Phase field and gradient enhanced damage models for quasi-brittle failure: A numerical comparative study

Mandal, Tushar Kanti; Nguyen, Vinh Phu; Heidarpour, Amin

doi:10.1016/j.engfracmech.2018.12.013

Cited by 68 publications

(27 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A detailed description on the different crack-driving forces that can be employed in conjuction with Equation (72) is provided in Miehe et al [256]. The coupled field Equations (71) and (72) are subject to the boundary conditions introduced in Equation 1…”

Section: Pfm Strong Formmentioning

confidence: 99%

“…The governing equations of the crack propagation problem emerge through the minimization of the total potential energy established in Equation (70), see, e.g., [69]. This gives rise to the coupled system of equilibrium and phase field governing equations established in Equations (71) and (72). The crack is not explicitly represented but derived from the solution of the coupled system as the region where c = 0 (typically values of c < 10e − 3).…”

Section: Crack Propagation By Pfmmentioning

confidence: 99%

“…In the taxonomy of damage theories, diffuse crack approximations fall within the family of Continuum Damage Mechanics, where however particular treatment of strain localisation is implicitly performed. de Borst and Verhoosel [70], see, also Mandal et al [71] highlighted the similarities between gradient enhanced damage methods and phase field methods. An insightful discussion on the similarities and differences between thick level sets and phase fields is provided in [72].…”

mentioning

confidence: 93%

See 2 more Smart Citations

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

et al. 2019

View full text Add to dashboard Cite

Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

show abstract

Section: Pfm Strong Formmentioning

confidence: 99%

Section: Crack Propagation By Pfmmentioning

confidence: 99%

mentioning

confidence: 93%

See 1 more Smart Citation

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Related to these remedies is the phase field method which closely resembles a gradient-based damage model [29]. The sharper approximation of crack width is one of the main advantages of the phase field methods to gradient-based damage models [30].…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture

2019

View full text Add to dashboard Cite

We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture.

show abstract

“…The method has been proven capable of modelling complex crack morphologies such as crack coalescence [9], crack branching [10], curvilinear crack paths [11], to name a few. For a more comprehensive review of the phase field and its implementation, interested readers are referred to the work of Ambati et al [12], Wu et al [13], Bourdin et al [14], Mandal et al [15]. Apart from this, the salient feature of the approach is that, existing finite element solvers can directly be used without any modification.…”

Section: Introductionmentioning

confidence: 99%

Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition

Hirshikesh

Jansari

Kannan

et al. 2019

Engineering Fracture Mechanics

View full text Add to dashboard Cite

Phase field and gradient enhanced damage models for quasi-brittle failure: A numerical comparative study

Cited by 68 publications

References 68 publications

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture

Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition

Contact Info

Product

Resources

About