CN103377306B - The system and method that particle link model is provided in computer-aided engineering analysis - Google Patents
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Abstract
A kind of system and method for providing the particle link model among the multiple discrete particles for representing physical definition domain in time stepping method simulation are disclosed, is used to obtain the continuous physical phenomenon numerically simulated.Physical definition domain is represented by multiple discrete particles.The domain of influence is specified by each discrete particle, and forms the particle link model for the discrete particle.Set up each node and every other discrete particle is connected in its domain of influence with by each discrete particle.The particle link model also defines the rule of the fracture of node.The continuous physical phenomenon in the physical definition domain is represented with simulating one group of equation values being able to carry out by the time stepping method in the physical definition domain.Physical characteristic includes material property and fracture energy release rate.Finally, the particle link model allows the size and directed change of each discrete particle.
Description
Technical Field
The present invention relates generally to computer aided engineering analysis and, more particularly, to a particle connection model provided in a plurality of discrete particles, the particle connection model representing a physical domain of a brittle material in a time-marching simulation for obtaining a numerically simulated physical phenomenon.
Background
Many modern engineering analyses are performed with the assistance of a computer system. One such Computer Aided Engineering (CAE) analysis is known as the Discrete Element Method (DEM), which is commonly used to numerically simulate the motion of a large number of discrete particles. With the advancement of computing power and numerical algorithms for nearest neighbor classification, it becomes possible to numerically model tens of thousands of particles. DEM is now widely accepted as an effective method of solving engineering problems in granular and non-continuous materials, particularly in particle flow, powder mechanics and rock mechanics.
Classical mechanics are based on solving Partial Differential Equations (PDEs) over a domain that assumes a continuous distribution of a substance, including finite element methods, boundary integration methods, gridless methods, and the like. In other disciplines, Molecular Dynamics (MD) has been used to determine atoms and molecules of forces and energies for simulations from the nanometer level to the microscopic level, but this is not suitable for macroscopic level simulations.
In contrast, DEM provides a different approach that does not require PDE equations for continuous media mechanics. However, there are drawbacks or disadvantages in the existing methods. In particular, there is no integrated technique for linking continuous media mechanics and breaking up particles after the continuous media has been compromised. A number of particular approaches have been proposed, but none of these prior art approaches are satisfactory. For example, one of the prior art assumes that the forces acting on the particles are only axial and therefore cannot correctly model a domain with any relative shear deformation or lateral deformation.
Accordingly, there is a need to provide an improved model in a plurality of discrete particles that represents a physical domain of brittle material in a time-marching simulation for obtaining a numerically simulated continuous physical phenomenon.
Disclosure of Invention
A particle connection model in a plurality of discrete particles representing a physical domain of brittle material in a time-marching simulation for obtaining a numerically simulated continuous physical phenomenon.
According to one aspect of the invention, the physical domain is represented by a plurality of discrete particles. An influence domain is specified by each discrete particle and forms a particle connection model for that discrete particle. Each node is established to connect each discrete particle to all other discrete particles within its domain of influence. The particle connection model also defines the rules for the breaking of the junctions.
The continuous physical phenomena (e.g., mechanical properties) of the physical domain are numerically represented by a set of formulas (i.e., the discrete particles are dominated by the particle connectivity model) to enable time-marching simulations of the physical domain to be performed. The physical properties include material properties and fracture energy release rate. The set of equations is used to calculate the forces between each pair of discrete particles, and the potential energy of the physical domain. The conservation of momentum and the energy balance of the physical domain are preserved. Finally, the particle connection model allows for a transformation of the size and orientation of each discrete particle.
A particle connection model according to an embodiment of the invention is based on physical properties of a material represented by a plurality of discrete particles having the following characteristics:
1) the characteristics of the junction between each pair of discrete particles are determined by the material constants, including: bulk modulus, shear modulus and density. The strength of the nodes is based on the fracture toughness of the material in the form of the rate of energy release at break;
2) all discrete particles are free to move individually within the physically defined domain;
3) there is no differential operation in the particle connection model (i.e., no PDE); and is
4) For computational efficiency, there is no integration operation in the particle connection model.
The objects, features and advantages of the present invention will become apparent upon review of the following detailed description of embodiments thereof, when taken in conjunction with the accompanying drawings.
