A Geometrically Nonlinear Correspondence Model for Continuum-Kinematics-Inspired Peridynamics

Javili A, Ekiz E, Steinmann P (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Journal of Peridynamics and Nonlocal Modeling Springer International Publishing

Book Volume: 7

Article Number: 6

Journal Issue: 1

DOI: 10.1007/s42102-025-00129-3

Abstract

Peridynamics (PD) has proven to be a promising theory to describe the behavior of materials allowing for singularities and fracture. The classical PD theory restricts the Poisson ratio. To address this issue, Continuum-kinematics-inspired Peridynamics (CPD) has been proposed as a variationally consistent formulation that can capture the Poisson effect exactly. Due to its geometrically exact nature, CPD does not suffer from zero-energy modes and displacement oscillations, making it an ideal nonlocal elasticity framework for large deformations. In a two-dimensional setting, CPD builds upon one-neighbor and two-neighbor interactions. One-neighbor interactions capture length-associated elasticity between pairs of points, equivalent to the original PD formalism. The two-neighbor interactions of CPD recover area-associated elasticity between triplet of points. This contribution provides for the first time a correspondence material model for CPD in a two-dimensional setting such that it recovers a well-established compressible neo-Hookean energy density of nonlinear elasticity at large deformations. At small deformations, the proposed model reduces to classical isotropic linear elasticity. The theory is illustrated via a series of numerical examples.

Authors with CRIS profile

Paul Steinmann Lehrstuhl für Technische Mechanik (LTM)

Involved external institutions

University of Texas at Austin

United States (USA) (US) Bilkent University / Bilkent Üniversitesi

Turkey (TR)

How to cite

APA:

Javili, A., Ekiz, E., & Steinmann, P. (2025). A Geometrically Nonlinear Correspondence Model for Continuum-Kinematics-Inspired Peridynamics. Journal of Peridynamics and Nonlocal Modeling, 7(1). https://doi.org/10.1007/s42102-025-00129-3

MLA:

Javili, Ali, Ekim Ekiz, and Paul Steinmann. "A Geometrically Nonlinear Correspondence Model for Continuum-Kinematics-Inspired Peridynamics." Journal of Peridynamics and Nonlocal Modeling 7.1 (2025).

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