大规模延性断裂模拟：板壳结构的应用

需积分: 16 18 浏览量更新于2024-07-20 收藏 3.94MB PDF 举报

"大规模延性断裂在板壳结构中的建模与仿真" 本文主要探讨的是大型延性断裂在板壳结构中的模拟与建模方法。研究由Bo Ren, Shaofan Li等人发表，涉及了土木工程、环境工程、水力电力与信息技术工程等多个领域的交叉学科。文章介绍了对大尺度延性断裂进行模拟的最新进展，特别是针对三维贯穿厚度裂纹的处理。延性断裂是材料科学中一个重要的研究领域，尤其在工程结构如板和壳体中，这种断裂可能会导致严重的结构失效。在这种断裂过程中，材料可以吸收大量的能量而不立即断裂，而是逐渐变形直至破坏。文章特别关注了动态裂纹扩展的模拟，这是预测结构完整性、评估安全性和设计抗断裂结构的关键。作者采用了一种无网格方法——复制核粒子方法（Reproducing Kernel Particle Method，简称RKPM）。这种方法在数值计算中具有显著优势，能够在无需重新网格化的情况下实现动态裂纹的传播，这极大地简化了计算过程并提高了模拟的效率。无网格方法在处理复杂几何形状和不规则裂纹路径时具有很高的灵活性，使其成为模拟大尺度断裂的理想工具。在当前的方法中，有几点创新之处。首先，开发了一种三维裂纹表面近似算法，这使得能够精确地描述裂纹在三维空间内的形态和行为。其次，提出了粒子分裂算法，用于处理裂纹穿透材料厚度的情况，确保了模型在裂纹扩展过程中的精度。此外，文中可能还涉及到两种材料模型——Gurson模型和Johnson-Cook模型，前者描述了材料的孔隙形成和扩张，后者则考虑了材料的温度、应变率和历史应力状态对其性能的影响。 Gurson模型是描述延性断裂的一种经典理论，它考虑了材料内部微孔的形成和增长，这对于理解塑性流动和断裂的起源至关重要。而Johnson-Cook模型则是用来描述金属材料高温和高应变率下的力学行为，适用于模拟高速冲击或热塑性成形等复杂情境。这项工作为理解和模拟大型延性断裂提供了一种强大的工具，对于工程设计、材料科学以及结构安全性的评估具有重要意义。通过结合无网格方法和先进的材料模型，研究人员能够更准确地预测板壳结构在极端条件下的断裂行为，从而为实际工程问题提供理论支持。

The macro-scale ductile crack growth criterion is postulated as

a material damage criterion. In speciﬁc, we measure the material

damage state of all the particles surrounding the current crack

tip, and subsequently we can calculate the accumulated damage

value for any ﬁber near the current crack tip. If the damage value

at one particular ﬁber exceeds the critical value, we then declare

it as the new crack tip, and subsequently, a crack length increment

is performed, and the crack tip moves from old position to a new

position.

In this work, we ﬁrst choose either the volume fraction of voids,

or the effective plastic strain as the damage measure D. We then

choose a radial distance R, and draw a circle centered at the current

crack tip on the plate surface shown as the blue circle in Fig. 1(a).

Subsequently we can compute the damage value for each particles

inside the thin circular slice volume encircled by the blue line. Now

we can determine the damage value for each ﬁber inside the circu-

lar slice by adding the damage value of each particle along the ﬁ-

ber. For example, the variable D

of ﬁber J is deﬁned as sum of

damage values of each particle on the ﬁber J, i.e. D

i¼1

, here

M ¼ 3 as shown in Fig. 1. We then apply the crack growth crite-

rion: D

P D

;

J ¼ 1; ...n

for every ﬁber inside the circle slice.

If there is a ﬁber J such that the condition D

> D

holds, we then

choose the ﬁber J as the new crack tip.

In practice, however, if the new crack tip is located behind the

current crack tip, it could lead to some complications such as

crack-direction-reverse phenomenon. To simplify the crack

approximation algorithm, we limit the potential new crack tip in-

side a fan region h

in the blue circle, shown as in Fig. 1(a). Here the

vector V1, which points from the previous crack tip to the current

crack tip, is shown as a dashed vector, and the angle h is deﬁned

between the vector V2 (from the current crack tip to particle inside

circle) and vector V1. Finally, the new crack tip will be selected by

criterion,

P D

and  h

=2 6 h 6 h

=2 ð20Þ

When using the criterion, Eq. (20), the computational accuracy of

predicting crack growth mainly depends on an appropriate damage

criterion. Moreover, an obvious limitation of this criterion is that

the crack reverse phenomenon is not considered.

