一维理想弹塑性体的SPH-HLLC耦合算法

王展铭; 陈龙奎; 黄生洪

doi:10.11883/bzycj-2024-0004

一维理想弹塑性体的SPH-HLLC耦合算法

doi: 10.11883/bzycj-2024-0004

中国科学技术大学工程科学学院材料力学行为与设计重点实验室，安徽合肥 230026

详细信息

作者简介:
王展铭（1997－　），男，博士研究生，wangzmrr@mail.ustc.edu.cn

通讯作者:
黄生洪（1974－　），男，博士，研究员，博士生导师，hshnpu@ustc.edu.cn

中图分类号: O389
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- 文章访问数: 205
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- PDF下载量: 80
- 被引次数: 0
出版历程
- 收稿日期: 2024-01-02
- 修回日期: 2024-05-14
- 网络出版日期: 2024-05-15
- 刊出日期: 2024-08-05

SPH-HLLC coupled method for one-dimentional elastic-perfectly plastic model

Key Laboratory of Mechanical Behavior and Design of Materials, School of Engineering Science, University of Science and Technology of China, Hefei 230026, Anhui, China

摘要

摘要: 通过弹塑性波分析求得HLLC（Harten-Lax-van Leer-contact）近似黎曼解，提出了SPH（smoothed particle hydrodynamics）与一维理想弹塑性体模型下近似的HLLC黎曼求解器耦合的一种构造简单的算法。在SPH计算中，支持域内每个粒子对都存在一个黎曼间断问题，它的黎曼解被代入控制方程中计算。其中一维理想弹塑性体的HLLC近似黎曼解的思想是：先假设整体处于弹性状态计算黎曼解，然后对计算结果进行塑性条件修正，最后用修正后的物理变量计算HLLC近似黎曼解。将提出的SPH-HLLC耦合算法与传统SPH算法在一维算例下的计算结果进行对比，结果表明，该算法能有效模拟一维理想弹塑性体材料的碰撞，并能有效抑制在不同材料之间的压强和偏应力震荡，这是传统SPH方法很难做到的。
- 弹塑性数值模拟 /
- 固体碰撞 /
- SPH黎曼耦合算法
Abstract: A 1D SPH (smoothed particle hydrodynamics) and approximate HLLC (Harten-Lax-van Leer-contact) Riemann solver coupled method for elastic-perfectly plastic model is proposed through elastic and plastic wave analysis. In SPH simulations, each particle pair in the supporting domain generates a Riemann problem, whose solutions are substituted into governing equations. The philosophy of HLLC approximate Riemann solver is to divide the procedure into three steps: assume the whole state in elastic deformation and compute Riemann problem, and then reconstruct flux under von Mises yielding conditions and compute the final HLLC Riemann solution with reconstructed fluxes. We compare the new SPH-HLLC method with the traditional SPH method in several numerical tests, which show that this method can effectively simulate collision and reflected rarefaction waves between the materials, and it can profoundly suppress oscillations of pressure and deviatoric stress at contact interface between different materials, which the traditional SPH method finds difficult to realize. Moreover, the new SPH-HLLC scheme shows better energy performance than the traditional SPH method in 2D test case where initial kinetic energy is successfully transformed into internal energy with new SPH-HLLC scheme while total energy significantly decreases with time using the traditional SPH method.
- elastic-plastic numerical simulation /
- solid collision /
- SPH-Riemann scheme

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图 1 铝碰撞算例的密度、压强、速度和偏应力计算结果

Figure 1. Density, pressure, velocity and deviatoric stress profile of Al collision test

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图 2 Wilkins算例的密度、压强、速度和偏应力计算结果

Figure 2. Density, pressure, velocity and deviatoric stress profile of Wilkins test

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图 3 铜铝撞击算例的压强、速度和偏应力计算结果

Figure 3. Pressure, velocity and deviatoric stress profile of Cu/Al collision test

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图 4 二维厚壁圆筒铍壳体碰撞测试的初始分布、传统算法结果以及新SPH-HLLC算法结果

Figure 4. Initial distribution, traditional algorithm results, and new SPH-HLLC algorithm results of two-dimensional thick walled cylindrical beryllium shell collision test

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图 5 二维厚壁圆筒铍壳体碰撞测试的无量纲能量随无量纲时间的变化

Figure 5. Variation of non-dimensional energy with non-dimensional time in collision test of two-dimensional thick walled cylindrical beryllium shells

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表 1 弹塑性碰撞测试

Table 1. Parameters related Al impact

算例		ρ/(kg·m⁻³)	u/(m·s⁻¹)	p/MPa	S/MPa	坐标区间/m	t/ms
铝碰撞	左侧	2700	200	0	−200	−1～0	0.1
铝碰撞	右侧	2700	−200	0	0	0～1	0.1

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表 2 Wilkins算例的相关参数

Table 2. Parameters related to Wilkins test

算例		ρ/(kg·m⁻³)	u/(m·s⁻¹)	Y₀/MPa	μ/GPa	a₀/(m·s⁻¹)	ρ₀/(kg·m⁻³)	s	Γ₀	坐标区间/mm	t/μs
Wilkins	左侧	2785	800	300	27.6	5328	2785	1.338	2	0 ～ 5	5
Wilkins	右侧	2785	0	300	27.6	5328	2785	1.338	2	5 ～ 50	5

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表 3 铜铝材料撞击算例的相关参数

Table 3. Parameters related to Cu/Al collision

算例		ρ/(kg·m⁻³)	u/(m·s⁻¹)	Y₀/MPa	μ/GPa	a₀/(m·s⁻¹)	ρ₀/(kg·m⁻³)	s	Γ₀	坐标区间/mm	t/μs
铜铝材料撞击	左侧	8930	60	90	45.0	3940	8930	1.490	2	0 ～ 25	2
铜铝材料撞击	右侧	2785	0	300	27.6	5328	2785	1.338	2	25～50	2

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表 4 二维厚壁圆筒铍壳体碰撞算例的相关参数

Table 4. Parameters related to collapse of a thick-walled cylindrical beryllium shell

算例	ρ₀/(kg·m⁻³)	\|u\|/(m·s⁻¹)	Y₀/MPa	μ/GPa	a₀/(m·s⁻¹)	s	Γ	t/μs
铍壳体	1845	417.1	330	151.9	12870	1.124	2	130

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表 5 计算前后总能比（结束时刻能量/初始时刻能量）

Table 5. Total energy ratio (final total energy/initial total energy)

方法	总能比/%
方法	l₀ = 0.2 mm	l₀ = 0.125 mm	l₀ = 0.08 mm
传统	90.40	92.75	94.69
SPH-HLLC	100.59	100.72	100.64

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