A unified regularized variational cohesive fracture theory with directional energy decomposition. (English) Zbl 07646839
Summary: In this paper, the cohesive fracture is revisited as an energy minimization problem. The energy functional is rigorously derived based on a pair of integral transformations and a novel directional energy decomposition method. The resulting description of the regularized crack is perfectly suitable for cohesive fracture. A well-defined crack direction is associated with each material point. The resulting constitutive relation shows that a damage-induced material orthotropy within the regularized crack is introduced in this theory, which is suitable for cohesive fracture. The proposed method can implement an arbitrarily given mixed-mode cohesive law. The tensile and shear fracture modes are covered in a unified manner and controlled by the tensile-to-shear strength ratio. These theoretical results are presented with detailed proofs and verified numerically by some representative examples involving tension, shear, and compression.
Keywords:
variational method; cohesive fracture; phase-field model; energy decomposition; mixed-mode cohesive law; damage mechanicsReferences:
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