On elastic clamping boundary conditions in plate models describing detaching bilayers

Abstract

Elastic clamping boundary conditions are derived, which describe root rotations and root displacements in plate models used to analyze detaching bimaterial layers subjected to arbitrary end loadings. The elasticity technique uses the reciprocity theorem and J-integral calculations and is applicable to isotropic and orthotropic bimaterial layers of different thicknesses, also with extreme elastic constants and mismatch. Explicit closed form expressions for all clamping coefficients are derived for bimaterial isotropic layers with mid-thickness cracks and zero second Dundurs’ parameter; the derivation relies on existing solutions for energy release rate and local fields. Closed form expressions are derived for the most relevant coefficients in homogeneous symmetric orthotropic layers and thin isotropic layers on isotropic half planes. The technique is applicable to general cases using analytical or numerical results for the energy release rate.