Drawings
These and other features, aspects, and advantages of the present invention will become better understood with regard to the following description, appended claims, and accompanying drawings where:
FIG. 1 is a flow diagram illustrating an exemplary process of providing a particle connection model among a plurality of discrete particles for numerically simulating a continuous physical phenomenon, according to one embodiment of the invention.
FIG. 2 is a two-dimensional graph illustrating the variation in size and orientation of exemplary discrete particles in a time-marching simulation, according to an embodiment of the invention.
FIG. 3 is a two-dimensional diagram showing two exemplary locations of exemplary discrete particles in a time-marching simulation, according to an embodiment of the present invention;
FIG. 4 is a two-dimensional diagram illustrating an exemplary influence domain of a first exemplary discrete particle, in accordance with an embodiment of the present invention;
FIG. 5 is a two-dimensional diagram illustrating another exemplary influence domain of a second exemplary discrete particle, in accordance with an embodiment of the present invention;
FIG. 6A is a two-dimensional diagram illustrating a first schematic configuration of discrete particles based on a particle connection model, according to an embodiment of the present invention;
FIG. 6B is a two-dimensional diagram illustrating a second schematic configuration of the discrete particles in FIG. 6A;
FIG. 7 is a diagram illustrating an exemplary three-dimensional discrete particle (i.e., sphere) according to one embodiment of the present invention;
FIG. 8 is a two-dimensional diagram illustrating a plurality of discrete particles representing an exemplary physical domain of definition, in accordance with one embodiment of the present invention;
FIG. 9 is a block diagram illustrating salient components of a computing device, according to an implementation of the present invention.
Detailed Description
Referring initially to fig. 1, a flow diagram of an illustrative process 100 for providing a particle connection model among a plurality of discrete particles representing a physical domain of definition composed of brittle material in a time-marching simulation for numerically obtaining a continuous physical phenomenon is shown in accordance with an embodiment of the present invention. The process 100 is implemented in software and is preferably understood in conjunction with other figures.
The process 100 begins with the definition in step 102 of receiving a plurality of discrete particles representing a physical domain of a brittle material. The physical definition domain can have any size or shape. Fig. 8 shows a plurality of discrete particles 802 (circles or discs) representing a physical domain of definition 800 (irregular geometric shape). For ease of illustration, all examples used herein are two-dimensional and the particles are round or spherical. However, the present invention can be applied to a physical definition domain in two or three dimensions. And the discrete particles can have different geometric shapes (e.g., rectangular, cubic, etc.) other than round or spherical. Although the discrete particles 802 of fig. 8 are uniformly arranged, this is not necessary in the present invention. Any other placement of discrete particles can also represent a physical domain of definition. The definition of discrete particles includes the initial position, orientation, and size of each discrete particle.
FIG. 2 shows a first orientation 202 (represented by the solid arrows)) And a second orientation 212 (represented by the dashed arrow) of the schematic discrete particles (i.e., the solid circles 200). The first and second orientations represent two different orientations of the discrete particles in a time-marching simulation, which initially start at time zero and end at a future time. For example, the first orientation can be at time "t" zero0"and the second orientation can be an orientation at another time" t ". Alternatively, they can be at two different times "t1"and" t2"two different orientations. The relative rotation angle ω 222 is between the first and second orientations.
Also shown in fig. 2 are first and second sizes of illustrative discrete particles. The first dimension is shown as a solid circle 200 and the second dimension is shown as a dashed circle 210. In this example, the second dimension 210 is larger (i.e., expanded) than the first dimension 200. The second size can be smaller (i.e., shrunk) than the first size (not shown). The expansion/contraction angle θ 200 represents the difference between the first and second dimensions.
Illustrated in fig. 3 are first 300 and second 310 locations of exemplary discrete particles in a global coordinate system. This position can be represented using known designs. For example, the vector r301 is a first position 300 measured in a cartesian coordinate system 330, and the motion vector u311 represents a second position 310 relative to the first position 300.
Referring again to fig. 1, in step 104, an impact domain refers to each discrete particle. This can be done by assigning a characteristic size to each discrete particle. For a circular or spherical domain of definition, the characteristic dimension can be a radius.
