scholarly journals Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yue Hou ◽  
Fengyan Sun ◽  
Wenjuan Sun ◽  
Meng Guo ◽  
Chao Xing ◽  
...  
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Field Method ◽  
Field Variable ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Bituminous Materials ◽  
Fracture Modeling

Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.

scholarly journals Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth

2020 ◽  
Vol 26 ◽  
pp. 71 ◽  
Author(s):  
Matthias Ebenbeck ◽  
Patrik Knopf
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Chemical Potential ◽  
Type Equation ◽  
Field Variable ◽  
Reaction Diffusion Equation ◽  
Diffuse Interface ◽  
Interface Model ◽  
Diffuse Interface Model

We investigate a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn–Hilliard type equation for the phase field variable, a reaction diffusion equation for the nutrient concentration and a Brinkman type equation for the velocity field. These PDEs are endowed with homogeneous Neumann boundary conditions for the phase field variable, the chemical potential and the nutrient as well as a “no-friction” boundary condition for the velocity. The control represents a medication by cytotoxic drugs and enters the phase field equation. The aim is to minimize a cost functional of standard tracking type that is designed to track the phase field variable during the time evolution and at some fixed final time. We show that our model satisfies the basics for calculus of variations and we present first-order and second-order conditions for local optimality. Moreover, we present a globality condition for critical controls and we show that the optimal control is unique on small time intervals.

Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

2007 ◽  
Author(s):  
Naoki Takada
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

Phase Field Modeling of Brittle Fracture Based on the Cell-Based Smooth FEM by Considering Spectral Decomposition

2020 ◽  
pp. 2050016 ◽  
Author(s):  
Fan Peng ◽  
Wei Huang ◽  
Y. E. Ma ◽  
Z. Q. Zhang ◽  
Yao Zhang
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Spectral Decomposition ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Constitutive Response ◽  
Order Stress ◽  
Effective Phase

The spectral decomposition of the strain tensor is an essential technique to deal with the fracture problems via phase field method, and some incorrect results may be obtained without it. A novel phase field model for brittle fracture is developed based on cell-based smooth finite element (CS-FEM) and the spectral decomposition is taken into account. In order to describe the nonlinearity behaviors which contain the varied stress and elastic constitutive response caused by spectral decomposition. A second-order stress tensor and a fourth-order constitutive tensor based on decomposition of strain tensor are derived. A fundamental framework of CS-FEM is established to solve the phase field fracture problems, implemented by user-defined element (UEL) subroutine of ABAQUS software. The proposed model is validated by a typical Mode II crack, and the results show that the derived tensors are effective. Phase field parameter, CS-FEM parameter and mesh inhomogeneity are investigated to provide some useful suggestion for further development. Some classical numerical examples are solved by using the present model. The studies demonstrate that the proposed method can successfully overcome mesh distortion; the number of smooth cell does not show influences on the accuracy. Moreover, some results show that this method has the advantage over the standard FEM in convergence and computing efficiency.

A Phase-Field Model for the Formation of Martensite and Bainite

2014 ◽  
Vol 922 ◽  
pp. 31-36 ◽  
Author(s):  
Tansel T. Arif ◽  
Rong Shan Qin
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Materials Science ◽  
Current Model ◽  
Phase Field Model ◽  
Field Method ◽  
Field Variable ◽  
Phase Field Method ◽  
Cubic Symmetry ◽  
Chemical Free Energy

The phase field method is rapidly becoming the method of choice for simulating the evolution of solid state phase transformations in materials science. Within this area there are transformations primarily concerned with diffusion and those that have a displacive nature. There has been extensive work focussed upon applying the phase field method to diffusive transformations leaving much desired for models that can incorporate displacive transformations. Using the current model, the formation of martensite, which is formed via a displacive transformation, is simulated. The existence of a transformation matrix in the free energy expression along with cubic symmetry operations enables the reproduction of the 24 grain variants of martensite. Furthermore, upon consideration of the chemical free energy term, the model is able to utilise both the displacive and diffusive aspects of bainite formation, reproducing the autocatalytic nucleation process for multiple sheaves using a single phase field variable. Transformation matrices are available for many steels, one of which is used within the model.

Mapped phase field method for brittle fracture

2021 ◽  
Vol 385 ◽  
pp. 114046
Author(s):  
Tianju Xue ◽  
Sigrid Adriaenssens ◽  
Sheng Mao
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method
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