Conventional finite element simulation models of debonding phenomena with high-adhesion cohesive zones and soft base materials require extremely fine initial meshes which trigger expensive solution costs. Large deformations and element distortions, especially in the soft base material, also cause convergence difficulties and numerical instabilities with the usage of a high-resolution initial mesh. To address this, automatic mesh adaptation schemes like Nonlinear Adaptivity (NLAD) are often prescribed which allow the mesh to be refined gradually with debonding. In most conventional cases, this enables the initial meshes to be relatively coarse and the refinement only occurs as the debonding progresses. However, cohesive zone based debonding is essentially a history dependent process – which implies that the adaptive criteria which drive mesh refinement and mesh distortion correction must also be formulated on interface damage and distortion history in addition to the local debonding behavior. In order to solve these intractable problems – the following solution strategy is proposed. • Allow user to start a contact-based cohesive zone (CZ) modeling analysis within a Nonlinear Adaptivity (NLAD) framework with reasonable meshes • Continue the debonding failure analysis with minimal user intervention by progressively adapting the mesh at the interface if and when the novel rate based debonding criteria are satisfied. Adaptation is simultaneously done by refinement, coarsening and general remeshing • Improve efficiency, solution stability and capture the fine details of the local stress/deformation fields and cohesive zone parameters due to automatic remeshing by controlling the mesh density evolution around the debonding zone • Coarsen the mesh automatically in regions where the material damage is complete to minimize active DOFs where they are not needed. Unlike most other adaptive CZM approaches, this procedure does not require any specialized element formulations, is not limited to any specific material type and is embedded in a standard nonlinear finite element code. User intervention is minimal and automatic fault tolerancing ensures that failed remeshings do not stop the solution. Correct closure of the debonded zone (healing) is also supported with adaptivity since the cohesive material law is modeled with contact and target elements. These elements are generated automatically during remeshing of the model without user intervention.