Research graph
References from Thermo-mechanical phase-field fracture modeling via deep Ritz method. Local targets link to admitted publications; unresolved targets remain external evidence.
The phenomena of rupture and flow in solids
10.1098/rsta.1921.0006 · 1921 · External reference
Revisiting brittle fracture as an energy minimization problem
10.1016/s0022-5096(98)00034-9 · 1998 · External reference
Numerical experiments in revisited brittle fracture
10.1016/s0022-5096(99)00028-9 · 2000 · External reference
Unresolved reference
2008 · External reference
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
10.1002/nme.2861 · 2010 · External reference
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
10.1016/j.cma.2010.04.011 · 2010 · External reference
A review on phase-field models of brittle fracture and a new fast hybrid formulation
10.1007/s00466-014-1109-y · 2015 · External reference
Phase-field modeling of fracture
2020 · External reference
Phase field modeling and computer implementation: A review
10.1016/j.engfracmech.2022.108234 · 2022 · External reference
Crack nucleation in variational phase-field models of brittle fracture
10.1016/j.jmps.2017.09.006 · 2018 · External reference
Morphogenesis and propagation of complex cracks induced by thermal shocks
10.1103/physrevlett.112.014301 · 2014 · External reference
A phase-field model for thermo-mechanical fracture
2023 · External reference
A thermo-mechanical phase-field fracture model: Application to hot cracking simulations in additive manufacturing
2022 · External reference
Phase-field modeling of drying-induced cracks: Choice of coupling and study of homogeneous and localized damage
2023 · External reference
A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation
10.1016/j.cma.2024.117165 · 2024 · External reference
Mechanical properties and failure behaviors of T1100/5405 composite T-joint under in-plane shear load coupled with initial defect and high-temperature
10.1016/j.compstruct.2023.117722 · 2024 · External reference
A Strategy for 3D Printed Al-Based Bi-Material Lattice Optimization: Thermal-Mechanical Coupling Performance with Load-Bearing and Energy-Absorption
10.1002/adfm.202521424 · 2026 · External reference
A Janus-Like Bio-Inspired Strategy for 3D-Printed Bimetallic Metamaterials with Excellent Thermal-Protection and Load Bearing Capacity
10.1002/advs.202524116 · 2026 · External reference
A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure
10.1016/j.engfracmech.2015.03.045 · 2015 · External reference
Phase field modeling of interfacial damage in heterogeneous media with stiff and soft interphases
10.1016/j.engfracmech.2019.106574 · 2019 · External reference
A multiscale framework based on phase field method and XFEM to simulate fracture in highly heterogeneous materials
10.1016/j.tafmec.2019.02.002 · 2019 · External reference
Phase-field modeling of fracture in heterogeneous materials: Jump conditions, convergence and crack propagation
10.1007/s00419-020-01759-3 · 2021 · External reference
A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach
10.1016/j.cma.2015.03.009 · 2015 · External reference
Linear and nonlinear solvers for variational phase-field models of brittle fracture
10.1002/nme.5300 · 2017 · External reference
On penalization in variational phase-field models of brittle fracture
10.1016/j.cma.2019.05.038 · 2019 · External reference
Phase-field fracture modeling for large structures
10.1016/j.jmps.2022.105118 · 2023 · External reference
Adaptive FEM-SPIM coupling for phase-field modeling of fracture
10.1002/nme.7609 · 2025 · External reference
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
10.1016/j.jcp.2018.10.045 · 2019 · External reference
Physics-informed machine learning
10.1038/s42254-021-00314-5 · 2021 · External reference
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
10.1016/j.cma.2021.113741 · 2021 · External reference
Physics-informed neural networks for heat transfer problems
10.1115/1.4050542 · 2021 · External reference
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
10.1016/j.cma.2020.113547 · 2021 · External reference
Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
10.4208/cicp.oa-2020-0164 · 2020 · External reference
Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equations
10.1007/s10444-023-10065-9 · 2023 · External reference
Understanding and mitigating gradient flow pathologies in physics-informed neural networks
10.1137/20m1318043 · 2021 · External reference
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
10.1007/s40304-018-0127-z · 2018 · External reference
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
10.1016/j.cma.2019.112790 · 2020 · External reference
A deep energy method for finite deformation hyperelasticity
10.1016/j.euromechsol.2019.103874 · 2020 · External reference
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
10.1016/j.tafmec.2019.102447 · 2020 · External reference
Adaptive fourth-order phase field analysis using deep energy minimization
10.1016/j.tafmec.2020.102527 · 2020 · External reference
Unresolved reference
2022 · External reference
Physics informed neural networks for phase field fracture modeling enhanced by length-scale decoupling degradation functions
10.3389/fphy.2023.1152811 · 2023 · External reference
Phase-field modeling of fracture with physics-informed deep learning
10.1016/j.cma.2024.117104 · 2024 · External reference
The novel physics-enhanced graph neural network for phase-field fracture modelling
10.1016/j.cma.2025.118284 · 2025 · External reference
Neural networks meet phase-field: A hybrid fracture model
10.1016/j.cma.2025.117937 · 2025 · External reference
Regularized variational theories of fracture: a unified approach
10.1016/j.jmps.2010.02.010 · 2010 · External reference
On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states
10.1007/s10704-024-00763-w · 2024 · External reference
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments
10.1016/j.jmps.2009.04.011 · 2009 · External reference
A hybrid phase field method for modeling thermal fractures in brittle rocks: fracture diversity from a modified driving force
10.1007/s10704-022-00660-0 · 2022 · External reference