3.2. Crack surface representation in plates

Once the new crack tip (a ﬁber) is selected, the old crack tip (a

ﬁber) will be split to two ﬁbers, i.e., all particles in that ﬁber should

be split into two particles in order to form two new ﬁbers. The par-

ticle splitting algorithm must keep conservation of volume, mass,

and kinematic energy. Assume that the previous crack orientation

vector (V1 in Fig. 1) and current crack orientation (V2 in Fig. 1)

split the computational domain into two part with angles /

and

, as shown in Fig. 1. The mass and volume of the new particles

are re-assigned according to the following rules,

Mass

new1

Mass

old

ð21Þ

Mass

new2

Mass

old

ð22Þ

Volume

new1

Volume

old

ð23Þ

Volume

new2

Volume

old

ð24Þ

The kinematic ﬁeld variables, such as original position, displace-

ment, velocity, and acceleration of the new particles are assigned

according to,

new1

¼ X

old

þ d ð25Þ

new2

¼ X

old

 d ð26Þ

Disp

new1

¼ Disp

old

þ d ð27Þ

Disp

new2

¼ Disp

old

 d ð28Þ

Vel

new1

¼ Vel

old

ð29Þ

Vel

new2

¼ Vel

old

ð30Þ

Acc

new1

¼ 0:0 ð31Þ

Acc

new2

¼ 0:0 ð32Þ

where d is a vector that is perpendicular to the new crack orienta-

tion V2 at plate surface and jdj1. By using this particle splitting

procedure, the old particle X

old

on the outer surface of a shell is split

to two new particles (X

new1

and X

new2

) with a tiny spatial distance

between them in reference conﬁguration, in which the 3D paramet-

ric visibility algorithm is used. After particle splitting, the old crack

tip ﬁber will be split into two new ﬁbers, and there is a small dis-

tance between them, shown as Fig. 2(a), where the old crack tips

are marked as black squares.

3.3. 3D parametric visibility condition algorithm

The objective of the particle splitting algorithm is to separate

crack tip into two sets of particles in order to form new crack sur-

faces in physical space. In numerical simulations, the most crucial

step is how to adjust interpolation ﬁeld surrounding the growing

crack tip to represent material separation in a computational do-

main. In contrast with FEM interpolation, meshfree interpolation

relies on a local connectivity map to associate one particle with

its neighboring particles. Therefore there must be an artiﬁcial algo-

rithm to ‘cut off’ the interpolation connection of particles due to

crack surface. In the 2D problem, Li and Simonsen (2005) consider

the crack surface as piece-wise straight line segments. They pro-

posed a 2D parametric visibility condition algorithm to re-interpo-

late the computational domain. Following a similar philosophy, in

this work we propose a 3D parametric visibility condition algo-

rithm, which can adjust meshfree interpolation ﬁeld along crack

surfaces in three-dimensional space.

For macro-scale fracture problems, the crack surface can be

treated as an opaque wall, which may be ﬁguratively thought as

a medium that blocks the sight between two particles in two sides

of the crack surface. In Fig. 2(a) the dashed vectors denote the

sights that are blocked by crack surface. From Fig. 2, one can ﬁnd

the old crack tip ﬁber (marked as black square) located at the mid-

dle of crack surface at reference conﬁguration. This paper approx-

imates the crack surface as piece-wise plane facets, one can

construct triangle plane facets by old crack tip ﬁbers which are al-

ways located in the middle of crack surfaces as shown in Fig. 2(b),

here the dashed triangle facets is constructed by connecting the

ﬁrst and last particles of crack tip ﬁbers. In meshfree interpolation,

every particle has its own local connectivity map to deﬁne its

neighboring particles, once the line segment between a speciﬁed

particle and its neighboring particle intersects with the crack sur-

face (the dashed vector in Fig. 2(a)), we say that these two particles

cannot ‘see’ each other. Then this neighboring particle must be re-

moved from the local connectivity map of the particle. Since crack

growth is incremental, one only needs to check and modify the

connectivity maps for a limited number of particles or quadrature

points around the current crack tip.

The crack growth algorithm in 3D shell structures presented

here is designed for through-thickness cracks, which can be

accomplished by the modiﬁcation of the local connectivity map

of speciﬁed particles that are identiﬁed by using geometric inter-

ception test between the line segment (Fig. 2(a)) and the triangle

surface element (Fig. 2(b)). In practice, since the triangle element

is composed of triangle facets, we can test the facets one by one,

eventually the meshfree re-interpolation update can be proceed

as we sort out visibility relations among all neighboring particles

B. Ren, S. Li / International Journal of Solids and Structures 49 (2012) 2373–2393

2377

剩余20页未读，继续阅读

gzxb888

粉丝: 0
资源: 1

大规模延性断裂模拟：板壳结构的应用

Modeling-and-Simulation-in-Python-pdf.pdf.pdf

Modeling and Simulation of Multi-Physics Systems with MATLAB：本课程介绍建模和仿真（8章，90多个模型和脚本）MATLAB、SImulink、SImscape、Stateflow-matlab开发

E-Bike System Modeling and Simulation_e-bike_BIKE_

Modeling-and-Simulation-of-MATLAB-Simulink-Communication-System:详解MATLAB Simulink通信系统建模与仿真刘学勇编着源码-源码通

Simulation-Modeling-And-Analysis-Third-Edition-Av_多媒体编程_PDF_

(by-Manuel-D.-Rossetti)-Simulation-Modeling-and-Ar-2551722-(z-lib.org).zip.001

Modeling and Control of N -Paralleled Grid-Connected

Large-scale directional connections among multi resting-state neural networks in human brain: A functional MRI and Bayesian network modeling study

Modeling and Analysis of Real-Time and Embedded Systems with UML and MARTE

Measurement, modeling and enhancement of BitTorrent-based VoD system

最新资源