Fully explicit numerical scheme for linearized wave propagation in nearly-incompressible soft hyperelastic solids

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Giulia Merlini, Jean-Marc Allain, Sébastien Imperiale
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引用次数: 0

Abstract

The numerical approximation of wave propagation problems in nearly or pure incompressible solids faces several challenges such as locking and stability constraints. In this work we propose a stabilized Leapfrog scheme based on the use of Chebyshev polynomials to relax the stability condition, which is strongly limited by the enforcement of incompressibility. The scheme is fully explicit, second order accurate and energy-preserving. For the space discretization we use a mixed formulation with high-order spectral elements and mass-lumping. A strategy is proposed for an efficient and accurate computation of the pressure contribution with a new definition of the discrete Grad-div operator. Finally, we consider linear wave propagation problems in nearly-incompressible hyperelastic solids subject to static preload.
近乎不可压缩软超弹性固体中线性化波传播的完全显式数值格式
近不可压缩或纯不可压缩固体中波传播问题的数值逼近面临着锁定和稳定性约束等挑战。在这项工作中,我们提出了一个基于使用切比雪夫多项式来放宽稳定性条件的稳定跃进方案,该方案受到不可压缩性的强制限制。该方案具有完全显式、二阶精度高、节能等特点。对于空间离散化,我们使用高阶谱元和质量集总的混合公式。通过对离散Grad-div算子的新定义,提出了一种高效准确计算压力贡献的策略。最后,我们考虑了在静力预载作用下几乎不可压缩的超弹性固体中的线性波传播问题。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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