Gradient-type generalizations of one-dimensional dynamical model of strain-limiting elasticity

Erbay, Husnu Ata and Şengül, Yasemin 2025. Gradient-type generalizations of one-dimensional dynamical model of strain-limiting elasticity. Zeitschrift für angewandte Mathematik und Physik 76 , 94. 10.1007/s00033-025-02474-1

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Abstract

In this work, we propose two different generalizations of one-dimensional strain-limiting elasticity model where the linearized strain is given as a nonlinear function of the stress. These formulations are called stress gradient-type and strain gradient-type generalizations, and their constitutive relations are presented in both differential form and integral form. One important feature of this framework is that contrary to the theory of strain-limiting elasticity, the propagation of linear stress waves becomes dispersive as a consequence of inclusion of stress or strain gradients. We study traveling stress wave solutions to the governing equations of the nonlinear models proposed in this work. For a sample case of the constitutive relation belonging to the stress gradient-type formulation, we obtain explicit expressions of smooth solitary wave solutions when the stress is small but finite. Finally, we show that, for both the stress gradient-type and strain gradient-type formulations, the propagation of small amplitude long waves is described by the well-known KdV equation with the same coefficients.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Birkhäuser Verlag
ISSN:	1420-9039
Date of First Compliant Deposit:	18 March 2025
Date of Acceptance:	17 March 2025
Last Modified:	23 Apr 2025 13:55
URI:	https://orca.cardiff.ac.uk/id/eprint/176956

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