A non-local dissipative Lagrangian modelling for generalized thermoelasticity in solids

Tao Xue, Xiaobing Zhang, Kumar K Tamma

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A generalized thermoelasticity theory emanating from the discretized Euler-Lagrange equation with dissipation in the non-local realm is formulated and proposed. The main idea of the present work is to interpolate the coupled thermal and deformation fields in solids via the discrete Lagrangian and Dissipation associated with the interaction of particles in a discrete system. The resulting governing equations for different fields are described with a full Lagrangian description such that the updating of the weight functions is eliminated in the numerical procedure. Numerical examples include (a) a one-dimensional bar with various thermal flux models, such as Fourier-type, Jeffrey-type, and Cattaneo-type thermal fluxes and (b) a two-dimensional plate with insulted cracks. In the one-dimensional case, the numerical results with a small particle influence domain show excellent agreement with the classical local model in each case while the non-locality leads to a stiffer thermal and deformation profiles of the system. In the two-dimensional case, the thermodynamic responses are easily predicted using the proposed Lagrangian-based approach. Moreover, a unified time integration is exploited to achieve the time marching of the coupled first/second order in time system.

Original languageEnglish (US)
Pages (from-to)247-265
Number of pages19
JournalApplied Mathematical Modelling
Volume73
DOIs
StatePublished - Sep 1 2019

Fingerprint

Generalized Thermoelasticity
Thermoelasticity
Modeling
Dissipation
Fluxes
Nonlocality
Euler-Lagrange Equations
Numerical Procedure
Time Integration
Discrete Systems
Weight Function
Updating
Governing equation
Crack
Thermodynamics
Interpolate
Cracks
Numerical Examples
Numerical Results
Hot Temperature

Keywords

  • Meshfree method
  • Non-local theory
  • Thermoelasticity

Cite this

A non-local dissipative Lagrangian modelling for generalized thermoelasticity in solids. / Xue, Tao; Zhang, Xiaobing; Tamma, Kumar K.

In: Applied Mathematical Modelling, Vol. 73, 01.09.2019, p. 247-265.

Research output: Contribution to journalArticle

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AB - A generalized thermoelasticity theory emanating from the discretized Euler-Lagrange equation with dissipation in the non-local realm is formulated and proposed. The main idea of the present work is to interpolate the coupled thermal and deformation fields in solids via the discrete Lagrangian and Dissipation associated with the interaction of particles in a discrete system. The resulting governing equations for different fields are described with a full Lagrangian description such that the updating of the weight functions is eliminated in the numerical procedure. Numerical examples include (a) a one-dimensional bar with various thermal flux models, such as Fourier-type, Jeffrey-type, and Cattaneo-type thermal fluxes and (b) a two-dimensional plate with insulted cracks. In the one-dimensional case, the numerical results with a small particle influence domain show excellent agreement with the classical local model in each case while the non-locality leads to a stiffer thermal and deformation profiles of the system. In the two-dimensional case, the thermodynamic responses are easily predicted using the proposed Lagrangian-based approach. Moreover, a unified time integration is exploited to achieve the time marching of the coupled first/second order in time system.

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