Closed‐Form Approach on Mode III Loadings of Thin Layers

Weak interface models are a potent tool to capture both deformations, stresses, and energy release rates for adhesives or other weak layers between stiffer joints. While the energy release rate for both modes I and II is rendered well, a fast and efficient model, capturing mode III loading of the weak layer is missing. The present study addresses this research gap by introducing a closed‐form analytical model for out‐of‐plane bended weak interface specimens. The classical approach of weak interface models is not applicable in the case of loading the specimen with out‐of‐plane bending. Tackling these difficulties, the present approach uses the principle of minimum potential energy in combination with the calculus of variations to derive the governing equations for an arbitrarily loaded weak interface specimen. This model renders stresses and displacements in a very good agreement with numerical reference solutions and is highly efficient and reduces the numerical costs for parameter studies and the evaluation of experiments. This enables one to measure the mode III energy release rate from a J‐integral‐based evaluation of this physical quantity. Our model allows a fast determination of the mode III fracture toughness from out‐of‐plane loaded double cantilever beam tests for adhesives or from rotated propagation saw tests for faceted and porous weak layers in stratified snowpacks.