The Thick Level Set method: Sliding deformations and damage initiation

• The Thick Level Set method (TLS) is applied to shear failure in a sandwich structure.
• Two difficulties of the TLS are encountered and solutions are proposed.
• An interphase material is introduced that allows for free-sliding deformations.
• A strength-related parameter is introduced to control the initiation stress level.

The Thick Level Set method (TLS) is a new approach to the modeling of damage growth. In the TLS, damage is defined as a function of the distance to a moving front. The level set method with signed distance function is used to keep track of the front location and to evaluate the distance to the front throughout the domain. The update of damage is done indirectly by moving the damage front based on integration of the configurational force across the damaged band. In this paper, the TLS is applied to shear failure of a sandwich structure. Two problems with the TLS are encountered in this study and solutions are proposed. Firstly, it is found that sliding deformations across a crack lead to unrealistic activation of stiffness recovery that is included for modeling damage under compression. In order to allow for free sliding, a special interphase constitutive law is proposed that takes the direction of the material interface into account when it comes to stiffness recovery. Secondly, it is found that in the TLS the crack propagation stress is lower than the damage initiation stress, which is in many cases unrealistic. It is proposed to use two values instead of one for the material resistance against damage growth, one related to initiation and the other related to propagation. The resistance changes from the first to the second value as the damaged zone grows. With the two innovations presented in this paper, it is possible to simulate cusp formation in shear failure. It is emphasized that the robustness of the TLS is a significant advantage in the simulation of cusp formation which involves multiple merging cracks.