Nonclassical Problems of Fracture/Failure Mechanics: on the Occasion of the 50th Anniversary of the Research (Review)

Contact Problems for Interface Cracks Under Harmonic Shear Loading

“…In both half-spaces the equation of motion and the generalized Hooke's law lead to the linear Lamé equations of elastodynamics for the displacement field with the standard initial and boundary conditions for displacements and stresses (namely, no initial deformations; given initial load at the crack faces, (1) and (2) ; continuity conditions at the bonding interface, * = (1) ∩ (2) ; and the Sommerfeld radiation-type condition at the infinity). Furthermore, the components of the displacement could be represented in terms of the boundary displacements and tractions using the Somigliana dynamic identity with the appropriate fundamental solutions ( ) ( , , − ) and ( ) ( , , − ) [1,7,12,16,17,20]:…”

“…The contact constraints (2)-(4) ensure that there is no interpenetration of the opposite crack faces, the normal component of the contact force is unilateral; and the opposite crack faces remain immovable with respect to each other in tangential direction while they are held by the friction force before the slipping occurs [16,17,20,24].…”

“…It shall be specifically noted that the opposite faces of the existing cracks almost always interact with each other under deformation, significantly changing the solution near the crack [13][14][15][16][17][18][19][20][21][22][23]. The nature of the dynamic contact interaction between opposite crack faces is very complex.…”

“…It is only possible to solve these problems using advanced numerical methods, since the analytical solutions are limited to a relatively small number of idealized model problems corresponding to very special geometrical configurations and loading conditions. Consequently, due to the nonlinearity of the problem and substantial computational difficulties, researchers often neglect effects of crack faces contact interaction, for comprehensive reviews please see [16,17].…”

Розв’язок Контактної Задачі Для Попередньо Напружених Циліндричного Штампа Та Шару, Що Лежить Без Тертя На Основі Без Початкових Напружень

“…Останнім часом наукові результати, що мають відношення до механіки твердих деформованих тіл та їх контактної взаємодії, охоплюють все ширші кола питань. Ці результати представлені багатьма працями монографічного та оглядового характеру, одними з яких є [1][2][3]. У праці [1] в межах лінеаризованої теорії пружності розглянуто контактну задачу для пружного циліндричного штампа та шару з початковими напруженнями, що лежить на жорсткій основі без тертя.…”