A Kirchhoff plate formulation in a state-based peridynamic framework

Abstract

In recent years, there has been rapid progress on peridynamics. It has been applied to many different material systems, used for coupled field analysis and is suitable for multi-scale analysis. This study mainly focuses on peridynamic analysis for plate-type structures. For this purpose, a new peridynamic Kirchhoff plate is developed. The new formulation is computationally efficient by having only one degree of freedom for each material point. Moreover, it is based on the state-based peridynamic formulation, which does not impose any limitation on material constants. After presenting how to impose simply supported and clamped boundary conditions in this new formulation, several numerical studies are considered to demonstrate the accuracy and capability of the proposed formulation.

Keywords

Peridynamics non-local Kirchhoff plate continuum mechanics state-based

Get full access to this article

View all access options for this article.

References

Silling

SA.

Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solid 2000; 48: 175–209.

dell’Isola

Andreaus

Placidi

At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola. Math Mech Solid 2015; 20: 887–928.

Oterkus

Madenci

Peridynamic theory for damage initiation and growth in composite laminate. Key Eng Mater 2012; 488: 355–358.

De Meo

Zhu

Oterkus

. Peridynamic modeling of granular fracture in polycrystalline materials. J Eng Mater Technol 2016; 138: 041008.

Ebrahimi

Steigmann

Komvopoulos

Peridynamics analysis of the nanoscale friction and wear properties of amorphous carbon thin films. J Mech Mater Struct 2015; 10: 559–572.

Oterkus

Madenci

Agwai

Fully coupled peridynamic thermomechanics. J Mech Phys Solid 2014; 64: 1–23.

Oterkus

Madenci

Oterkus

, et al. Hygro-thermo-mechanical analysis and failure prediction in electronic packages by using peridynamics. In: 2014 IEEE 64th Electronic Components and Technology Conference (ECTC), 2014.

Gerstle

Silling

Read

, et al. Peridynamic simulation of electromigration. Comput Mater Continua 2008; 8: 75–92.

Oterkus

Madenci

Oterkus

Fully coupled poroelastic peridynamic formulation for fluid-filled fractures. Eng Geol 2017; 225: 19–28.

10.

Amani

Oterkus

Areias

, et al. A non-ordinary state-based peridynamics formulation for thermoplastic fracture. Int J Impact Eng 2016; 87: 83–94.

11.

Madenci

Oterkus

Peridynamic theory and its applications. New York: Springer, 2014.

12.

Javili

Morasata

Oterkus

, et al. Peridynamics review. Math Mech Solid. 2019; 24: 3714-3739.

13.

Taylor

Steigmann

DJ.

A two-dimensional peridynamic model for thin plates. Math Mech Solid 2015; 20: 998–1010.

14.

O’Grady

Foster

Peridynamic plates and flat shells: a non-ordinary, state-based model. Int J Solid Struct 2014; 51: 4572–4579.

15.

Diyaroglu

Oterkus

, et al. Peridynamics for bending of beams and plates with transverse shear deformation. Int J Solid Struct 2015; 69-70: 152–168.

16.

Leissa

Qatu

. Vibrations of continuum systems. New York: McGraw-Hill, 2011.