The peridynamic formulation for transient heat conduction

By Florin Bobaru, Monchai Duangpanya. 2010

434 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e14d67eeab0e5433d9ab607f475b45cf018067b6

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities (2012, methodology): “Note also that the formulation is consistent with the 1D formulation [8].”
A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks (2018, background): “In numerical simulations, the prescribed temperature, an essential boundary condition, can be directly applied at the boundarymaterial points as the nonlocalDirichlet boundary conditions (Bobaru and Duangpanya 2010, 2012).”
The Meaning, Selection, and Use of the Peridynamic Horizon and its Relation to Crack Branching in Brittle Materials (2012, methodology): “The microelastic peridynamic model or the peridynamic model of heat transfer converge, in the limit of the horizon going to zero, to the corresponding classical models (see Silling and Lehoucq 2008, Bobaru et al. 2009, Bobaru and Duangpanya 2010).”
Fully coupled peridynamic thermomechanics (2012, methodology): “Note that for the uncoupled case, this equation reduces to the PD heat conduction equation as given by Bobaru and Duangpanya (2010, 2012). Substituting for the thermal response (heat flow density) function, h f as suggested by Agwai (2011) leads to its final form as”
A two‐dimensional ordinary, state‐based peridynamic model for linearly elastic solids (2014, background): “This convergence, when reducing horizon size, is called ı -convergence [13, 14].”
A non-ordinary state-based peridynamics formulation for thermoplastic fracture (2016, background): “Bobaru and Duangpanya [26] formulated a one-dimensional BB-PD theory for the heat conduction equation and also extended it to solve two-dimensional problems with discontinuities [27].”
Peridynamic thermal diffusion (2014, neutral): “There are other forms as given by Bobaru and Duangpanya [18, 19] and Gerstle et al. [17].”
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, methodology): “Among those applications we have image analyses [14, 24, 25, 32], machine learning [36], nonlocal Dirichlet forms [6], kinetic equations [8, 31], phase transitions [11, 23], and nonlocal heat conduction [12].”
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, background): “6], kinetic equations [12, 38], phase transitions [15, 31], nonlocal heat conduction [16], and the peridynamic model for mechanics [48] and its one-dimensional variants [49, 50] for which L arises directly.”