lecture Notes in Applied and Computational Mechanics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45079-5_8
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DOI: https://doi.org/10.1007/978-3-540-45079-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07357-1
Online ISBN: 978-3-540-45079-5
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