On the Determination of a Peridynamic Constant in a Linear Constitutive Model

Aguiar, Adair Roberto

doi:10.1007/s10659-015-9531-8

Cited by 16 publications

(16 citation statements)

References 5 publications

(21 reference statements)

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“…According to Aguiar [47], relations between material properties of classical homogeneous isotropic linear elastic materials and elastic peridynamic materials are given more specifically. In the reference configuration, the reference direction e r < > and angular state e n < , '> can be defined, respectively as:…”

Section: Peridynamic Elasticitymentioning

confidence: 99%

Review of Peridynamics: Theory, Applications, and Future Perspectives

Ladányi

Gonda

2021

SV-JME

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The modelling and simulation of material degradations, particularly fractures in solids of different lengths and time scales, remains challenging despite the numerous approaches that have been developed. In this review, the focus is set on research work concerned with a very promising non-local method: peridynamic modelling. With this approach, continuous phenomena may be described, and the complete evolution (i.e., initiation, propagation, branching, or coalescence) of cracks and other discontinuities can be followed in solids in an integrated framework. Evaluating the large number of publications on this topic, the authors chose to present concisely the key concepts, applications, and results in identifying possible future paths: the incorporation of mechanics of large deformations and material nonlinearities, and the development of high-efficiency peridynamic solvers. This review does not intersect with recent relevant reviews, which reflects its significance to readers.

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Section: Peridynamic Elasticitymentioning

confidence: 99%

Review of Peridynamics: Theory, Applications, and Future Perspectives

Ladányi

Gonda

2021

SV-JME

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“…Even though the form of governing equation has been established, specific modeling for constitutive equations is often left for a practitioner of peridynamics. For example, Ghajari et al [42] and Aguiar [43] have discussed how to determine peridynamic constants for orthotropic materials and isotropic materials, respectively.…”

Section: Introductionmentioning

confidence: 99%

Linear peridynamics for triclinic materials

Mikata

2020

Mathematics and Mechanics of Solids

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The governing equation of linear peridynamics is developed for the most general anisotropic materials (triclinic materials). As a departure from the standard peridynamic theory, the linear constitutive equation in the form of a micromodulus is determined by directly requiring the resulting peridynamic equation to converge to a comparable classical elastodynamic equation for a triclinic material as the generalized material horizon approaches zero. As a result, a new peridynamic governing equation is obtained for triclinic peridynamic materials. As an application of the newly obtained peridynamic equation, a plane wave solution is analytically obtained and discussed, and dispersion curves are plotted for triclinic peridynamic materials.

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“…This form of the SED function recovers the bond‐based PD material parameter ( micro‐modulus ) in which the force density vectors are equal in magnitude. Recently, Aguiar suggested a SED function for an isotropic, linearly elastic PD material that contains four PD material constants whose determination also requires calibration against the classical SED function.…”

Section: Introductionmentioning

confidence: 99%

Peridynamic integrals for strain invariants of homogeneous deformation

Madenci

2017

Z Angew Math Mech

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This study presents the peridynamic integrals. They enable the derivation of the peridynamic (nonlocal) form of the strain invariants. Therefore, the peridynamic form of the existing classical strain energy density functions can readily be constructed for linearly elastic and hyperelastic isotropic materials without any calibration. A general form of the force density vector is derived based on the strain energy density function that is expressed in terms of the first invariant of the right Cauchy-Green strain tensor and the Jacobian. In the case of linear elastic response for isotropic materials, the peridynamic force density vector is derived based on the classical form of the strain energy density function for three-and two-dimensional analysis. Also, a new form of the strain energy density function leads to a force density vector similar to that of bond-based peridynamics. Numerical results concern the verification of the peridynamic predictions with these force density vectors by considering a rectangular plate under uniform stretch.The peridynamic (PD) theory was introduced by Silling [1], and later generalized by Silling et al. [2]. The PD equation of motion is an integro-differential equation, and the integrand is free of the spatial derivatives of the displacement field. It permits damage nucleation at multiple damage sites in unspecified locations and its propagation along unguided paths with complex interactions.Conceptually rather simple, the bond-based PD introduced by Silling [1] is free of the assumption of small displacement gradients. However, it does not distinguish between dilatation and distortion. Therefore, it presents only one independent elastic constant; the second elastic constant has a fixed value depending on the analysis dimension. The corresponding strain energy density (SED) function is expressed in terms of the stretch between two material points, and one PD material parameter, referred to as the micro-modulus. This micro-modulus is determined through calibration against the classical SED by considering a simple loading condition, such as isotropic expansion. The determination of the micro-modulus for three-and two-dimensional analysis under plane strain and stress assumptions is described by Gerstle et al. [3]. Later, Bobaru et al. [4] proposed different forms of the micro-modulus function and discussed their effect on convergence of the computations. Recently, Chen et al. [5] presented a constructive approach for selecting the most appropriate kernel function in the bond-based PD equation of motion with respect to its convergence characteristics. The state-based PD introduced by Silling et al. [2] retains the two independent elastic constants such as the Young's modulus and Poisson's ratio. However, the determination of the force density-stretch relation requires an explicit form of the SED function. Silling et al.[2] suggested a SED function for three-dimensional analysis based on the deformation state and force state for a material referred to as a "linear peridynamic solid". T...

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On the Determination of a Peridynamic Constant in a Linear Constitutive Model

Cited by 16 publications

References 5 publications

Review of Peridynamics: Theory, Applications, and Future Perspectives

Review of Peridynamics: Theory, Applications, and Future Perspectives

Linear peridynamics for triclinic materials

Peridynamic integrals for strain invariants of homogeneous deformation

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