A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

Abali, Bilen Emek; Klunker, André; Barchiesi, Emilio; Placidi, Luca

doi:10.1002/zamm.202000289

Cited by 38 publications

(16 citation statements)

References 119 publications

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“…However, its generalization to damage mechanics has difficulties, since damage mechanics is not acquired directly from the variational formalism. With this work, we expect to shed some light on this formalism and motivate to develop numerical methods based on a purely variational formulation [20,70]. By using the additional balance law from the extended N formalism is expected to be beneficial in such a setting for modeling the propagation of discontinuities in primitive variables (crack for the displacement field).…”

Section: Discussionmentioning

confidence: 99%

Energy based methods applied in mechanics by using the extended Noether's formalism

Abali¹

2022

Preprint

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Physical systems are modeled by field equations, these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former is axiomatically given and the latter is thermodynamically derived. This method has difficulties in damage mechanics in generalized continua. An alternative method to derive governing equations is based on a variational framework known as the extended N 's formalism. Albeit being very prominent, its use is less known in applied mechanics as a field theory. In this work, we demonstrate the power of extended N 's formalism by using tensor algebra and usual continuum mechanics nomenclature.

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Section: Discussionmentioning

confidence: 99%

Energy based methods applied in mechanics by using the extended Noether's formalism

Abali¹

2022

Preprint

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“…Understanding these interactions is an important step toward developing better predictive models for designing materials with tailored properties [101][102][103][104] and microstructures [105][106][107][108]. Damage in materials is studied by phase-field models [109][110][111][112][113], and we use phase-field approach herein for twin interactions. These interactions [114] may result in the formation of twin-twin junctions that may cause strain hardening [115] and crack initiation [116,117], leading to a strong influence on the overall material performance.…”

Section: Studying Twin Interactions Toward Microstructure Tailoring A...mentioning

confidence: 99%

Phase-field approach to evolution and interaction of twins in single crystal magnesium

et al. 2022

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Crack initiation and propagation as well as abrupt occurrence of twinning are challenging fracture problems where the transient phase-field approach is proven to be useful. Early-stage twinning growth and interactions are in focus herein for a magnesium single crystal at the nanometer length-scale. We demonstrate a basic methodology in order to determine the mobility parameter that steers the kinetics of phase-field propagation. The concept is to use already existing molecular dynamics simulations and analytical solutions in order to set the mobility parameter correctly. In this way, we exercise the model for gaining new insights into growth of twin morphologies, temporally-evolving spatial distribution of the shear stress field in the vicinity of the nanotwin, multi-twin, and twin-defect interactions. Overall, this research addresses gaps in our fundamental understanding of twin growth, while providing motivation for future discoveries in twin evolution and their effect on next-generation material performance and design.

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“…We have implemented a transient, fully coupled solution strategy by using open-source packages from the FEniCS Project [163]. We refer to [164,165,166] for implementations in FEniCS by means of a staggered scheme. Herein, the implementation is using a monolithic approach, where displacement and phase fields are solved at once.…”

Section: Multiphysics Simulationmentioning

confidence: 99%

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

Amirian,

Jafarzadeh,

Abali

et al. 2022

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A computational method is proposed for simulating and informing on controlling failure pattern development in anisotropic brittle solids experiencing extreme mechanical loading. Constitutive equations are derived by using thermodynamics in order to establish a fully coupled and transient fracture mechanics model. A phase-field approach is developed for modeling twinning, fracture, and fracture-induced twinning in single crystals at nanometer length-scale. At the nanoscale, this continuum mechanics based formulation is implemented in a monolithic computational scheme ensuring necessary accuracy for the following problems: (i) twin evolution in 2D single crystal magnesium and boron carbide under simple shear deformation; (ii) crack-induced twinning for single crystal magnesium under pure mode I and mode II loading; and (iii) study of fracture in homogeneous single crystal boron carbide under biaxial compressive loading. The results are verified by steady-state phase-field approach and validated by available experimental data in the literature. The success of this computational method relies on using two separate phase-field (order) parameters related to fracture and twinning. A finite element method-based code is developed within the Python-based open-source platform FEniCS. We make the code publicly available and the developed algorithm may be extended for the study of phase transformations under dynamic loading or thermally-activated mechanisms, where the competition between various deformation mechanisms is accounted for within the current comprehensive model approach.

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A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

Cited by 38 publications

References 119 publications

Energy based methods applied in mechanics by using the extended Noether's formalism

Energy based methods applied in mechanics by using the extended Noether's formalism

Phase-field approach to evolution and interaction of twins in single crystal magnesium

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

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