Peridynamics for Coupled Field Equations

Abstract 490 16.1 Introduction 490 16.2 Diffusion equation 492 16.2.1 Thermal diffusion 492 16.2.2 Moisture diffusion 493 16.2.3 Electrical conduction 493 16.3 Coupled field equations 494 16.3.1 Thermomechanics 494 16.3.1.1 Thermal diffusion with a structural coupling term 494 16.3.1.2 Equation of motion with a thermal coupling term 495 16.3.2 Porelasticity 495 16.3.2.1 Mechanical deformation due to fluid pressure 495 16.3.2.2 Fluid flow in porous medium. 496 16.3.3 Electromigration 497 16.3.4 Hygrothermomechanics 499 16.4 Numerical solution to peridynamic field equations 500 16.4.1 Correction of PD material parameters 500 16.4.2 Boundary conditions 502 16.4.2.1 Essential boundary conditions 502 16.4.2.2 Natural boundary conditions 503 16.4.2.3 Example 1 506 16.4.2.4 Example 2 507 16.4.2.5 Example 3 509 of 16.5 Applications 511 16.5.1 Coupled nonuniform heating and deformation 511 16.5.2 Coupled nonuniform moisture and deformation in a square plate 514 16.5.3 Coupled fluid pore pressure and deformation 519 16.5.4 Coupled electrical, temperature, deformation, and vacancy diffusion 523 16.6 Remarks 527 References 528 Abstract Although the peridynamic (PD) theory is originally introduced for the solution of deformation field equations, it is applicable to other fields, including thermal diffusion, moisture diffusion, electric potential distribution, vacancy diffusion, and neutronic diffusion in either an uncoupled or a coupled manner. It is a nonlocal theory with an internal length parameter, and thus permits the determination of the field variable in spite of discontinuities. This chapter presents the PD representation of the other field equations, and their coupling with the deformation field. Also, it describes in detail the application of boundary conditions, and establishes the accuracy of their implementation. Solutions to specific coupled field problems concern thermomechanics, hygrothermomechanics, poroelasticity, and electromigration.