Modeling of cohesive crack growth using an adaptive mesh refinement via the modified-SPR technique

Abstract

In this paper, an adaptive finite element procedure is presented in modeling of mixed-mode cohesive crack propagation via the modified superconvergent path recovery technique. The adaptive mesh refinement is performed based on the ZienkiewiczZhu error estimator. The weighted-SPR recovery technique is employed to improve the accuracy of error estimation. The Espinosa-Zavattieri bilinear cohesive zone model is applied to implement the traction-separation law. It is worth mentioning that no previous information is necessary for the path of crack growth and no region of the domain is necessary to be filled by the cohesive elements. The maximum principal stress criterion is employed for predicting the direction of extension of the cohesive crack in order to implement the cohesive elements. Several numerical examples are analyzed numerically to demonstrate the capability and efficiency of proposed computational algorithm.

Modeling of cohesive crack growth in partially saturated porous media; a study on the permeability of cohesive fracture

“…A fracture criterion was proposed by Camacho and Ortiz (1996) for the mixed mode fracture and widely used in literature. The cohesive fracture model has been widely used in fracture mechanics problems, including: the quasi-static crack propagation of saturated porous media by Simoni and Secchi (2003), Schrefler et al (2006) and Secchi et al (2007), the cohesive crack growth of brittle materials by Song et al (2006), Birgisson et al (2008) and Khoei et al (2009), and the dynamic fracture propagation of saturated porous media by Khoei et al (2010).…”

“…The technique was proposed by Schrefler et al (2006) and Secchi et al (2007) based on an adaptive mesh refinement in porous materials. The cohesive crack growth was performed by Khoei et al (2009) using the adaptive FE strategy in the framework of cohesive interface elements. A new formulation was developed for double-nodded interface elements by Khoei et al (2010) in the dynamic fracture propagation of saturated porous media, in which a new transversal conductivity relation was introduced.…”

p‐Adaptive Refinement Based on Stress Recovery Technique Considering Ordinary Kriging Interpolation in L‐Shaped Domain

“…The ideas of Zienkiewicz and Zhu [3][4][5] using the superconvergent patch recovery (SPR) are often preferred by researchers since they are robust and simple to use. Some references [6][7][8][9][10][11] contain extensive reviews of the different proposals for improving the SPR technique. They used the conventional LSM (least square method) to obtain recovered stresses from the ℎ-version of finite element solution at the sampling quadrature points.…”

“…Recently, some researchers [6,7] used a weighted superconvergent patch recovery technique in which the recovered stresses are calculated by using weighting parameters. In addition to these, the recover-based technique has been also extended to mesh based PUMs and the X-FEM (extended finite element method) [15].…”

Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach

“…For example, cohesive zones may be inserted dynamically during a simulation based on a criterion such as the stress state between adjacent elements (Pandolfi and Ortiz 2002), possibly combined with re-meshing to allow for more arbitrariness in propagation direction (Khoei et al 2009). Importantly, cohesive zones are a very useful concept and integrate easily with existing methods.…”