Phase-field topology optimization model that removes the curvature effects

Takaki, Tomohiro; Kato, Junji

doi:10.1299/mej.16-00462

Cited by 6 publications

(2 citation statements)

References 65 publications

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“…The great success of the phase‐field method in material science is due to the advantages of the phase‐field method also listed in the recent work of Takaki and Kato: tracking the interface position is not necessary such that the finite element mesh can be fixed during the topology evolution. The evolution equation itself can be derived from the total energy given in Equation .…”

Section: Discussionmentioning

confidence: 99%

A phase field model for stress‐based evolution of load‐bearing structures

Muench

Gierden

Wagner

2018

Numerical Meth Engineering

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Summary We present a continuum‐type optimality algorithm for the evolution of load‐bearing solid structures with linear elastic material. The objective of our model is to generate structures with help of a sensitivity function accounting for equivalent stress. Similar to Evolutionary Structural Optimization, a threshold of equivalent stress is evaluated. However, we do not consider a material rejection ratio. The evolution process is governed by an Allen‐Cahn equation in the context of phase field modeling. The steady state of phase transition is the final geometry of the structure. The model accounts for the desired filling level, geometry of the design space, static loadings, and boundary conditions. Our variational approach drops conservation of mass and couples density as well as stiffness of the continuum by a sophisticated function to the phase field variable. Continuous regions of voids and material evolve from the initial state of homogeneously distributed material. The complexity of evolving structures depends on two numerical parameters, which we discuss in several examples.

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Section: Discussionmentioning

confidence: 99%

A phase field model for stress‐based evolution of load‐bearing structures

Muench

Gierden

Wagner

2018

Numerical Meth Engineering

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“…In this study, therefore, the motion of diffuse interface without the curvature effect is modeled. 28) Although our modeling is made for the solidification problem, the present model can be applied to other phase transformations including solid-state phase transformations.…”

Section: Melting and Solidificationmentioning

confidence: 99%

Multi-Phase-Field Modeling of Transformation Kinetics at Multiple Scales and Its Application to Welding of Steel

2019

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Production processes of structural materials generally involve a variety of microstructural evolutions, spatiotemporal scales of which are different by several orders of magnitude. In this study, a multi-phase-field model for simulating transformation phenomena at multiple scales is developed by considering mesoscopic kinetics of interest based on diffuse interface description without curvature effect. In particular, the present model is developed for simulations of microstructural evolutions during welding of carbon steels. In this model, the motion of dendrite envelope is described to simulate solidification not at a dendritic scale but at a scale of grain structure. Moreover, the pinning effect is described based on a mean-field approximation, which allows for simulations of grain growth with existence of very fine particles. The present model is applied to two-dimensional simulations for welding processes of carbon steel. The microstructural evolution involving the melting, solidification, austenite grain growth and pinning effect due to very fine particles is demonstrated.

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