Browsing by Author "Ekiz, Ekim"

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Ali Dinçer'in hayatı ve 1977-1980 Ankara Belediye Başkanlığı dönemi
(Bilkent University, 2018) Kaynak, Batuhan Emre; Ekiz, Ekim; Keykan, Vehbi Kerem; Temiz, Hande; Erbay, Alperen
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
Continuum-kinematics-inspired peridynamics: thermo-mechanical problems
(Springer, 2021-03-31) Javili, Ali; Ekiz, Ekim; McBride, A. T.; Steinmann, P.
The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two- and three-neighbour interactions, however, are fundamentally different from state-based PD in that the basic elements of continuum kinematics are preserved exactly. We elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically consistent constitutive laws through a Coleman–Noll-like procedure. Notably, we show that various choices for temperature, or coldness, satisfy the dissipation inequality and provide meaningful temperature, or coldness, evolution equations together with Fourier-like conduction relations
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.
Open Access
The variational explanation of Poisson’s ratio in bond-based peridynamics and extension to nonlinear Poisson’s ratio
(Springer International Publishing, 2021-11-24) Ekiz, Ekim; Javili, Ali
It is commonly stated that the Poisson’s ratio associated with bond-based peridynamics is 14 for three-dimensional isotropic elasticity. This manuscript critically revisits this statement from a variational perspective for both two-dimensional and three-dimensional problems. To do so, a purely geometrical description of Poisson’s ratio is considered. Unlike the commonly established treatment of the problem, the Poisson’s ratio here is calculated via minimizing the internal energy density, rather than quantifying it and comparing it to its counterpart in classical linear elasticity. The advantage of the proposed approach is threefold. Firstly, elements of Cauchy linear elasticity such as “strain”, “stress” and “elastic parameters” are entirely absent throughout the derivations here. This is particularly important since peridynamics is a non-local formulation, and therefore, using local notions such as “strain” and “stress” implies locality and is misleading. Secondly, unbound by linear elasticity, the proposed approach unlocks the limitation of the analysis to small deformations. Hence, it can be immediately applied to large deformations, resulting in a nonlinear Poisson’s ratio that is no longer constant. Thirdly, the two-dimensional analysis here is purely two-dimensional, corresponding to a two-dimensional manifold in a three-dimensional space. That is, the two-dimensional formulation is neither plane stress nor plane strain that are rather degenerate three-dimensional cases. This contribution introduces the notion of nonlinear Poisson’s ratio in peridynamics for the first time and proves that the nonlinear Poisson’s ratio at the reference configuration coincides with 14 for three-dimensional and 13 for two-dimensional problems.