研究非格林弹性一维棒非线性波传播的迭代法

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

IMA Journal of Applied Mathematics Pub Date : 2024-06-11 DOI:10.1093/imamat/hxae017

R. Bustamante, P. Arrue, O. Orellana, R. Meneses

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引用次数: 0

摘要

研究了非线性波在一维棒材中的传播问题，其中线性化应变张量被视为考奇应力张量的函数。具体而言，研究了非格林弹性固体的两个构成方程，引入了一种新颖的数值迭代法，能够获得一个岩石非线性构成方程和一个显示应变限制行为的构成方程的近似解。数值结果与线性化弹性固体的精确解进行了比较。

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An iteration method to study nonlinear wave propagation for a non-Green elastic 1D bar

The problem of propagation of nonlinear waves in a 1D bar is studied, wherein the linearized strain tensor is considered as a function of the Cauchy stress tensor. Specifically, two constitutive equations for non-Green elastic solids are investigated, introducing a novel numerical iterative method capable to obtain approximate solutions of one nonlinear constitutive equation for rock, and one constitutive equation that shows a strain limiting behaviour. The numerical results are compared with exact solutions for the case of a linearized elastic solid.

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来源期刊

IMA Journal of Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

24 months

期刊介绍： The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered. The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.