A micromechanics-informed phase field model for brittle fracture accounting for unilateral constraint. (January 2021)

• Record Type: Journal Article
• Authors: Liu, Yangyuanchen; Cheng, Cheng; Ziaei-Rad, Vahid; Shen, Yongxing
• Is Part Of: Engineering fracture mechanics. Volume 241(2021)
• Publication Date: 2021-01
• Subjects: Phase field approach to fracture -- Variational theory of fracture -- Micromechanics -- Homogenization theory -- Unilateral constraint; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2020.107358
• Languages: English
• ISSNs: 0013-7944

Abstract

Highlights: A micromechanics-informed phase field model for fracture is proposed. The proposed model is made closely match the response of the representative volume element, including the frictionless self-contact condition. The material degradation is consistently determined without artificial assumptions. The model can be expressed in terms of invariants and pseudo-invariants of the strain tensor, and hence easy to be applied to an arbitrary crack orientation. The methodology involved can be generalized to more complicated material constitutive relations, such as anisotropy or inelasticty. Abstract: We propose a new direction-dependent model for the unilateral constraint involved in the phase field approach to fracture and also in the continuous damage mechanics models. The construction of this phase field model is informed by micromechanical modeling through the homogenization theory, where the representative volume element (RVE) has a planar crack in the center. The proposed model is made closely match the response of the RVE, including the frictionless self-contact condition. This homogenization approach allows to identify a direction-dependent phase field model with the tension–compression split obtained from cracked microstructures. One important feature of the proposed model is that unlike most other models, the material degradation is consistently determined without artificial assumptions or ad hoc parameters with no physical interpretation, thus, a more realistic modeling is resulted. With standard tests such as uniaxial loadings, three-point bending, simple shear, and through-crack tests, the proposed model predicts reasonable crack paths. Moreover, with the RVE response as a benchmark, the proposed model gives rise to an accurate stress–strain curve under shear loads, more accurate than most existing models.