Argatov Ivan I, Mishuris Gennady S, Popov Valentin L
College of Aerospace Engineering, Chongqing University, Chongqing, China; Institut für Mechanik, Technische Universität Berlin, Berlin, Germany.
Department of Mathematics, Aberystwyth University, Aberystwyth, UK.
Math Mech Solids. 2024 Oct;29(10):1958-1969. doi: 10.1177/10812865241240484. Epub 2024 May 6.
Non-axisymmetric frictionless JKR-type adhesive contact between a rigid body and a thin incompressible elastic layer bonded to a rigid base is considered in the framework of the leading-order asymptotic model, which has the form of an overdetermined boundary value problem. Based on the first-order perturbation of the Neumann operator in the Dirichlet problem for Poisson's equation, the decohesion initiation problem is formulated in the form of a variational inequality. The asymptotic model assumes that the contact zone and its boundary contour during the detachment process are unknown. The absence of the solvability theorem is illustrated by an example of the instability of an axisymmetric flat circular contact.
在一阶渐近模型框架下，考虑刚体与粘结在刚性基底上的不可压缩弹性薄层之间的非轴对称无摩擦JKR型粘结接触，该模型具有超定边值问题的形式。基于泊松方程狄利克雷问题中诺伊曼算子的一阶扰动，脱粘起始问题被表述为变分不等式的形式。渐近模型假设在分离过程中接触区及其边界轮廓是未知的。通过轴对称平面圆形接触的不稳定性示例说明了可解性定理的缺失。
