Browsing by Subject "Non-local elasticity"

Now showing 1 - 3 of 3

Open Access
Aspects of constitutive modeling in continuum-kinematics-inspired peridynamics
(2022-10) Ekiz, Ekim
Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics (PD) that is also thermo- dynamically and variationally consistent. Unlike the original formulation of PD, CPD can accurately capture the Poisson effect. CPD consists of one-, two- and three-neighbor interactions. The isotropic CPD formulation of non-local elasticity therefore involves three material constants associated with length, area and volume. This manuscript aims to establish the relationships between the material parameters of CPD and isotropic linear elasticity for two- and three-dimensional problems. Two alternatives for the CPD energy density are introduced. Analytical solutions of the energy densities for affine deformations are derived. It is shown that the three material parameters of CPD reduce to two independent pa- rameters in the linearized framework, and can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lame parameters. The analysis here provides a physical interpretation for the ﬁrst Lame constant. Finally, the admissible ranges for CPD material parameters are established.
Open Access
From two- to three-dimensional continuum-kinematics-inspired peridynamics: More than just another dimension
(Elsevier BV, 2022-08-19) Ekiz, Ekim; Steinmann, P.; Javili, A.
Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. Unlike the original formulation of peridynamics (PD), CPD can accurately capture the Poisson effect. For a three-dimensional analysis, CPD builds upon one-, two- and three-neighbor interactions. The isotropic three-dimensional CPD formulation of non-local elasticity therefore involves three material constants associated with length, area and volume. This manuscript aims to establish the relationships between the material parameters of CPD and isotropic linear elasticity for three-dimensional problems. In addition to addressing significant technical difficulties that arise when advancing from two- to three-dimensional problems, this contribution unravels several key features that are entirely absent in a two-dimensional analysis (Ekiz et al., 2022). It is shown that the three material parameters of CPD reduce to two independent parameters in the linearized framework, and can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. The analysis here provides a physical interpretation for the first Lamé constant, for the first time. Finally, we establish the admissible ranges for CPD material parameters.
Open Access
Peridynamics review
(SAGE Publications Inc., 2019) Javili, Ali; Morasata, Rico; Öterkuş, E.; Öterkuş, S.
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.