Browsing by Subject "Elastic material parameters"

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
Relationships between the material parameters of continuum-kinematics-inspired peridynamics and isotropic linear elasticity for two-dimensional problems
(Elsevier Ltd, 2021-12-06) Ekiz, Ekim; Steinmann, P.; Javili, Ali
Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. CPD can capture the Poisson effect exactly, unlike the original formulation of peridynamics (PD). Due to its geometrically exact nature, CPD does not suffer from zero-energy modes and displacement oscillations that may be observed in state-based PD formulations. For a two-dimensional analysis, CPD builds upon one-neighbor and two-neighbor interactions. The one-neighbor interactions of CPD are equivalent to the bond-based interactions of the original PD formalism. Two-neighbor interactions, however, are key in CPD since the basic notions of classical continuum kinematics, namely length and area, are preserved exactly. The isotropic two-dimensional CPD formulation of non-local elasticity therefore involves two material constants, namely C1 and C2, associated with length and area, respectively. This manuscript aims to establish relationships between the material parameters of CPD and isotropic linear elasticity for an affine deformation in a two-dimensional setting. It is shown that each of the CPD material parameters can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. Finally, we establish the admissible ranges for CPD material parameters.