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首页> 外文期刊>Journal of Computational Physics >Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids
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Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

机译：LAX-Wendroff和TVD有限体积方法，用于对弹性塑料固体的影响的单向热机械数值模拟

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摘要

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems. (C) 2017 Elsevier Inc. All rights reserved.
机译：我们在这项工作中展示了两种有限的体积方法，用于模拟小型塑料框架内的弹性塑料固体介质上的双压力冲击问题。首先，提出了具有线性和非线性硬化的LAX-Wendroff的延伸到弹性塑性构成型号。其次，基于磁通差分裂[1]和超低光束限制器[2]的高阶TVD方法与近似弹性塑料Riemann求解器相结合，用于非线性淬火，并遵循Fogarty [3]的线性塑料。通过耗散加热和热软化来占热机械耦合，并假设绝热条件。本文基本上专注于一维问题，因为存在分析解决方案或者可以轻松开发。因此，将这两种数值方法与分析解决方案进行比较，并对涉及不连续和连续解决方案的测试用例进行显式有限元方法。这允许在加载，卸载和重新加载阶段之前更详细地研究它们各自的性能。特别强调还支付了计算的塑料株的准确性，根据所用数值方法发现的一些差异。距离一维问题的LAX-Wendoff二维离散化也附加了一端，以证明这种数值方案的可扩展性与多维问题。 （c）2017年Elsevier Inc.保留所有权利。

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