Abstract
The focus of this discussion will be the recent evolution of both spatial and temporal discretization techniques in contact and impact mechanics. With regard to spatial discretization, attention will be focused on the movement from traditional “node to surface” methodologies for description of contact interaction, to new “surface to surface” algorithms that in most cases have their motivation in the mortar method. While an anticipated result of this evolution was the increased numerical accuracy produced by integral forms of the contact constraints, it has also been seen that considerable robustness in large sliding applications results from the non-local character of the formulation. In this discussion both of these advantages of the surface to surface framework will be demonstrated, as will recent extensions that enable reliable simulation of self-contact phenomena.
When extending computational contact formulations to the transient regime, the consideration of reliable time integrators for impact phenomena is of interest. Accordingly, we examine some of the issues associated with time stepping in semidiscrete formulations of contact/impact, with particular emphasis on the energy-momentum paradigm as applied to impact mechanics. We consider a form of the energy-momentum approach which encompasses dissipative phenomena (such as inelasticity and friction), and focus on a numerical approach that allows for velocity discontinuities to be incorporated into the contact updating scheme.
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Bibliography
G. Anagnostou, C. Mavriplis, and A.T. Patera. On the mortar element method: Generalizations and implementations. In Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 157–173. SIAM, 1990.
F. Armero and E. Petocz. Formulation and analysis of conserving algorithms for dynamic contact/impact problems. Computer Methods in Applied Mechanics and Engineering, 1998.
F.B. Belgacem, P. Hild, and P. Laborde. Approximation of the unilateral contact problem by the mortar finite element method. Comptes Rendus De L’Academie Des Sciences, 324:123–127, 1997.
V. Chawla and T.A. Laursen. Energy consistent algorithms for frictional contact problems. International Journal for Numerical Methods in Engineering, 42:799–827, 1998.
N. El-Abbasi and K.-J. Bathe. Stability and patch test performance of contact discretizations and a new solution algorithm. Computers and Structures, 79:1473–1486, 2001.
O. Gonzalez. Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering, 190: 1763–1783, 2000.
P. Hild. Numerical implementation of two nonconforming finite element methods for unilateral contact. Computer Methods in Applied Mechanics and Engineering, 184: 99–123, 2000.
K.L. Johnson. Contact Mechanics. Cambridge University Press, 1985.
T.A. Laursen and V. Chawla. Design of energy conserving algorithms for frictionless dynamic contact problems. International Journal for Numerical Methods in Engineering, 40:863–886, 1997.
T.A. Laursen and G.R. Love. Improved implicit integrators for transient impact problems—geometric admissibility within the conserving framework. International Journal for Numerical Methods in Engineering, 53:245–274, 2002.
T.A. Laursen and J.C. Simo. A continuum-based finite element formulation for the implicit solution of multibody, large deformation frictional contact problems. International Journal for Numerical Methods in Engineering, 36:3451–3485, 1993.
G.R. Love and T.A. Laursen. Improved implicit integrators for transient impact problems—dynamic frictional dissipation within an admissible conserving framework. Computer Methods in Applied Mechanics and Engineering, 192:2223–2248, 2003.
T.W. McDevitt and T.A. Laursen. A mortar-finite element formulation for frictional contact problems. International Journal for Numerical Methods in Engineering, 48: 1525–1547, 2000.
X.N. Meng and T.A. Laursen. On energy consistency of large deformation plasticity models, with application to the design of unconditionally stable time integrators. Finite Elements in Analysis and Design, 38:949–963, 2002a.
X.N. Meng and T.A. Laursen. Energy consistent algorithms for dynamic finite deformation plasticity. Computer Methods in Applied Mechanics and Engineering, 191: 1639–1675, 2002b.
M.A. Puso and T.A. Laursen. A mortar segment-to-segment contact method for large deformation solid mechanics. Computer Methods in Applied Mechanics and Engineering, 193:601–629, 2004a.
M.A. Puso and T.A. Laursen. A mortar segment-to-segment frictional contact method for large deformations. Computer Methods in Applied Mechanics and Engineering, 193:4891–4913, 2004b.
J.C. Simo and N. Tarnow. The discrete energy-momentum method. part i. conserving algorithms for nonlinear elastodynamics. ZAMP, 43:757–793, 1992.
P. Wriggers and C. Miehe. Contact constraints within coupled thermomechanical analysis-a finite element model. Computer Methods in Applied Mechanics and Engineering, 113:301–319, 1994.
B. Yang, T.A. Laursen, and X.N. Meng. Two dimensional mortar contact methods for large deformation frictional sliding. International Journal for Numerical Methods in Engineering, 62:1183–1225, 2005.
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© 2007 CISM, Udine
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Laursen, T.A. (2007). Emerging Spatial and Temporal Discretization Methods in Contact and Impact Mechanics. In: Wriggers, P., Laursen, T.A. (eds) Computational Contact Mechanics. CISM International Centre for Mechanical Sciences, vol 498. Springer, Vienna. https://doi.org/10.1007/978-3-211-77298-0_1
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DOI: https://doi.org/10.1007/978-3-211-77298-0_1
Publisher Name: Springer, Vienna
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