A rate-dependent cohesive crack model based on anisotropic damage coupled to plasticity

Abstract

SUMMARYIn quasi-brittle material the complex process of decohesion between particles in microcracks and localization of the displacement field into macrocracks is limited to a narrow fracture zone, and it is often modelled with cohesive crack models. Since the anisotropic nature of the decohesion process in separation and sliding is essential, it is particularly focused in this paper. Moreover, for cyclic and dynamic loading the unloading, load reversal (including crack closure) and rate dependency are essential features that are included in a new model. The modelling of degradation is based on a 'localized' version of anisotropic continuum damage coupled to inelasticity. The concept of strain energy equivalence between the states in the effective and nominal settings is adopted in order to define the free energy of the interface. The proposed fracture criterion is of the Mohr type, with a smooth transition of the failure and kinematics (slip and dilatation) characteristics between tension and shear. The chosen potential, of the Lemaitre-type, for evolution of the dissipative processes is additively decomposed into plastic and damage parts, and nonassociative constitutive equations are obtained. The constitutive equations are integrated by applying the backward Euler rule and by using Newton iteration. The proposed model is assessed analytically and numerically and a typical calibration procedure for concrete is proposed.

Discrete crack modelling in a new X‐FEM format with emphasis on dynamic response

“…Consider a mixed control tension test with monotonically increasing displacement in normal direction ðv n > 0Þ while the shear stress is zero ðt ¼ 0Þ: According to [23] the damage vector in this case is just developed in the normal direction ðd ¼ d n e n Þ and they derived explicit expressions of the fracture energy. Figure 7 gives the response of the constitutive The damage vector develops in this case in the tangential direction ðd ¼ d t e t Þ and it is possible to derive explicit expressions even for this case of rate-independent simple tension.…”

“…Explicit expressions of t and d are presented in [23]. The damage vector determines the degradation, but by introducing an effective quantity, d; the effects of micro-crack-closure-reopening (MCR) can be considered.…”

“…The detailed assessment of the proposed constitutive model is outlined in [23]. Analytical expressions are derived for the important special cases (rate-independent) simple tension and simple shear, together with a number of numerical assessments of mixed-mode fracturing.…”

“…The model is defined by 12 parameters and in [23] is a procedure for calibration of this parameters proposed. In Table I is a typical calibration for normal performance concrete proposed, which also are used in the forthcoming numerical examples.…”

“…Interface models for cementious composites based on plasticity are proposed in [21], together with damage-based models for application on polycrystalline microstructures according to [22]. For quasi-brittle material subjected to dynamic loading, a rate-dependent cohesive crack model based on anisotropic damage coupled to plasticity was recently proposed in [23].…”