A finite element method for contact problems of solid bodies—Part I. Theory and validation

Chan, S.K.; Tuba, I. S.

doi:10.1016/0020-7403(71)90032-4

Cited by 207 publications

(43 citation statements)

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“…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

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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.

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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

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“…rIl=rI-xwk (1) k where n is the usual (incremental) total potential leading to the incremental equilibrium equations without contact conditions, and c k W k is the incremental potential of the contact forces. This term can be interpreted as a Lagrange multiplier contribution to impose the contact conditions.…”

Section: Formulation Of Contact Problemmentioning

confidence: 99%

A solution method for planar and axisymmetric contact problems

Bathe

Chaudhary

1985

Numerical Meth Engineering

427

121

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SUMMARYA solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure arc the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm.

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“…Traditionally, the non-penetration condition has been enforced exactly by the Lagrange multiplier technique [1][2][3][4][5] or approximately by a penalty method [6; 7; 5]. The traditional Lagrange multiplier technique is essentially a two-ÿeld formulation.…”

Section: Introductionmentioning

confidence: 99%

A contact formulation based on localized Lagrange multipliers: formulation and application to two‐dimensional problems

Rebel

Park

Felippa

2002

Numerical Meth Engineering

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SUMMARYThe non-penetration condition in contact problems is traditionally based on the classical Lagrange multiplier method. This method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non-matching. To deal with this problem we introduce a novel element in the Lagrange multiplier approach of contact modelling, namely, a contact frame placed in between contacting bodies. It acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models. Only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic. The contact frame has its own independent freedoms, which allows the formulation to pass contact patch tests by design.

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A finite element method for contact problems of solid bodies—Part I. Theory and validation

Cited by 207 publications

References 0 publications

The biomechanics of the human patella during passive knee flexion

The biomechanics of the human patella during passive knee flexion

A solution method for planar and axisymmetric contact problems

A contact formulation based on localized Lagrange multipliers: formulation and application to two‐dimensional problems

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