Variational formulation of loading-induced damage anisotropy: Theoretical framework for second-order anisotropic damage and Lip-field regularization
Year: 2025
Type: article
Abstract: Variational approaches for damage and fracture are now well established. Most of them are restricted to isotropic (scalar) damage, but tensorial internal variables are needed to properly account for loading-induced damage anisotropy. The objective of the present work is to present a theoretical framework for the variational formulation of second-order tensorial damage, in order to exploit the finesse and physical consistency of an anisotropic modeling of damage. Theoretical developments are conducted in order to investigate conceptual locks for such a type of formulation. A regularized anisotropic damage model is developed in a Lip-field framework, using the concept of accumulated damage. This quantity is introduced to define a scalar dissipation potential, whereas the tensorial damage variable appears in the free-energy potential. The proposed constitutive modeling serves both as a proof of concept and as a support for the analysis of the advantages and disadvantages of explicitly accounting for damage anisotropy through a tensorial damage variable. The proposed formulation is implemented in an ad-hoc finite element code in order to perform simple computations.
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,220
OpenAlex ID: W4415402004