An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory

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Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening (2016, methodology): “The time integration is achieved through an explicit scheme, in conjunction with the adaptive dynamic relaxation method described by Kilic and Madenci (2010).”
A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks (2018, methodology): “The pairwise force density vector including the thermal effects is written as (Kilic and Madenci 2010; Oterkus et al. 2017)”
Peridynamics for bending of beams and plates with transverse shear deformation (2015, methodology): “In order to obtain the static solution, the adaptive dynamic relaxation technique given by Kilic and Madenci (2010) is used, and the horizon size is chosen as 3.015 x where x is the uniform grid spacing.”
An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis (2015, methodology): “The dynamic relaxation method has been introduced for quasi-static peridynamic simulations by Kilic and Madenci [43].”
Fully coupled peridynamic thermomechanics (2012, methodology): “Uncoupled thermomechanics using the bond-based PD theory was developed by Kilic and Madenci (2010).”
A peridynamics formulation for quasi-static fracture and contact in rock (2017, methodology): “This method has been introduced by Kilic and Madenci (2010) for quasi-static peridynamic simulations.”