水下爆炸冲击问题的物质点法研究
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摘要
开展水下爆炸以及结构在水下爆炸载荷作用下的动力响应研究在军事国防和民用建设领域均具有重要意义。水下爆炸及其结构的冲击响应研究是十分复杂的问题，它涉及爆轰物理学、冲击动力学、流固耦合、弹塑性动力学等诸多学科，对其进行理论分析和实验研究是一个巨大的挑战。近年来，随着计算机技术的不断提高以及各种数值方法的迅速发展，数值模拟已经成为水下爆炸问题研究领域中的重要研究手段。
流场或结构的极大变形、运动物质交界面、多相介质耦合作用以及自由表面等特性存在于水下爆炸整个过程中，这使得采用传统基于网格的数值方法对水下爆炸问题进行研究成为一项非常困难的工作。物质点法（Material Point Method, MPM）是一种新型的无网格粒子算法，它结合了基于物质描述的拉格朗日方法和基于空间描述的欧拉方法二者的优点，在处理大变形时不存在基于网格的数值方法出现的网格畸变问题，而且物质点法能方便的跟踪材料的变形历史以及实现对物质界面的精确描述，这些优点使物质点法在冲击动力学诸多领域中得到了广泛应用。本文在前人研究的基础上，进一步发展了物质点算法，并将物质点法扩展到水下爆炸冲击研究领域中。
推导了物质点法控制方程的空间以及时间离散格式，给出了物质点法显式积分算法，编写了基于物质点法基本理论的计算程序。建立了高能炸药爆轰计算模型，采用物质点法数值模拟了高能炸药爆轰过程，计算得到的爆轰波主要表征参数与解析解和实验数据吻合较好，为下一步水下爆炸冲击问题研究奠定了基础。针对水下爆炸冲击波在自由场中传播具有球面对称性质这一特点，本文提出了球对称形式的物质点法，为了验证所提方法的准确性，对球形炸药水下爆炸问题进行了数值计算，计算结果与实验数据以及经验公式计算结果吻合较好。在此基础上提出了基于物质点法的重映射算法，采用此方法可有效提高三维水下爆炸问题的求解效率。建立了二维水下爆炸计算模型，数值模拟了二维水下爆炸问题，数值计算结果与光滑粒子流体动力学方法（Smoothed ParticleHydronamics, SPH）计算结果以及经验公式计算结果进行了比较，结果吻合较好，物质点法与SPH算法计算精度相当，但在物质交界面的处理上物质点法具有明显的优势。
对近自由面水下爆炸一系列物理现象进行了数值模拟。给出了物质点法多介质耦合求解过程，研究了自由表面对冲击波的切断现象，并成功再现了近自由水面上水冢的形成过程。采用物质点法定量研究了空气隔层削波规律，结果表明空气隔层可以有效削减水下爆炸冲击波强度。
建立了金属材料的弹塑性本构模型及其在爆炸冲击状态下的状态方程，研究了结构在水下爆炸载荷作用下的瞬态塑性动力学响应。由于柯西应力材料导数会受到刚体转动的影响，本文引入了客观的Jaumann应力率进行应力的更新，并给出了物质点法显式应力更新算法。在物质点法中引入了多种材料失效准则，并在计算中考虑了材料的动态失效问题。为了克服冲击波造成的强间断给数值求解带来的困难，引入人工粘性对间断面进行光滑处理。并对引入人工粘性后的物质点法应力更新格式进行了修正。给出了基于物质点法的流固耦合求解格式，物质点法将流体和固体在同一求解域内进行计算，流固耦合算法简单直接，十分适合求解与近场水下爆炸相关的流固耦合问题。
当前无网格法的研究仍处于起步阶段，还有很多需要完善的地方。在分析软件的开发方面，有些商用软件已经集成了一些基于无网格算法的程序模块，然而这些计算模块功能简单仅仅作为程序的辅助功能出现，其核心算法仍然是传统基于网格的数值方法。本文基于物质点法开发了具有一定通用性的数值计算程序，为水下爆炸冲击问题研究提供了全新的数值计算平台。
The research of underwater explosion and structural dynamic response under underwaterexplosion load has important significance in the field of military defense and civilconstruction. Due to underwater explosion and shock response is a complex questioninvolving detonation physics, impact dynamics, fluid-structure interaction and theelastic-plastic dynamic, there is a huge challenge in its theoretical analysis and experimentalresearch. In recent years, with the rapid development of computer technology and numericalmethods, numerical simulation has become an important means to study the underwaterexplosion.
In the whole process of underwater explosion, there exist special features such as largedeformations, moving material interfaces, fluid-structure interaction and so on which makingthe application of the traditional numerical method based on grid for simulation study ofunderwater explosion problem is a very difficult job. The material point method is a novelmeshless algorithm. it inherits the advantages of both Lagrangian method and Euler method,overcoming mesh distortion problem associated with the traditional grid-based numericalmethods in dealing with large deformation problems. The material point particles haveLagrangian nature, so that it can facilitate the tracking material deformation history as well asan accurate description of the material interface. These advantages make the material pointmethod has been widely used in the field of impact dynamics. The material point method hasbeen further developed and extended to the field of underwater explosion in this paper.
