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The Phase-Field Method in Optimal Design
2006We describe the phase-field method, a new approach to optimal design originally introduced in Bourdin and Chambolle (2000, 2003). It is based on the penalization of the variation of the properties of the designs, and its variational approximation (in the sense of Г-convergence.
Blaise Bourdin, Antonin Chambolle
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A phase-field method for shape optimization of incompressible flows
Computers & Mathematics with Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Futuan Li, Xianliang Hu
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Phase-field modeling by the method of lattice Boltzmann equations
Physical Review E, 2010In this paper, at first, a lattice Boltzmann method for binary fluids, which is applicable at low viscosity values, is developed. The presented scheme is extension of the free-energy-based approach to a multi-relaxation-time collision model. Various benchmark problems such as the well-known Laplace law for stationary bubbles and capillary-wave test are
Fakhari, Abbas, Rahimian, Mohammad H.
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Bone Remodeling from the Perspective of the Phase Field Method
2019In this work, we have developed a mechanobiological model of bone remodeling involving a mineralization of bone in a moving diffuse interface separating the marrow containing all specialized cells from newly formed bone. The phase field describes the degree of mineralization within the diffuse interface at the level of individual trabeculae; it varies ...
Boisse, Julien +2 more
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From classical thermodynamics to phase-field method
Progress in Materials Science, 2022Yuhong Zhao, Long-Qing Chen
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A phase field numerical manifold method for crack propagation in quasi-brittle materials
Engineering Fracture Mechanics, 2021Yongtao Yang, Hong Zheng
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An effective phase field method for topology optimization without the curvature effects
Computers and Mathematics With Applications, 2023Yibao Li
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Mapped phase field method for brittle fracture
Computer Methods in Applied Mechanics and Engineering, 2021Sheng Mao +2 more
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Adaptive phase field method using novel physics based refinement criteria
Computer Methods in Applied Mechanics and Engineering, 2021Haim Waisman, S Natarajan
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