This study presents the derivation of ordinary state-based peridynamic heat conduction equation based on the Lagrangian formalism. The peridynamic heat conduction parameters are related to those of the classical theory. An explicit time stepping scheme is adopted for numerical solution of various benchmark problems with known solutions. It paves the way for applying the peridynamic theory to other physical fields such as neutronic diffusion and electrical potential distribution.

This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density-stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension

Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in 2000. The roots of PD can be traced back to the early works of Gabrio Piola according to dell’Isola et al. PD has been attractive to researchers as it is a non-local formulation in an integral form, unlike the local differential form of classical continuum mechanics. Although the method is still in its infancy, the literature on PD is fairly rich and extensive. The prolific growth in PD applications has led to a tremendous number of contributions in various disciplines. This manuscript aims to provide a concise description of the PD theory together with a review of its major applications and related studies in different fields to date. Moreover, we succinctly highlight some lines of research that are yet to be investigated.

This study concerns the derivation of the coupled peridynamic (PD) thermomechanics equations based on thermodynamic considerations. The generalized peridynamic model for fully coupled thermomechanics is derived using the conservation of energy and the free-energy function. Subsequently, the bond-based coupled PD thermomechanics equations are obtained by reducing the generalized formulation. These equations are also cast into their nondimensional forms. After describing the numerical solution scheme, solutions to certain coupled thermomechanical problems with known previous solutions are presented

A novel peridynamic model for predicting thermomechanical behaviour of three-dimensional shell structures with 6 degrees of freedom has been proposed. Also, a numerical algorithm for dealing with complex shell structures is provided for the first time in the peridynamic literature. The peridynamic damage criterion based on critical energy release rate is provided for shell structures. The capability of the developed peridynamic model is demonstrated by predicting deformations for a flat shell, a curved shell, and a stiffened structure. To further demonstrate the capabilities of the proposed model, damage on flat shell in a double torsion problem, flat shell with pre-existing crack, thermal fracturing of a glass cup and damage in a dropped egg are simulated.

Progressive failure analysis of structures is still a major challenge. There exist various predictive techniques to tackle this challenge by using both classical (local) and nonlocal theories. Peridynamic (PD) theory (nonlocal) is very suitable for this challenge, but computationally costly with respect to the finite element method. When analyzing complex structures, it is necessary to utilize structural idealizations to make the computations feasible. Therefore, this study presents the PD equations of motions for structural idealizations as beams and plates while accounting for transverse shear deformation. Also, their PD dispersion relations are presented and compared with those of classical theory

This study presents the ordinary state-based peridynamic (PD) constitutive relations for viscoelastic deformation under mechanical and thermal loads. The behavior of the viscous material is modeled in terms of Prony series. The constitutive constants are the same as those of the classical historyintegral model, and they are also readily available from relaxation tests. The state variables are conjugate to the PD elastic stretch measures; hence, they are consistent with the kinematic assumptions of the elastic deformation. The PD viscoelastic deformation analysis successfully captures the relaxation behavior of the material. The numerical results concern first the verification problems, and subsequently, a double-lap joint with a viscoelastic adhesive where failure nucleates and grows.

A new fully coupled poroelastic peridynamic formulation is presented and its application to fluid-filled fractures is demonstrated. This approach is capable of predicting porous flow and deformation fields and their effects on each other. Moreover, it captures the fracture initiation and propagation in a natural way without resorting to an external failure criterion. The peridynamic predictions are verified by considering two benchmark problems including one-and two-dimensional consolidation problems. Moreover, the growth of a pre-existing hydraulically pressurized crack case is presented. Based on these results, it is concluded that the current peridynamic formulation has a potential to be used for the analysis of more sophisticated poroelastic problems including fluid-filled rock fractures as in hydraulic fracturing.