The space and time discrete format of the control equation of material point method isdeduced and the explicit integral algorithm of material point method is given. Based on thebasic theory of material point method the corresponding calculation program is developed.The simulation model of high explosive detonation is established. The detonation process ofhigh explosive is simulated using the material point method. The calculated results are ingood agreement with analytical solutions and experimental data and laid the foundation forthe next research of underwater explosion and shock problems. For underwater explosionshock wave propagation in free field with spherical symmetry properties characteristics, aspherically symmetric form of material point method is presented. In order to verify theaccuracy of the proposed method, the spherical charge underwater explosion in the free field is numerical calculated. The calculation results are in good agreement with the experimentaldata and calculation results obtained by the empirical formula. On this basis, the remappingalgorithm based on the material point method is presented. The use of this method caneffectively improve the efficiency in solving the three-dimensional underwater explosionproblem. Two-dimensional underwater explosion is simulated and the calculated results arecompared with the results by the SPH method and empirical formula. The results indicate thatthe calculation accuracy is as high as that of SPH, but the material point method has obviousadvantages in dealing with the material interfaces.
A series of phenomenon of underwater explosion near the free surface is numericalcalculated. The solving process of multi-material coupling in material point method ispresented. The cut-off effect of the free surface to the shock wave is studied, and theformation process of water mound near the free surface is reproduced successfully. Thephenomenon of air interlayer decay the shock wave has carried on the quantitative research.The results showed that the air interlayer can reduce the shock waves effectively.
Elastoplastic constitutive model of materials as well as the equation of state in thecondition of explosion shock is established and the transient plastic dynamic response ofstructure under explosion shock load is studied. Because of the Cauchy stress materialderivative is affected by the rotation of rigid body, the objective of Jaumann stress rate isintroduced to update stress and the stress update algorithm in the material point method ispresented. Material failure model was introduced to the material point method, and thedynamic failure problems is taken into account in the calculation. In order to overcome thenumerical difficulties of solving the strong discontinuity caused by shock wave, artificialviscosity is introduced in the pressure term. The stress update algorithm is modified after theartificial viscosity was introduced. The solving process of fluid-structure interaction in thematerial point method is presented. The fluid and solid is in the same computational domainin material point method and the fluid-structure interaction solution algorithm is simpe anddirect. It is very suitable for solving fluid-structure interaction problem associated with theunderwater explosion in near field.
The meshless method research is still in the initial stage and not perfect yet. Althoughsome commercial software already contains some meshless method calculation module, thefunction of these simple calculation module only as auxiliary functions of the program, its core is still the traditional numerical method based on grid algorithm. The calculationprogram developed based on the material point method provides a new numerical computingplatform for study of underwater explosion problems.
流场或结构的极大变形、运动物质交界面、多相介质耦合作用以及自由表面等特性存在于水下爆炸整个过程中，这使得采用传统基于网格的数值方法对水下爆炸问题进行研究成为一项非常困难的工作。物质点法（Material Point Method, MPM）是一种新型的无网格粒子算法，它结合了基于物质描述的拉格朗日方法和基于空间描述的欧拉方法二者的优点，在处理大变形时不存在基于网格的数值方法出现的网格畸变问题，而且物质点法能方便的跟踪材料的变形历史以及实现对物质界面的精确描述，这些优点使物质点法在冲击动力学诸多领域中得到了广泛应用。本文在前人研究的基础上，进一步发展了物质点算法，并将物质点法扩展到水下爆炸冲击研究领域中。
推导了物质点法控制方程的空间以及时间离散格式，给出了物质点法显式积分算法，编写了基于物质点法基本理论的计算程序。建立了高能炸药爆轰计算模型，采用物质点法数值模拟了高能炸药爆轰过程，计算得到的爆轰波主要表征参数与解析解和实验数据吻合较好，为下一步水下爆炸冲击问题研究奠定了基础。针对水下爆炸冲击波在自由场中传播具有球面对称性质这一特点，本文提出了球对称形式的物质点法，为了验证所提方法的准确性，对球形炸药水下爆炸问题进行了数值计算，计算结果与实验数据以及经验公式计算结果吻合较好。在此基础上提出了基于物质点法的重映射算法，采用此方法可有效提高三维水下爆炸问题的求解效率。建立了二维水下爆炸计算模型，数值模拟了二维水下爆炸问题，数值计算结果与光滑粒子流体动力学方法（Smoothed ParticleHydronamics, SPH）计算结果以及经验公式计算结果进行了比较，结果吻合较好，物质点法与SPH算法计算精度相当，但在物质交界面的处理上物质点法具有明显的优势。
对近自由面水下爆炸一系列物理现象进行了数值模拟。给出了物质点法多介质耦合求解过程，研究了自由表面对冲击波的切断现象，并成功再现了近自由水面上水冢的形成过程。采用物质点法定量研究了空气隔层削波规律，结果表明空气隔层可以有效削减水下爆炸冲击波强度。
建立了金属材料的弹塑性本构模型及其在爆炸冲击状态下的状态方程，研究了结构在水下爆炸载荷作用下的瞬态塑性动力学响应。由于柯西应力材料导数会受到刚体转动的影响，本文引入了客观的Jaumann应力率进行应力的更新，并给出了物质点法显式应力更新算法。在物质点法中引入了多种材料失效准则，并在计算中考虑了材料的动态失效问题。为了克服冲击波造成的强间断给数值求解带来的困难，引入人工粘性对间断面进行光滑处理。并对引入人工粘性后的物质点法应力更新格式进行了修正。给出了基于物质点法的流固耦合求解格式，物质点法将流体和固体在同一求解域内进行计算，流固耦合算法简单直接，十分适合求解与近场水下爆炸相关的流固耦合问题。
当前无网格法的研究仍处于起步阶段，还有很多需要完善的地方。在分析软件的开发方面，有些商用软件已经集成了一些基于无网格算法的程序模块，然而这些计算模块功能简单仅仅作为程序的辅助功能出现，其核心算法仍然是传统基于网格的数值方法。本文基于物质点法开发了具有一定通用性的数值计算程序，为水下爆炸冲击问题研究提供了全新的数值计算平台。