Adaptive multi-patch isogeometric analysis with gradient damage model for thermo-mechanical quasi-brittle fracture
10.1016/j.cma.2025.118261 · 2025 · External reference
A Strategy for 3D Printed Al-Based Bi-Material Lattice Optimization: Thermal-Mechanical Coupling Performance with Load-Bearing and Energy-Absorption
10.1002/adfm.202521424 · ExternalCitation · doi-reference
A Janus-Like Bio-Inspired Strategy for 3D-Printed Bimetallic Metamaterials with Excellent Thermal-Protection and Load Bearing Capacity
10.1002/advs.202524116 · ExternalCitation · doi-reference
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
10.1002/nme.2861 · ExternalCitation · doi-reference
Linear and nonlinear solvers for variational phase-field models of brittle fracture
10.1002/nme.5300 · ExternalCitation · doi-reference
Adaptive FEM-SPIM coupling for phase-field modeling of fracture
10.1002/nme.7609 · ExternalCitation · doi-reference
Phase-field modeling of fracture in heterogeneous materials: Jump conditions, convergence and crack propagation
10.1007/s00419-020-01759-3 · ExternalCitation · doi-reference
A review on phase-field models of brittle fracture and a new fast hybrid formulation
10.1007/s00466-014-1109-y · ExternalCitation · doi-reference
Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equations
10.1007/s10444-023-10065-9 · ExternalCitation · doi-reference
A hybrid phase field method for modeling thermal fractures in brittle rocks: fracture diversity from a modified driving force
10.1007/s10704-022-00660-0 · ExternalCitation · doi-reference
On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states
10.1007/s10704-024-00763-w · ExternalCitation · doi-reference
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
10.1007/s40304-018-0127-z · ExternalCitation · doi-reference
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
10.1016/j.cma.2010.04.011 · ExternalCitation · doi-reference
A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach
10.1016/j.cma.2015.03.009 · ExternalCitation · doi-reference
On penalization in variational phase-field models of brittle fracture
10.1016/j.cma.2019.05.038 · ExternalCitation · doi-reference
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
10.1016/j.cma.2019.112790 · ExternalCitation · doi-reference
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
10.1016/j.cma.2020.113547 · ExternalCitation · doi-reference
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
10.1016/j.cma.2021.113741 · ExternalCitation · doi-reference
Phase-field modeling of fracture with physics-informed deep learning
10.1016/j.cma.2024.117104 · ExternalCitation · doi-reference
A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation
10.1016/j.cma.2024.117165 · ExternalCitation · doi-reference
Neural networks meet phase-field: A hybrid fracture model
10.1016/j.cma.2025.117937 · ExternalCitation · doi-reference
Adaptive multi-patch isogeometric analysis with gradient damage model for thermo-mechanical quasi-brittle fracture
10.1016/j.cma.2025.118261 · ExternalCitation · doi-reference
The novel physics-enhanced graph neural network for phase-field fracture modelling
10.1016/j.cma.2025.118284 · ExternalCitation · doi-reference
Mechanical properties and failure behaviors of T1100/5405 composite T-joint under in-plane shear load coupled with initial defect and high-temperature
10.1016/j.compstruct.2023.117722 · ExternalCitation · doi-reference
A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure
10.1016/j.engfracmech.2015.03.045 · ExternalCitation · doi-reference
Phase field modeling of interfacial damage in heterogeneous media with stiff and soft interphases
10.1016/j.engfracmech.2019.106574 · ExternalCitation · doi-reference
Phase field modeling and computer implementation: A review
10.1016/j.engfracmech.2022.108234 · ExternalCitation · doi-reference
A deep energy method for finite deformation hyperelasticity
10.1016/j.euromechsol.2019.103874 · ExternalCitation · doi-reference
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
10.1016/j.jcp.2018.10.045 · ExternalCitation · doi-reference
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments
10.1016/j.jmps.2009.04.011 · ExternalCitation · doi-reference
Regularized variational theories of fracture: a unified approach
10.1016/j.jmps.2010.02.010 · ExternalCitation · doi-reference
Crack nucleation in variational phase-field models of brittle fracture
10.1016/j.jmps.2017.09.006 · ExternalCitation · doi-reference
Phase-field fracture modeling for large structures
10.1016/j.jmps.2022.105118 · ExternalCitation · doi-reference
A multiscale framework based on phase field method and XFEM to simulate fracture in highly heterogeneous materials
10.1016/j.tafmec.2019.02.002 · ExternalCitation · doi-reference
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
10.1016/j.tafmec.2019.102447 · ExternalCitation · doi-reference
Adaptive fourth-order phase field analysis using deep energy minimization
10.1016/j.tafmec.2020.102527 · ExternalCitation · doi-reference
Revisiting brittle fracture as an energy minimization problem
10.1016/s0022-5096(98)00034-9 · ExternalCitation · doi-reference
Numerical experiments in revisited brittle fracture
10.1016/s0022-5096(99)00028-9 · ExternalCitation · doi-reference
Physics-informed machine learning
10.1038/s42254-021-00314-5 · ExternalCitation · doi-reference
The phenomena of rupture and flow in solids
10.1098/rsta.1921.0006 · ExternalCitation · doi-reference
Morphogenesis and propagation of complex cracks induced by thermal shocks
10.1103/physrevlett.112.014301 · ExternalCitation · doi-reference
Physics-informed neural networks for heat transfer problems
10.1115/1.4050542 · ExternalCitation · doi-reference
Understanding and mitigating gradient flow pathologies in physics-informed neural networks
10.1137/20m1318043 · ExternalCitation · doi-reference
Physics informed neural networks for phase field fracture modeling enhanced by length-scale decoupling degradation functions
10.3389/fphy.2023.1152811 · ExternalCitation · doi-reference
Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
10.4208/cicp.oa-2020-0164 · ExternalCitation · doi-reference
