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 shockloading 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 List of symbols A Cross-sectional area for one-dimensional problems m 2 c v Specific heat capacity under constant volume [J/(kg K)] E Young's modulus (Pa) G c Critical energy release rate J/m 2 h Thickness for two-dimensional problems (m) K θ Bulk modulus (GPa) k T Thermal conductivity [W/(mK)] u (x, t) Displacement of point x at time t (m) u (x, t) Velocity of point x at time t (m/s) u (x, t) Acceleration of point x at time t m/s 2 u x (x, t) Scalar value of horizontal displacement of point x at time t (m) α Linear thermal expansion coefficient K −1 β cl Thermal modulus in classical mechanics (Pa/K) Communicated by Francesco dell'Isola.

Peridynamics for the thermomechanical behavior of shell structures

“…Amani et al [26] introduced non-ordinary state-based PD model for thermoplastic problems and Madenci and Oterkus [27,28] introduced ordinary-state based model for plastic and thermo-viscoelastic deformations. Recently, Gao and Oterkus [29,30] developed ordinary statebased PD model for fully coupled thermo-elastic problems. The developed PD models are used to predict damages due to thermal effects [31,32].…”

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

“…Peridynamics can be applicable for both elastic and plastic materials [6][7][8][9][10], composite and polycrystalline materials [11][12][13][14][15][16], multiphysics [17][18][19], large deformation problems [20], topology optimization [21] and multiscale modeling [22,23]. Peridynamics can also be suitable for structural idealization to analyze slender structures by using PD beam models [24][25][26][27] or thin wall structures by using PD plate and shell models [27][28][29][30][31][32].…”

On existence and uniqueness of weak solutions for linear pantographic beam lattices models

“…It has also to be investigated the whole damage mechanisms occurring in them, with methods which may be inspired to peridynamics, see, e.g., [72][73][74][75][76]. The relationship between peridynamics and higher gradient continuum theories, on the other hand, was already know to Piola himself [77,78], see also [79], and we believe that it deserves to be fully investigated.…”