scholarly journals Computable Early C. elegans Embryo with a Data-driven Phase Field Model

2020 ◽  
Author(s):  
Xiangyu Kuang ◽  
Guoye Guan ◽  
Ming-Kin Wong ◽  
Lu-Yan Chan ◽  
Zhongying Zhao ◽  
...  
Keyword(s):  
Cell Proliferation ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Data Driven ◽  
Model Parameters ◽  
C Elegans ◽  
Model Animal ◽  
Embryonic Morphogenesis ◽  
Cell Cell

Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis, consisting of both cell proliferation and cell migration. Despite the fact that much is known about specific regulations at the molecular level, how cell proliferation and migration together drive the morphogenesis at the cellular and organismic levels is not well understood. Here, using Caenorhabditis elegans as the model animal, we present a data-driven phase field model to compute the early embryonic morphogenesis within a confined eggshell. By using three-dimensional time-lapse cellular morphological information generated by imaging experiments to set the model parameters, we can not only reproduce the precise evolution of cell location, cell shape and cell-cell contact relationship in vivo, but also reveal the critical roles of cell division and cell-cell attraction in governing the early development of C. elegans embryo. In brief, we provide a generic approach to compute the embryonic morphogenesis and decipher the underlying mechanisms.

scholarly journals Computable early Caenorhabditis elegans embryo with a phase field model

2022 ◽  
Vol 18 (1) ◽  
pp. e1009755
Author(s):  
Xiangyu Kuang ◽  
Guoye Guan ◽  
Ming-Kin Wong ◽  
Lu-Yan Chan ◽  
Zhongying Zhao ◽  
...  
Keyword(s):  
Cell Proliferation ◽  
Caenorhabditis Elegans ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Time Lapse ◽  
Underlying Mechanism ◽  
Model Animal

Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis, consisting of both cell proliferation and cell migration. Despite the fact that much is known about specific regulations at molecular level, how cell proliferation and migration together drive the morphogenesis at cellular and organismic levels is not well understood. Using Caenorhabditis elegans as the model animal, we present a phase field model to compute early embryonic morphogenesis within a confined eggshell. With physical information about cell division obtained from three-dimensional time-lapse cellular imaging experiments, the model can precisely reproduce the early morphogenesis process as seen in vivo, including time evolution of location and morphology of each cell. Furthermore, the model can be used to reveal key cell-cell attractions critical to the development of C. elegans embryo. Our work demonstrates how genetic programming and physical forces collaborate to drive morphogenesis and provides a predictive model to decipher the underlying mechanism.

scholarly journals Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials

2021 ◽  
Author(s):  
Christoph Herrmann ◽  
Daniel Schneider ◽  
Ephraim Schoof ◽  
Felix Schwab ◽  
Britta Nestler
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Compressive Load ◽  
Phase Field Model ◽  
Model Parameters ◽  
Ductile Crack ◽  
Critical Energy Release Rate ◽  
Compression Load

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically, in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack, propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties, concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension-compression load asymmetry of the stress-strain response, are covered by the model. The behaviour is analysed on basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The used material parameters correspond to graphite lamellae and pearlite.

scholarly journals A unified phase-field model of fracture in viscoelastic materials

2021 ◽  
Author(s):  
Franz Dammaß ◽  
Marreddy Ambati ◽  
Markus Kästner
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Energy Functional ◽  
Internal Variables ◽  
Model Parameters ◽  
Rate Dependency ◽  
Viscoelastic Materials

AbstractThe phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy functional which consists of free energy and dissipation due to fracture. The free energy includes a contribution which is related to viscous dissipation that plays an essential role in coupling the phase-field and the viscous internal variables. The governing equations for the phase-field and the viscous internal variables are deduced in a consistent thermodynamic manner from the pseudo-energy functional. The resulting model establishes a two-way coupling between crack phase-field and relaxation mechanisms, i.e. viscous internal variables explicitly enter the evolution of phase-field and vice versa. Depending on the specific choice of the model parameters, it has flexibility in capturing the possible coupled responses, and the approaches of recently published formulations are obtained as limiting cases. By means of a numerical study of monotonically increasing load, creep and relaxation phenomena, rate-dependency of failure in viscoelastic materials is analysed and modelling assumptions of the present formulation are discussed.

scholarly journals Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4956
Author(s):  
Christoph Herrmann ◽  
Daniel Schneider ◽  
Ephraim Schoof ◽  
Felix Schwab ◽  
Britta Nestler
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Compressive Load ◽  
Phase Field Model ◽  
Model Parameters ◽  
Ductile Crack ◽  
Critical Energy Release Rate ◽  
Compression Load

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension–compression load asymmetry of the stress–strain response, are covered by the model. The behaviour is analysed on the basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The material parameters used correspond to graphite lamellae and pearlite.

MARMOT Phase-Field Model for the U-Si System

2016 ◽  
Author(s):  
Larry Kenneth Aagesen ◽  
Daniel Schwen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

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