Fig. 4 shows that a first exemplary discrete particle 400 (black filled circle) specifies the area of influence (dashed circle area 404). The discrete particles disposed within the influence field 404 are solid circles 402, while the discrete particles disposed outside the influence field 404 are dashed circles 412. In this example, the feature size is a radius 414 of the impact field 404. It should be noted that the influence field is a volume and not a region in three dimensions. The influence field 404 is used in the particle connection model to limit the number of adjacent discrete particles for any given discrete particle. The characteristic dimension can be constant for all discrete particles or different for each individual discrete particle. An exemplary three-dimensional discrete particle (i.e., a sphere 700) is shown in fig. 7.
The second exemplary discrete particle 500 is designated as the impact domain 504 in fig. 5. Similarly, discrete particles disposed outside of the defined field 504 are dashed circles 512, while discrete particles disposed within the defined field 504 are solid circles 502. It should be noted that the set of discrete particles in fig. 4 and 5 are identical. Each discrete particle (e.g., particles 400 and 500) has its own domain of influence.
After the impact domain has been specified, the particle connection model for the discrete particles is associated with the physical properties of the physical definition domain in step 106. The particle connection model establishes individual nodes to connect each discrete particle with all other discrete particles within its domain of influence. The nodes are determined by material properties, such as bulk modulus, shear modulus, material density and fracture toughness. Furthermore, the particle connection model defines the rules for node breakage. The physical properties of the physical domain include the material properties and the fracture energy release rate of the material of the physical domain.
Fig. 6A shows a first schematic configuration of a discrete particle of interest "Pi" 620 based on a particle connection model, according to an embodiment of the present invention. For ease of illustration, the first schematic configuration depicts three other discrete particles "Pj" 628 connected to discrete particle "Pi" 620 via respective nodes 621. There can be more or less than three other discrete particles "Pj" 628 within the domain of influence of the discrete particle "Pi" 620. The position of the discrete particle "Pi" 620 is represented by the vector "ri"622, and the position of each other discrete particle is specified by the vector" rjAnd "624 designation. The first construct can be a time-marching segment in the simulation at a time of the physical domain of definition.
A second schematic configuration is shown in fig. 6B. The second schematic configuration being after the first schematic configurationAt the time. Corresponding discrete particles of interest "Pi" 630 and other discrete particles "Pj" 638 are connected to respective nodes 631. Two position vectors "ri"632 and" rj"634 is used for the new location. It should be noted that the orientation and size of each discrete particle (designated by the dashed lines in fig. 6B) is different in the first and second configurations. Nodes 621, 631 are adjusted accordingly and subject to the fragmentation rules defined in the set of mathematical equations set forth in the following paragraphs.
Each discrete particle has its own initial position, orientation, and size (e.g., volume in three dimensions or area in two dimensions) as an initial state. A junction is formed for each pair of particles in the influence field 404. For example, using a circle, the radius of the impact field, R414, is the feature size or impact distance.
After the deformation in the time-marching simulation, each discrete particle may have moved to a second position (motion u 311), a second orientation (rotation angle ω 222), and/or a second size (expansion/contraction θ 220).
The particle attachment model for a physical domain of definition (i.e., a particular material) is defined below:
1. material characteristics:
2. each discrete particle "i" ("Pi" 620) in the influence domain and its neighboring discrete particle "j" ("Pj" 628)
Influencing the distance R
(characteristic dimension 414)
Initial volume of influence
Current volume of influence
Particle constant (3-D) ck=8(3K-2G)/R
cs=8G/R
Particle constant (2-D) ck=6E/(1-v)/R
cs=12G/R
Critical energy density (3-D) wcs=5Gc/R
wck=wcs/4
Critical energy density (2-D) wcs=3/2πGc/R
wck=wcs/5
Wherein,is the domain of influence of the initial discrete particle "i", andis the domain of influence in the following time. VjIs the volume of each discrete particle disposed within the domain of influence.
1. The interactions between adjacent discrete particles include:
1) expansion of
2) Rotate
3) Decomposition by deformation
4) Force on each discrete particle
5) Density of deformation energy
6) Rule for the breakage of a node — a node breaks if the following critical values are reached:
when the node is stretched
When the node is compressed
The fracture energy release rate Gc is the energy dissipated during fracture of each cell of the newly formed fracture surface area and can be obtained via known techniques, for example, via material property testing.
