A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Svolos, Lampros; Mourad, Hashem M.; Manzini, Gianmarco; Garikipati, Krishna

doi:10.1016/j.jmps.2022.104910

Cited by 20 publications

(3 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, an isogeometric approach is adopted to get higher continuity in the basis function. Svolos et al . (2022) proposed a fourth-order PF model from a higher-order micromechanics approach using continuous/discontinuous Galerkin (C/DG) method.…”

Section: Introductionmentioning

confidence: 99%

“…Here, an isogeometric approach is adopted to get higher continuity in the basis function. Svolos et al (2022) proposed a fourth-order PF model from a higher-order micromechanics approach using continuous/discontinuous Galerkin (C/DG) method. Zhu et al (2022) applied an improved data transfer operator (HBFT) for modeling crack propagation in rock using an adaptive fourth-order PF model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Aurojyoti

Rajagopal

2023

View full text Add to dashboard Cite

PurposeThis study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C1 basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.Design/methodology/approachThe weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C0 non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C1) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.FindingsIt is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.Originality/valueFourth-order PFM is implemented using C1 non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Aurojyoti

Rajagopal

2023

View full text Add to dashboard Cite

show abstract

“…This characterizes the change that occurs during a phase transition. In the ordered phase, the order parameter differs from zero [21].…”

mentioning

confidence: 98%

Assessment of the possibility of using the fruits of the oriental persimo (Diospyros kaki L.) as a source of filter membranes based on the tensor approach

Khalilov,

Ismayilova,

Gasimova

et al. 2023

EEJET

View full text Add to dashboard Cite

Like all raw materials of plant origin, persimmon fruits are considered a material rich in carbohydrates. This subtropical plant grows almost throughout the entire territory of the Republic of Azerbaijan. Despite the widespread distribution of this plant in the republic, very few types of products are produced from it. The main reason why persimmon fruits are not used effectively from a production point of view is that they have astringent properties. Since fruit carbohydrates play an important role in eliminating the tart taste of persimmons, the study of the carbohydrate complex was considered as a basic condition. After fractionation of carbohydrates with a water-alcohol mixture, certain stresses arise in the filter residue, which consists of cellulose-lignin. These stresses are analyzed using tensors. It has been established that the size of the filter pores is about 0.005÷0.05 microns, and the volume of these pores is 0.062÷0.195 cm3/g. The clearance coefficient averaged 19.97 %. It is known that the outer layer of a plant cell consists of cellulose and other structural compounds. These substances determine the porosity of the material. The mass fraction of the final product of the fractional residue, more precisely cellulose, averaged 0.63 %. The use of the resulting filter membrane in the clarification of fruit juices has shown its usefulness in industry. It has been established that the selectivity of these membranes for various amino acids is 5÷18 %, and for minerals 1÷30 %. The lipid resistance of the membranes was high. It should be noted that cellulose has the ability to restore its structure and at the last stage acts only as a filter membrane. This explains the usefulness of the cellulose-lignin mixture as a membrane material

show abstract

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

Leng,

Svolos,

Boureima

et al. 2024

Numerical Meth Engineering

View full text Add to dashboard Cite

Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

show abstract

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Cited by 20 publications

References 93 publications

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Assessment of the possibility of using the fruits of the oriental persimo (Diospyros kaki L.) as a source of filter membranes based on the tensor approach

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

Contact Info

Product

Resources

About

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Cited by 20 publications

References 93 publications

Modeling fracture in brittle materials by higher-order phase field method using C1 non-Sibsonian interpolants

Modeling fracture in brittle materials by higher-order phase field method using C1 non-Sibsonian interpolants

Assessment of the possibility of using the fruits of the oriental persimo (Diospyros kaki L.) as a source of filter membranes based on the tensor approach

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

Contact Info

Product

Resources

About

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants