Three-Dimensional Contact Problems

Alexandrov, V. M.; Пожарский, Д. А.

doi:10.1007/978-94-010-9893-9

Cited by 43 publications

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“…The mechanical indenter was simulated as a rigid cylindrical punch with a bottom surface profile of a 12th-order polynomial to represent a nearly flat bottom that caused an additional displacement, d, at the top surface of 41 d r ð Þ¼ br 12 12 ; r a ð2Þ…”

Section: Discussionmentioning

confidence: 99%

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Ferroelastic domain switching dynamics under electrical and mechanical excitations

et al. 2014

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In thin film ferroelectric devices, switching of ferroelastic domains can significantly enhance electromechanical response. Previous studies have shown disagreement regarding the mobility or immobility of ferroelastic domain walls, indicating that switching behaviour strongly depends on specific microstructures in ferroelectric systems. Here we study the switching dynamics of individual ferroelastic domains in thin Pb(Zr 0.2 ,Ti 0.8 )O 3 films under electrical and mechanical excitations by using in situ transmission electron microscopy and phase-field modelling. We find that ferroelastic domains can be effectively and permanently stabilized by dislocations at the substrate interface while similar domains at free surfaces without pinning dislocations can be removed by either electric or stress fields. For both electrical and mechanical switching, ferroelastic switching is found to occur most readily at the highly active needle points in ferroelastic domains. Our results provide new insights into the understanding of polarization switching dynamics as well as the engineering of ferroelectric devices.

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Section: Discussionmentioning

confidence: 99%

“…Determining the total load and stress distribution caused by this displacement are described in ref. 41. The fitting parameter, b, was chosen such that the total load applied by the indenter was as indicated in the main text.…”

Section: Discussionmentioning

confidence: 99%

Ferroelastic domain switching dynamics under electrical and mechanical excitations

et al. 2014

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“…For the frictionless case ( = 0), such a system is given in Reference [10]. For problem B * , the boundary conditions for ' = 0 yield a 0 ( ; ÿ) = a 2 ( ; ÿ) = 0, and we get a system of four functional equations for the functions a 1 , b n (n = 0; 1; 2) in the arguments , ± 1 and ± 2.…”

Section: Construction Of the Green's Functions For Wedgesmentioning

confidence: 99%

“…The checks for 1 , 2 indicate the convergence for both problems. For the Papkovich-Neuber function 0 a representation in form of (12), (13) [10,20] determining the stress-strain state near the edge. In particular, they are meromorphic in the complex -plane, and their poles in this plane provide di erent stress asymptotics near the edge for both problems A * and B * .…”

Section: Construction Of the Green's Functions For Wedgesmentioning

confidence: 99%

“…Keer et al [6] investigated a frictionless contact problem for a quarter-space and a rectangular punch using a modiÿed ÿnite element method. Frictionless three-dimensional contact problems for a wedge have been considered in References [10,11], for the motion of a punch with friction in an elastic half-space in Reference [12]. The variational approach to three-dimensional contact problems with friction was developed by Eck et al [13], where Signorini contact problems with Coulomb friction have been considered.…”

Section: Introductionmentioning

confidence: 99%

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3‐D Contact problems for elastic wedges with Coulomb friction

Bach

Пожарский

2003

Math Methods in App Sciences

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SUMMARY3-D quasi-static contact problems for elastic wedges with Coulomb friction are reduced to integral equations and integral inequalities with unknown contact normal pressures. To obtain these equations and inequalities, Green's functions for the wedges, where one face of the wedges is either stress-free or ÿxed, are needed. Using Fourier and Kontorovich-Lebedev integral transformations, all the stresses and displacements in the wedges can be constructed in terms of solutions of Fredholm integral equations of the second kind on the semiaxis. The Green's functions can be calculated as uniformly convergent power series in (1 − 2 ), where is Poisson's ratio. An exponential decay of the kernels and right-hand sides of the Fredholm integral equations provides the applicability of the collocation method for simple and fast calculation of the Green's functions. For a half-space, which is a special case of an elastic wedge, the kernels degenerate and the functions reduce to the well-known Boussinesq and Cerruti solutions.Analysing the contact problems reveals that the Green's functions govern the kernels of the above mentioned integral equations and inequalities. Under the assumption that the punch has a smooth shape, the contact pressure is zero on the boundary of the unknown contact zone. Solving the contact problems with the help of the Galanov-Newton method, the normal contact pressure, the contact zone and the normal displacement around the contact zone can be determined simultaneously. In view of the numerical results, the in uence of the friction forces on the punch force and the punch settlement is discussed.

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Micromechanical Failure Criteria of Composites

2019

Design and Analysis of Composite Structures for Automotive Applications

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Three-Dimensional Contact Problems

Cited by 43 publications

References 0 publications

Ferroelastic domain switching dynamics under electrical and mechanical excitations

Ferroelastic domain switching dynamics under electrical and mechanical excitations

3‐D Contact problems for elastic wedges with Coulomb friction

Micromechanical Failure Criteria of Composites

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