Correction to: Small strain multiphase-field model accounting for configurational forces and mechanical jump conditions

Abstract In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the regularized crack. The key novelty is the combination of a strain energy split with a partial rank-I relaxation in the vicinity of the diffuse interface. The former is necessary to account for physically meaningful crack kinematics like crack closure, the latter ensures the mechanical jump conditions throughout the diffuse region. The model is verified by a convergence study, where a circular bi-material disc with and without a crack is subjected to radial loads. For the uncracked case, analytical solutions are taken as reference. In a second step, the model is applied to crack propagation, where a meaningful influence on crack branching is observed, that underlines the necessity of a reasonable homogenization scheme. The presented model is particularly relevant for the combination of any variational strain energy split in the fracture phase-field model with a diffuse modeling approach for material heterogeneities.

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Phase-field elasticity model based on mechanical jump conditions

Computational Mechanics ◽

10.1007/s00466-015-1141-6 ◽

2015 ◽

Vol 55 (5) ◽

pp. 887-901 ◽

Cited By ~ 33

Author(s):

Daniel Schneider ◽

Oleg Tschukin ◽

Abhik Choudhury ◽

Michael Selzer ◽

Thomas Böhlke ◽

...

Keyword(s):

Phase Field ◽

Jump Conditions ◽

Model Based ◽

Mechanical Jump Conditions

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Simulations for a New Phase-Field Model for Phase Transitions Driven by Configurational Forces

Journal of Physics Conference Series ◽

10.1088/1742-6596/1622/1/012074 ◽

2020 ◽

Vol 1622 ◽

pp. 012074

Author(s):

Mei Chen

Keyword(s):

Phase Transitions ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Configurational Forces ◽

New Phase

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Phase-inherent linear visco-elasticity model for infinitesimal deformations in the multiphase-field context

Advanced Modeling and Simulation in Engineering Sciences ◽

10.1186/s40323-020-00178-x ◽

2020 ◽

Vol 7 (1) ◽

Author(s):

Felix K. Schwab ◽

Andreas Reiter ◽

Christoph Herrmann ◽

Daniel Schneider ◽

Britta Nestler

Keyword(s):

Compatibility Condition ◽

Field Method ◽

Model Material ◽

Sharp Interface ◽

Diffuse Interface ◽

Jump Conditions ◽

Material Behaviour ◽

Infinitesimal Deformations ◽

Mechanical Jump Conditions ◽

Continuous Traction

AbstractA linear visco-elasticity ansatz for the multiphase-field method is introduced in the form of a Maxwell-Wiechert model. The implementation follows the idea of solving the mechanical jump conditions in the diffuse interface regions, hence the continuous traction condition and Hadamard’s compatibility condition, respectively. This makes strains and stresses available in their phase-inherent form (e.g. $$\varepsilon ^{\alpha }_{ij}$$ ε ij α , $$\varepsilon ^{\beta }_{ij}$$ ε ij β ), which conveniently allows to model material behaviour for each phase separately on the basis of these quantities. In the case of the Maxwell-Wiechert model this means the introduction of phase-inherent viscous strains. After giving details about the implementation, the results of the model presented are compared to a conventional Voigt/Taylor approach for the linear visco-elasticity model and both are evaluated against analytical and sharp-interface solutions in different simulation setups.

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Configurational Forces in a Phase Field Model for Dynamic Brittle Fracture

Advanced Structured Materials - Advances in Mechanics of Materials and Structural Analysis ◽

10.1007/978-3-319-70563-7_16 ◽

2018 ◽

pp. 343-364

Author(s):

Alexander Schlüter ◽

Charlotte Kuhn ◽

Ralf Müller

Keyword(s):

Brittle Fracture ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Configurational Forces ◽

Dynamic Brittle Fracture

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Numerical homogenization of the Eshelby tensor at small strains

Mathematics and Mechanics of Solids ◽

10.1177/1081286517724607 ◽

2017 ◽

Vol 25 (7) ◽

pp. 1504-1514 ◽

Cited By ~ 1

Author(s):

Charlotte Kuhn ◽

Ralf Müller ◽

Markus Klassen ◽

Dietmar Gross

Keyword(s):

Boundary Value Problem ◽

Stress Tensor ◽

Representative Volume Element ◽

Boundary Value ◽

Small Strain ◽

Volume Element ◽

Configurational Forces ◽

Numerical Homogenization ◽

Representative Volume ◽

Eshelby Stress

Numerical homogenization methods, such as the FE2 approach, are widely used to compute the effective physical properties of microstructured materials. Thereby, the macroscopic material law is replaced by the solution of a microscopic boundary value problem on a representative volume element in conjunction with appropriate averaging techniques. This concept can be extended to configurational or material quantities, like the Eshelby stress tensor, which are associated with configurational changes of continuum bodies. In this work, the focus is on the computation of the macroscopic Eshelby stress tensor within a small-strain setting. The macroscopic Eshelby stress tensor is defined as the volume average of its microscopic counterpart. On the microscale, the Eshelby stress tensor can be computed from quantities known from the solution of the physical microscopic boundary value problem. However, in contrast to the physical quantities of interest, i.e. stress and strain, the Eshelby stress tensor is sensitive to rigid body rotations of the representative volume element. In this work, it is demonstrated how this must be taken into account in the computation of the macroscopic Eshelby stress tensor. The theoretical findings are illustrated by a benchmark simulation and further simulation results indicate the microstructural influence on the macroscopic configurational forces.

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