Referring again to fig. 1, in step 108, the process 100 obtains a numerically simulated continuous physical phenomenon (e.g., fracture of a brittle material) of a physical domain under a loading condition obtained by performing a time-marching simulation using a plurality of discrete particles and an associated particle connection model. The time-marching simulation begins at time zero (i.e., the initial condition) and progresses over time increments in each of a number of solution cycles until a predetermined condition is satisfied. Each solution cycle corresponds to a particular time. The behavior of discrete particles is governed by the particle connection model.
According to one aspect, the invention is directed to one or more computer systems capable of implementing the functionality described herein. An example of a computer system 900 is shown in fig. 9. Computer system 900 includes one or more processors, such as a processor 904. Processor 904 is connected to a computer system internal communication bus 902. Various software implementations are described with respect to the illustrative computer system. After reading this description, it will become apparent to a person skilled in the art how to implement the invention using other computer systems and/or computer architectures.
Computer system 900 also includes a main memory 908, preferably Random Access Memory (RAM), and may also include a secondary memory 910. The secondary memory 910 may include, for example, one or more hard disk drives 912 and/or one or more removable storage drives 914, such as a floppy magnetic disk drive, a magnetic tape drive, and an optical disk drive. The removable storage drive 914 reads data from the removable storage unit 918 or writes data to the removable storage unit 918 in a well known manner. A removable storage unit 918, represented by a floppy disk, magnetic tape, optical disk, etc., reads from and writes to the removable storage drive 914. As will be appreciated, the removable storage unit 918 includes a computer usable storage medium having stored therein computer software and/or data.
In alternative embodiments, secondary memory 910 may include other similar means for allowing computer programs or other instructions to be loaded into computer system 900. Such means may include, for example, a removable storage unit 922 and an interface 920. Examples of which may include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an erasable programmable read-only memory (EPROM), Universal Serial Bus (USB) flash memory, or PROM) and associated socket, and other removable storage units 922 and interfaces 920 that allow software and data to be transferred from the removable storage unit 922 to computer system 900. Generally, computer system 900 is controlled and coordinated by Operating System (OS) software, which performs processes scheduling, memory management, and network and I/O services, for example.
There may also be a communications interface 924 connected to bus 902. Communications interface 924 allows software and data to be transferred between computer system 900 and external devices. Examples of communications interface 924 may include a modem, a network interface (e.g., an ethernet card), a communications port, a Personal Computer Memory Card International Association (PCMCIA) slot and card, and the like. Software and data transferred via communications interface 924 are in the form of signals which can be electronic, electromagnetic, optical, or other signals capable of being received by communications interface 924. The computer 900 communicates with other computing devices in a data network based on special rules (i.e., protocols). One of the protocols is TCP/IP (transmission control protocol/internet protocol) which is commonly used in the internet. In general, communication interface 924 manages the assembly of data files into smaller data packets for delivery in a data network or the reassembly of received data packets into original data files. In addition, communication interface 924 processes the address portion of each packet so that it arrives at the correct destination or intercepts packets destined for computer 900. In this document, the terms "computer processing media" and "computer usable media" are used to generally refer to media such as a removable storage drive 914 and/or hard disk installed in hard disk drive 912. These computer program products are means for providing software to computer system 900. The present invention is directed to such computer program products.
Computer system 900 may also include an input/output (I/O) interface 930 that provides computer system 900 with access to a display, keyboard, mouse, printer, scanner, plotter, and the like.
Computer programs (also called computer control logic) are stored as application modules 906 in main memory 908 and/or secondary memory 910. Computer programs may also be received via communications interface 924. Such computer programs, when executed, enable computer system 900 to perform the features of the present invention as discussed herein. In particular, the computer programs, when executed, enable processor 904 to perform the features of the present invention. Accordingly, such computer programs represent controllers of the computer system 900.
In an embodiment where the invention is implemented using software, the software may be stored in a computer program product and loaded into computer system 900 using removable storage drive 914, hard drive 912 or communications interface 924. An application module 906, which when executed by the processor 904, causes the processor 904 to perform the functions of the present invention as described herein.
Main memory 908 may be loaded with one or more application modules 906 (e.g., discrete meta methods), which application modules 906 can be executed by one or more processors 904 with or without user input through an I/O interface to achieve desired tasks. In operation, when at least one processor 904 executes one of the application modules 906, the results are computed and stored in the secondary memory 910 (i.e., hard drive 912). The status of the finite element analysis is reported to the user via the I/O interface 930 in text or graphic form from a detector coupled to the computer.
