Quasistatic delamination models for Kirchhoff‐Love plates

Abstract

A quasistatic rate-independent brittle delamination problem and also an adhesive unilateral contact problem is considered on a prescribed normally-positioned surface in a plate with a finite thickness. By letting the thickness of the plate go to zero, two quasistatic rate-independent crack models with prescribed path for Kirchhoff-Love plates are obtained as limit of these quasistatic processes.

Quasistatic Delamination of Sandwich-Like Kirchhoff-Love Plates

“…This is done by applying the abstract scheme developed in [50]. Since most of the requirements can be obtained as simple adaptations from [21], we mainly highlight the differences.…”

“…One should emphasize the quite essential differences from a delamination surface being positioned "vertically", which was investigated in [20,21]. In those papers the vertically positioned surface scaled as ε, in contrast to the horizontally positioned Γ C considered in this paper.…”

“…The variational dimension reduction process leads to a Kirchhoff-Love model for the plate. The case of a "vertically" positioned delaminating surface has been studied in [21] and, using a Barenblatt-like cohesive crack surface energy, also in [20]. For a static delamination on a generally-positioned delamination surface in Kirchhoff-Love plates, we refer to [29,30].…”

“…Another difference due to the "sandwich" position of the contact surface is that the delamination parameter z is now independent of x 3 , which means that here it will not be rescaled and remains the same also for the limit 2D problem. Moreover, [21] considers also a delamination model obtained for κ τ = κ ν = κ → +∞, cf. (3.6).…”

Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination

“…These cohesive energies are considered, in particular, in the existing analytical studies of delamination problems, e.g. [11,37,27,28]. Apart from fracture mechanics, this type of integrals also appear in the study of Winkler foundations [41], with applications as varied as the understanding of the seismic response of piers, chromosome function, or the mechanical response of carbon nanotubes embedded in elastic media (see [34] and the references therein).…”