Ordinary state based peridynamic modelling for fully coupled thermoelastic problems

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Abstract

An ordinary state based peridynamic model is developed for transient fully coupled thermoelastic problems. By adopting an integral form instead of spatial derivatives in the equation of motion, the developed model is still valid at discontinuities. In addition, the ordinary state based peridynamic model eliminates the limitation on Poisson’s ratio which exists in bond based peridynamics. Interactions between thermal and structural responses are also considered by including the coupling terms in the formulations. These formulations are also cast into their non-dimensional forms. Validation of the new model is conducted by solving some benchmark problems and comparing them with other numerical solutions. Thin plate and block under shock loading conditions are investigated. Good agreements are obtained by comparing the thermal and mechanical responses with those obtained from boundary element method and finite element solutions. Subsequently, a three -point bending test simulation is conducted by allowing crack propagation. Then a crack propagation for a plate with a pre-existing crack is investigated under pressure shock loading condition. Finally, a numerical simulation based on the Kalthoff experiment is conducted in a fully coupled manner. The crack propagation processes and the temperature evolutions are presented. In conclusion, the present model is suitable for modelling thermoelastic problems in which discontinuities exist and coupling effects cannot be neglected.
Original languageEnglish
Number of pages31
JournalContinuum Mechanics and Thermodynamics
Early online date9 Jul 2018
DOIs
Publication statusE-pub ahead of print - 9 Jul 2018

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crack propagation
Crack propagation
discontinuity
shock
formulations
thin plates
boundary element method
Bending tests
Poisson ratio
Boundary element method
Equations of motion
casts
equations of motion
cracks
simulation
Derivatives
Cracks
Computer simulation
Experiments
interactions

Keywords

  • state based peridynamics
  • fully coupled
  • thermoelasticity
  • crack propagation

Cite this

@article{17f92d9a7eb94594a9b15f50603df906,
title = "Ordinary state based peridynamic modelling for fully coupled thermoelastic problems",
abstract = "An ordinary state based peridynamic model is developed for transient fully coupled thermoelastic problems. By adopting an integral form instead of spatial derivatives in the equation of motion, the developed model is still valid at discontinuities. In addition, the ordinary state based peridynamic model eliminates the limitation on Poisson’s ratio which exists in bond based peridynamics. Interactions between thermal and structural responses are also considered by including the coupling terms in the formulations. These formulations are also cast into their non-dimensional forms. Validation of the new model is conducted by solving some benchmark problems and comparing them with other numerical solutions. Thin plate and block under shock loading conditions are investigated. Good agreements are obtained by comparing the thermal and mechanical responses with those obtained from boundary element method and finite element solutions. Subsequently, a three -point bending test simulation is conducted by allowing crack propagation. Then a crack propagation for a plate with a pre-existing crack is investigated under pressure shock loading condition. Finally, a numerical simulation based on the Kalthoff experiment is conducted in a fully coupled manner. The crack propagation processes and the temperature evolutions are presented. In conclusion, the present model is suitable for modelling thermoelastic problems in which discontinuities exist and coupling effects cannot be neglected.",
keywords = "state based peridynamics, fully coupled, thermoelasticity, crack propagation",
author = "Yan Gao and Selda Oterkus",
year = "2018",
month = "7",
day = "9",
doi = "10.1007/s00161-018-0691-1",
language = "English",
journal = "Continuum Mechanics and Thermodynamics",
issn = "0935-1175",

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TY - JOUR

T1 - Ordinary state based peridynamic modelling for fully coupled thermoelastic problems

AU - Gao, Yan

AU - Oterkus, Selda

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N2 - An ordinary state based peridynamic model is developed for transient fully coupled thermoelastic problems. By adopting an integral form instead of spatial derivatives in the equation of motion, the developed model is still valid at discontinuities. In addition, the ordinary state based peridynamic model eliminates the limitation on Poisson’s ratio which exists in bond based peridynamics. Interactions between thermal and structural responses are also considered by including the coupling terms in the formulations. These formulations are also cast into their non-dimensional forms. Validation of the new model is conducted by solving some benchmark problems and comparing them with other numerical solutions. Thin plate and block under shock loading conditions are investigated. Good agreements are obtained by comparing the thermal and mechanical responses with those obtained from boundary element method and finite element solutions. Subsequently, a three -point bending test simulation is conducted by allowing crack propagation. Then a crack propagation for a plate with a pre-existing crack is investigated under pressure shock loading condition. Finally, a numerical simulation based on the Kalthoff experiment is conducted in a fully coupled manner. The crack propagation processes and the temperature evolutions are presented. In conclusion, the present model is suitable for modelling thermoelastic problems in which discontinuities exist and coupling effects cannot be neglected.

AB - An ordinary state based peridynamic model is developed for transient fully coupled thermoelastic problems. By adopting an integral form instead of spatial derivatives in the equation of motion, the developed model is still valid at discontinuities. In addition, the ordinary state based peridynamic model eliminates the limitation on Poisson’s ratio which exists in bond based peridynamics. Interactions between thermal and structural responses are also considered by including the coupling terms in the formulations. These formulations are also cast into their non-dimensional forms. Validation of the new model is conducted by solving some benchmark problems and comparing them with other numerical solutions. Thin plate and block under shock loading conditions are investigated. Good agreements are obtained by comparing the thermal and mechanical responses with those obtained from boundary element method and finite element solutions. Subsequently, a three -point bending test simulation is conducted by allowing crack propagation. Then a crack propagation for a plate with a pre-existing crack is investigated under pressure shock loading condition. Finally, a numerical simulation based on the Kalthoff experiment is conducted in a fully coupled manner. The crack propagation processes and the temperature evolutions are presented. In conclusion, the present model is suitable for modelling thermoelastic problems in which discontinuities exist and coupling effects cannot be neglected.

KW - state based peridynamics

KW - fully coupled

KW - thermoelasticity

KW - crack propagation

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SN - 0935-1175

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