A finite element method for a class of contact-impact problems

Hughes, Thomas J.R.; Taylor, Robert L.; Sackman, Jerome L.; Curnier, A.; Kanok‐Nukulchai, Worsak

doi:10.1016/0045-7825(76)90018-9

Cited by 426 publications

(138 citation statements)

References 6 publications

Supporting

Mentioning

123

Contrasting

Unclassified

Order By: Relevance

“…The finite element method has provided the ground for a number of efficient solutions to this problem by the implementation of contact elements (e.g. Alart and Curnier, 1991;Chan and Tuba, 1971;Hughes et a l , 1976). The effectiveness of such elements in joint biomechanics was illustrated by, for example, Chan and Rim (1976), Rapperport et a l, (1987), Huber-Betzer et al, (1990), Weinans et a l, (1990) andRubin et al, (1993).…”

Section: ¿Eus Rmentioning

confidence: 99%

The biomechanics of the human patella during passive knee flexion

Heegaard

Leyvraz

Curnier

et al. 1995

Journal of Biomechanics

166

119

View full text Add to dashboard Cite

Abstract-The fundamental objectives of patello-femoral joint biomechanics include the determination of its kinematics and of its dynamics, as a function of given control parameters like knee flexion or applied muscle forces. On the one hand, patellar tracking provides quantitative information about the joint's stability under given loading conditions, whereas patellar force analyses can typically indicate pathological stress distributions asso ciated for instance with abnormal tracking, The determination of this information becomes especially relevant when facing the problem of evaluating surgical procedures in terms of standard (i.e. non-pathological) knee functionality. Classical examples of such procedures include total knee replacement (TKR) and elevation of the tibial tubercle (Maquet's procedure).Following this perspecti ve, the current study was oriented to ward an accurate and reliable determination of the human patella biomechanics during passive knee flexion. To this end, a comprehensive three-dimensional computer model, based on the finite element method, was developed for analyzing articular biomechanics. Unlike previously published studies on patello-femoral biomechanics, this model simultaneously computed the joint's kinematics, associated tendinous and ligamentous forces, articular contact pressures and stresses occurring in the joint during its motion. The components constituting the joint (i.e. bone, cartilage, tendons) were modeled using objective forms of non-linear elastic materials laws. A unilateral contact law allowing for large slip between the patella and the femur was implemented using an augmented Lagrangian formulation, Patellar kinematics computed for two knee specimens were close to equivalent experimental ones (average deviations below 0.5° for the rotations and below 0.5 mm for the translations) and provided validation of the model on a specimen by specimen basis. The ratio between the quadriceps pulling force and the patellar tendon force was less than unity throughout the considered knee flexion range (30-150°), with a minimum near 90° of flexion for both specimens. The contact patterns evolved from the distal part of the retropatellar articular surface to the proximal pole during progressive flexion. The lateral facet bore more pressure than the medial one, with corresponding higher stresses (hydrostatic) in the lateral compartment of the patella. The forces acting on the patella were part of the problem unknowns, thus leading to more realistic loadings for the stress analysis, which was especially important when considering the wide range of variations of the contact pressure acting on the patella during knee flexion.

show abstract

Section: ¿Eus Rmentioning

confidence: 99%

The biomechanics of the human patella during passive knee flexion

Heegaard

Leyvraz

Curnier

et al. 1995

Journal of Biomechanics

166

119

View full text Add to dashboard Cite

show abstract

“…After these above mentioned theoretical developments, the main research was then concentrated towards the development of numerical methods to solve optimization problems under inequality constraints, for example, in Hughes et al [66]. Examples of such methods are the condensation method, the interior method, the barrier method, the penalty method, the exact proximity method, the exact multiplier method, and the augmented Lagrangian multiplier method.…”

Section: Summary Of the Main Resultsmentioning

confidence: 99%

Multisymplectic Variational Integrators for Nonsmooth Lagrangian Continuum Mechanics

Demoures

Gay–Balmaz

Raţiu

2016

Forum of Mathematics, Sigma

View full text Add to dashboard Cite

This paper develops the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid plate or the collision of two elastic bodies. The integrators are obtained by combining, at the continuous and discrete levels, the variational multisymplectic formulation of nonsmooth continuum mechanics with the generalized Lagrange multiplier approach for optimization problems with nonsmooth constraints. These integrators verify a spacetime multisymplectic formula that generalizes the symplectic property of time integrators. In addition, they preserve the energy during the impact. In the presence of symmetry, a discrete version of the Noether theorem is verified. All these properties are inherited from the variational character of the integrator. Numerical illustrations are presented.

show abstract

“…It is interesting to refer that one of the first attempts to analyse classical contact problems with finite elements was carried out by Francavilla and Zienkiewicz [15] and a much more rigorous analysis was published in the following year by Hughes et al [16] already including independent force variables.…”

Section: General Considerationsmentioning

confidence: 99%

“…, n g . 12 Check if node N kr can be associated with face F ks by verifying the violation of local co-ordinates (14), if not, cycle 13 Calculate, by a ranking strategy, the 'cost' of forming the element N kr ∪ F ks : C krs , which is a function of the gap estimateḡ and of step 12 14 If the 'cost' C krs is less than the previous minimum, C min krs then C min krs ← C krs and mark face F ks for association with node N kr 15 End do 16 If node N kr has some face associated, then define the element N kr ∪ F ks forming the new connectivities 17…”

Section: The Algorithm For Contact Detectionmentioning

confidence: 99%

Algorithms for the analysis of 3D finite strain contact problems

Areias

Sá

Curnis

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYFrom the constraint imposition aspects in 3D to friction regularization, various ideas are exposed in this paper. A variation of the Rockafellar Lagrangian is proposed which results in continuous second-order derivatives if Lagrange multiplier estimates are greater or equal than one. This fact allows the adoption of a full second-order (i.e. Lagrange-Newton) method avoiding sequential unconstrained minimization techniques. An algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods. A modified constraint definition to deal with non-smooth situations is presented. Aspects of friction implementation, including a regularization scheme which ensures stepwise objectivity, are detailed. Finally, several illustrative examples are carried out with success.

show abstract

A finite element method for a class of contact-impact problems

Cited by 426 publications

References 6 publications

The biomechanics of the human patella during passive knee flexion

The biomechanics of the human patella during passive knee flexion

Multisymplectic Variational Integrators for Nonsmooth Lagrangian Continuum Mechanics

Algorithms for the analysis of 3D finite strain contact problems

Contact Info

Product

Resources

About