While the invention has been described with reference to specific embodiments thereof, the embodiments are merely illustrative, and not restrictive of the invention. Those skilled in the art will appreciate that numerous modifications and variations to the specifically disclosed exemplary embodiments are contemplated. Although the discrete particles of the two-dimensional view have been shown in outline for ease of illustration, the present invention can be applied to three-dimensional particles, for example, spheres. In general, the scope of the invention is not limited to the specific exemplary embodiments disclosed herein, and modifications that can be readily devised by those skilled in the art are intended to be included within the spirit and scope of the application and the scope of the appended claims.
Claims (14)
1. A method of providing a particle connection model among a plurality of discrete particles representing a physical domain in a time-marching simulation to obtain numerically simulated continuous physical phenomena, the method comprising:
receiving a definition of a plurality of discrete particles representing a physical domain of definition made of a brittle material in a computer system having an application module installed thereon;
assigning an impact domain to each discrete particle;
associating a particle connection model for a plurality of discrete particles with physical properties of the physical domain of definition, the particle connection model defining respective nodes for connecting the each discrete particle with another one or more discrete particles within the domain of influence of the each discrete particle, and the particle connection model defining rules for determining node breakage, wherein the physical properties include deformation and breakage energy release rate; and
obtaining numerically simulated continuous physical phenomena by performing a time-marching simulation of the physical domain subject to loading conditions using the discrete particles whose behavior is governed by the particle connection model.
2. The method of claim 1, wherein the definition of the plurality of discrete particles comprises an initial position, orientation, and size of each of the discrete particles.
3. The method of claim 1, wherein the particle connection model further comprises moving the each discrete particle from a first position to a second position during the time-marching simulation; expanding or contracting said each particle from a first size to a second size; rotating the center of each particle from a first orientation to a second orientation.
4. The method according to claim 1, wherein the fracture energy release rate is obtained from a material property test of the sample of brittle material.
5. The method of claim 1, wherein the loading condition comprises a tensile force to tear a crack of the physically-defined domain.
6. The method of claim 5, wherein the continuous physical phenomenon comprises crack propagation in the physically defined domain.
7. The method of claim 1, wherein the rule is based on a set of critical deformation energy densities derived from relative deformations between each pair of discrete particles.
8. The method of claim 7, wherein the set of critical deformation energy densities is further dependent on a characteristic dimension of each of the discrete particles and a fracture energy release rate, wherein the characteristic dimension is used to define an impact domain.
9. A system for providing a particle connection model among a plurality of discrete particles representing a physical domain in a time-marching simulation for obtaining numerically simulated continuous physical phenomena, the system comprising:
a main memory for storing computer readable code for an application module;
at least one processor coupled to the main memory, the at least one processor executing the computer-readable code in the main memory to cause the application module to perform operations according to the following method:
receiving a definition of a plurality of discrete particles representing a physically defined domain made of a brittle material;
assigning an impact domain to each discrete particle;
associating a particle connection model for a plurality of discrete particles with physical properties of the physical domain of definition, the particle connection model defining respective nodes for connecting the each discrete particle with another one or more discrete particles within the domain of influence of the each discrete particle, and the particle connection model defining rules for determining node breakage, wherein the physical properties include deformation and breakage energy release rate; and
obtaining numerically simulated continuous physical phenomena by performing a time-marching simulation of the physical domain subject to loading conditions using the discrete particles whose behavior is governed by the particle connection model.
10. The system of claim 9, wherein the definition of the plurality of discrete particles comprises an initial position, orientation, and size of each of the discrete particles.
11. The system of claim 9, wherein the particle connection model further comprises moving the each discrete particle from a first position to a second position during the time-marching simulation; expanding or contracting said each particle from a first size to a second size; rotating the center of each particle from a first orientation to a second orientation.
12. The system according to claim 9, wherein the fracture energy release rate is obtained from a material property test of the sample of brittle material.
13. The system of claim 9, wherein the rule is based on a set of critical deformation energy densities derived from relative deformations between each pair of discrete particles.
14. The system of claim 13, wherein the set of critical deformation energy densities is further dependent on a characteristic dimension of each of the discrete particles and a fracture energy release rate, wherein the characteristic dimension is used to define an impact domain.
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