Shakedown in frictional contact problems for the continuum

Shakedown in frictional contact problems for the continuum

Elastic systems with frictional interfaces subjected to periodic loading are often found to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic– plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them—i.e. that the...

Covariant description for frictional contact problems

Shakedown in elastic contact problems with Coulomb friction

Elastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e....

Solving Frictional Contact Problems with Multigrid Efficiency

The construction of fast and reliable solvers for contact problems with friction is even nowadays a challenging task. It is well known that contact problems with Coulomb friction have the weak form of a quasi-variational inequality [KO88, HHNL88, NJH80]. For small coefficients of friction, a solution can be obtained by means of a fixed point iteration in the boundary stresses [NJH80]. This fixe...

On Solving Frictional Contact Problems Part Iii: Unilateral Contact

In this paper, we study mixed variational nite element methods for the unilateral problems arising in contact mechanics.The presented discrete spaces can handle the case of non matching meshes in the contact area. We rst state the static problem and then extend it to the frictional contact case, and end with the dynamic frictional problem.