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

Muench, Ingo; Gierden, Christian; Wagner, Werner

doi:10.1002/nme.5909

Cited by 7 publications

(5 citation statements)

References 56 publications

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“…While the linear and cubic functions satisfy equation ( 33) perfectly, however, the tangent hyperbolicus function does not. If θ = 14 a residual error of 1 − h tanh (φ = 1) = h tanh (φ = 0) ≈ 10 −6 remains [38].…”

Section: Khachaturyan Approachmentioning

confidence: 99%

Phase field model for the martensitic transformation: comparison of the Voigt/Taylor and Khachaturyan approach

Schmidt

Ammar

Dornisch

et al. 2021

Continuum Mech. Thermodyn.

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Iron and steels are allotropes, meaning they exhibit different crystal configurations. The martensitic transformation is crucial for a variety of processes, such as hardening. It is induced by a combination of undercooling and mechanical deformation. Due to the changing material properties within the phases, and due to topological changes that might occur during the transformation, a phase field approach was chosen that incorporates both the mechanical and the chemical aspect of this problem. A comparison of the Voigt/Taylor approach to the Khachaturyan approach within a multi-variant phase field modeling of the martensitic transformation including a chemical and a mechanical energy contribution is presented in this paper. The model was implemented in the finite element codes FEAP and Z-set independently. Numerical examples are given in order to highlight the features of this model.

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Section: Khachaturyan Approachmentioning

confidence: 99%

Phase field model for the martensitic transformation: comparison of the Voigt/Taylor and Khachaturyan approach

Schmidt

Ammar

Dornisch

et al. 2021

Continuum Mech. Thermodyn.

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show abstract

“…To compare results between standard FEM and IGA, we restrict ourself to linear strain ε = SymGrad[u] as proposed in [5,6]. However, we refer to [7,8], if Green or Cosserat strain is of interest.…”

Section: The Phase Field Modelmentioning

confidence: 99%

Topology Optimization with Isogeometric Analysis and Phase Field Modeling

Muench

Klassen

Wagner

2019

Proc Appl Math and Mech

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We use a Phase Field Model (PFM) for the evolution of load-bearing structures on base of the equivalent stress criterion. Similar to Evolutionary Structural Optimization, the equivalent stress from all integration points is collected to evaluate a threshold. The approach couples density and stiffness to the phase field variable. The topology evolves from homogeneously filled regions by nucleation of holes. In numerical examples we compare results using standard Finite Elements (FEM) and Isogeometric Analysis (IGA), respectively. Latter allows for higher continuity between elements, which is essential to avoid the well-known mesh-pinning effect.

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“…However, we find out, that in some cases where singularities occur, the order parameter φ can exceed its valid range. We suggest therefore another interpolation function such as in [2] with the properties s(φ ≤ 0) ≈ 0 and s(φ ≥ 1) ≈ 1. Compared to a linear interpolation exceeding has no effect on the energy landscape, which in turn means the order parameter will stay in its valid range.…”

Section: Remarksmentioning

confidence: 99%

Martensitic transformation at a crack under mode I and II loading

Schmidt

Dornisch

Müller

2019

Proc Appl Math and Mech

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Metastable austenitic steels can undergo phase transformation. As an allotrope two crystal configurations are of interest: the softer austenitic parent phase and the martensitic phases. Here, the bain orientation relationship leads to distinct orientations for the martensitic variants with a different transformation strain [7]. A phase field approach is used to model the transformation, where a multi-valued order parameter φ identifies the austenitic parent phase and the martensitic variants. This allows to define bulk and surface energies as regularized functions in terms of the order parameter and its gradient. The kinetics of the martensitic transformation are temperature dependent. Temperatures below an equilibrium temperature favour the growth of the martensitic phase, whereas temperatures above the equilibrium favour the austenitic phase. Approaching the equilibrium temperature slows down the transformation [5]. In this work we consider a static crack under mode I and mode II loading.

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

Cited by 7 publications

References 56 publications

Phase field model for the martensitic transformation: comparison of the Voigt/Taylor and Khachaturyan approach

Phase field model for the martensitic transformation: comparison of the Voigt/Taylor and Khachaturyan approach

Topology Optimization with Isogeometric Analysis and Phase Field Modeling

Martensitic transformation at a crack under mode I and II loading

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