Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis

Holm Altenbach; Oleksiy Larin; Konstantin Naumenko; Olha Sukhanova; Mathias Würkner; Holm Altenbach; Oleksiy Larin; Konstantin Naumenko; Olha Sukhanova; Mathias Würkner

doi:10.3934/matersci.2022043

AIMS Materials Science

2022, Volume 9, Issue 5: 702-718. doi: 10.3934/matersci.2022043

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Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis

1.
Otto-von-Guericke-University Magdeburg, Institute of Mechanics, D-39106 Magdeburg, Germany
2.
Department of Dynamics and Strength, NTU "Kharkiv Polytechnic Institute", 2 Kyrpychova str., 61002, Kharkiv, Ukraine

Received: 21 July 2022 Revised: 20 August 2022 Accepted: 29 August 2022 Published: 08 September 2022

The aim of this paper is to compare the classical continuum mechanics and the peridynamic models in the structural analysis of a monolithic glass plate subjected to ball drop. Governing equations are recalled in order to highlight the differences and basic features of both approaches. In this study the behavior of glass is assumed to be linear-elastic and damage processes are ignored. The generalized Hooke's law is assumed within the classical theory, while the linear peridynamic solid constitutive model is applied within the peridynamic analysis. Mechanical models for the ball drop simulation are discussed in detail. An emphasis is placed on the discretization including finite element mesh, peridynamic node lattice and time stepping, as well as appropriate constraints and contact conditions in both finite element and non-local peridynamics models. Deflections of the plate after the ball drop are presented as functions of time and the results based on the finite element and peridynamic analysis are compared. Good agreements between the deflection values in selected points of the plate as well as deflection fields at several time points indicate, that the model assumptions for the non-local peridynamic analysis including the horizon size, the short-range force contact settings and the support conditions are well suited. The developed peridynamics models can be applied in the future to analyze damage patterns in glass plates.
- float glass,
- low velocity impact,
- peridynamics,
- structural analysis
Citation: Holm Altenbach, Oleksiy Larin, Konstantin Naumenko, Olha Sukhanova, Mathias Würkner. Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis[J]. AIMS Materials Science, 2022, 9(5): 702-718. doi: 10.3934/matersci.2022043

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Abstract

The aim of this paper is to compare the classical continuum mechanics and the peridynamic models in the structural analysis of a monolithic glass plate subjected to ball drop. Governing equations are recalled in order to highlight the differences and basic features of both approaches. In this study the behavior of glass is assumed to be linear-elastic and damage processes are ignored. The generalized Hooke's law is assumed within the classical theory, while the linear peridynamic solid constitutive model is applied within the peridynamic analysis. Mechanical models for the ball drop simulation are discussed in detail. An emphasis is placed on the discretization including finite element mesh, peridynamic node lattice and time stepping, as well as appropriate constraints and contact conditions in both finite element and non-local peridynamics models. Deflections of the plate after the ball drop are presented as functions of time and the results based on the finite element and peridynamic analysis are compared. Good agreements between the deflection values in selected points of the plate as well as deflection fields at several time points indicate, that the model assumptions for the non-local peridynamic analysis including the horizon size, the short-range force contact settings and the support conditions are well suited. The developed peridynamics models can be applied in the future to analyze damage patterns in glass plates.

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