The research of underwater explosion and structural dynamic response under underwaterexplosion load has important significance in the field of military defense and civilconstruction. Due to underwater explosion and shock response is a complex questioninvolving detonation physics, impact dynamics, fluid-structure interaction and theelastic-plastic dynamic, there is a huge challenge in its theoretical analysis and experimentalresearch. In recent years, with the rapid development of computer technology and numericalmethods, numerical simulation has become an important means to study the underwaterexplosion.
In the whole process of underwater explosion, there exist special features such as largedeformations, moving material interfaces, fluid-structure interaction and so on which makingthe application of the traditional numerical method based on grid for simulation study ofunderwater explosion problem is a very difficult job. The material point method is a novelmeshless algorithm. it inherits the advantages of both Lagrangian method and Euler method,overcoming mesh distortion problem associated with the traditional grid-based numericalmethods in dealing with large deformation problems. The material point particles haveLagrangian nature, so that it can facilitate the tracking material deformation history as well asan accurate description of the material interface. These advantages make the material pointmethod has been widely used in the field of impact dynamics. The material point method hasbeen further developed and extended to the field of underwater explosion in this paper.
The space and time discrete format of the control equation of material point method isdeduced and the explicit integral algorithm of material point method is given. Based on thebasic theory of material point method the corresponding calculation program is developed.The simulation model of high explosive detonation is established. The detonation process ofhigh explosive is simulated using the material point method. The calculated results are ingood agreement with analytical solutions and experimental data and laid the foundation forthe next research of underwater explosion and shock problems. For underwater explosionshock wave propagation in free field with spherical symmetry properties characteristics, aspherically symmetric form of material point method is presented. In order to verify theaccuracy of the proposed method, the spherical charge underwater explosion in the free field is numerical calculated. The calculation results are in good agreement with the experimentaldata and calculation results obtained by the empirical formula. On this basis, the remappingalgorithm based on the material point method is presented. The use of this method caneffectively improve the efficiency in solving the three-dimensional underwater explosionproblem. Two-dimensional underwater explosion is simulated and the calculated results arecompared with the results by the SPH method and empirical formula. The results indicate thatthe calculation accuracy is as high as that of SPH, but the material point method has obviousadvantages in dealing with the material interfaces.
A series of phenomenon of underwater explosion near the free surface is numericalcalculated. The solving process of multi-material coupling in material point method ispresented. The cut-off effect of the free surface to the shock wave is studied, and theformation process of water mound near the free surface is reproduced successfully. Thephenomenon of air interlayer decay the shock wave has carried on the quantitative research.The results showed that the air interlayer can reduce the shock waves effectively.
Elastoplastic constitutive model of materials as well as the equation of state in thecondition of explosion shock is established and the transient plastic dynamic response ofstructure under explosion shock load is studied. Because of the Cauchy stress materialderivative is affected by the rotation of rigid body, the objective of Jaumann stress rate isintroduced to update stress and the stress update algorithm in the material point method ispresented. Material failure model was introduced to the material point method, and thedynamic failure problems is taken into account in the calculation. In order to overcome thenumerical difficulties of solving the strong discontinuity caused by shock wave, artificialviscosity is introduced in the pressure term. The stress update algorithm is modified after theartificial viscosity was introduced. The solving process of fluid-structure interaction in thematerial point method is presented. The fluid and solid is in the same computational domainin material point method and the fluid-structure interaction solution algorithm is simpe anddirect. It is very suitable for solving fluid-structure interaction problem associated with theunderwater explosion in near field.
The meshless method research is still in the initial stage and not perfect yet. Althoughsome commercial software already contains some meshless method calculation module, thefunction of these simple calculation module only as auxiliary functions of the program, its core is still the traditional numerical method based on grid algorithm. The calculationprogram developed based on the material point method provides a new numerical computingplatform for study of underwater explosion problems.
引文
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