186,353 research outputs found
A formulation for frictionless contact problems using a weak form introduced by Nitsche
No full textIn this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of con- tact forces that are computed from the stresses in the contin- uum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of- freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces
Trends in Computational Contact Mechanics
No full textContact mechanics is a science that has a great impact on everyday life and is present in many different fields. These include civil, mechanical and environmental engin- eering, but also medicine since locomotion as well as functional joints do not work without friction. In one application friction is needed – like traction of car tyres – and in another application friction produces wear and costs – like in bearings. Thus it is of the utmost interest to have reliable and efficient methods and associated ana- lysis tools that can be applied to a vast range of contact problems.
Using the power of today’s computers many complex contact problems can be solved with numerical simulation tools. Despite the progress that has been reached with respect to the implementation of contact algorithms in commercial codes, vivid research is still going on in the area of contact mechanics. Thus, within the last years, computational contact mechanics has been a topic of intense research. The aim of the development is to devise robust solution schemes and new discretization techniques, which can be applied to different problem classes in engineering and science.
These are wide-ranging and include computational aspects of discretization tech- niques using finite and boundary element methods. Special solution algorithms for single- and multi-processor computing environments are of great interest for efficient solutions. Furthermore, multi-scale approaches have been applied suc- cessfully to contact problems and multi-field formulations were used for thermo- mechanical or electro-thermo-mechanical applications involving contact. Discrete element models include always contact and pose a challenge for the numerical treat- ment due to the high number of particles. Finally, problems like rolling wheels and tyres need special contact formulations and special algorithmic approaches.
Technical applications incorporate different interface problems. Examples are failure processes in heterogeneous materials, textile and laminated composites, in- teraction between road and tyres, hip implants or artificial knee joints as well as spraying of particles on surfaces and impact analysis of cars.
The present book summarizes work in the area of computational contact mechanics that was presented at the 1st International Conference on Computational Contact Mechanics in Lecce, Italy. The authors discuss different theoretical methodologies, algorithms for the solution of contact problems and apply these to different engineering problems
Application of augmented lagrangian techniques for nonlinear constitutive laws in contact interfaces
No full textThe use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm
A non-linear stress-strain relation endowed with fractional derivative elements
No full textIn this paper a non-linear stress-strain relation based on an integral formulation with a power-law kernel is proposed. This constitutive law is able to reproduce both the viscoelastic behavior and the inelastic irreversible phenomenon. It is shown how the proposed stress-strain law is capable to fit experimental data obtained from tensile tests on two kind of metal alloys. Such best-fitting procedure have shown the accuracy of the proposed model and its results are compared to other ones obtained with the aid of classical non-linear constitutive law
On the efficiency of new and old strategies for solving contact problems
No full textThe most recent progresses in the field of numerical treatment of contact problems permit to obtain high eficiency with a close correlation to the microscopical characteristics of the contact surfaces. In this paper a modification of standard strategies to satisfy contact constraintsispresented which yields a non-linear, srnaooth change of contact stiffness around the solution. Thus the adopted approach leads to an iterative method which does not depict numerical instabilities within the solution search process. This fact permits to achieve a better convergence rate with respect to standard methods
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