Variational formulation for weak-interface mechanics

Classical weak interface models often fall short when applied to thick and compliant interfaces, where stress and displacement fields become highly nonuniform. This work presents a variational formulation based on the principle of minimum potential energy to address these limitations. Trigonometric deformation modes are introduced as additional free functions to represent complex stress states within the interface while ensuring compatibility with adjacent adherends. This approach naturally enforces physically meaningful boundary conditions, such as vanishing shear stresses at free surfaces, and provides accurate stress and displacement predictions even for moderately thick layers. A closed-form expression for the energy release rate for cracks within the interface is derived, enabling efficient evaluation of fracture criteria. The model is validated against finite element simulations and demonstrates improved performance over classical equilibrium- or complementary-energy-based models. Applications include systems with adhesive layers and architectured interfaces. We also illustrate its use in snow mechanics as a representative example of weak-layer collapse phenomena. • Accurate weak interface stresses derived from complex kinematics in weak interfaces. • Variational model incorporates stress boundary conditions at the weak interface. • Compact expression for the energy release rate holds true in case of body forces. • Efficient implementation of the present model available.