CN108877944A - Virtual cropping method based on the grid model for being included in Kelvin's viscoelastic model - Google Patents
Virtual cropping method based on the grid model for being included in Kelvin's viscoelastic model Download PDFInfo
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Abstract
The invention discloses a kind of Virtual cropping methods based on the grid model for being included in Kelvin's viscoelastic model, construct Kelvin's viscoelastic model, the displacement increment in the time is solved by the parameter of Virtual cropping material and clipping time, new displacement, the strain and stress of each node are calculated again, generate simulation notch, Kelvin's viscoelastic model is incorporated for grid, approximate calculation is replaced with stress deformation, solves the problems, such as the problem of related different distortion form in grid distortion, continuously cutting and the mesh free model in finite element model.And calculation amount is greatly reduced, optimize performance.The position of force time point need to be only calculated for deformation by this model, and after removing power, since the balance of power is broken, grid restores automatically, reduces calculation amount；For cutting, rejecting between being open has viscoelastic grid lines, makes grid auto Deformation, compared to traditional approximate opening shape, size, more meets reality, and easy to operate.
Description
Technical field
The present invention relates to Virtual cropping, it is based especially on the Virtual cropping for being included in the grid model of Kelvin's viscoelastic model
Method.
Background technique
In recent years, with the continuous development of virtual reality technology, simulation operation is carried out by virtual reality and obtains possibility.It is empty
Medical staff's great convenience is given in quasi- operation, they can be used the technology and carry out doing simulated exercises repeatedly, promotes oneself
Technology.The process for simulating operation is presented on platform by current virtual operation by modeling, rendering, calculating, has been used limited
Meta-model, mesh free model etc..However, finite element model, mesh free model have some disadvantages.For finite element model, it
Deeply depend on grid, and distort or low-quality grid will cause very big error.In engagement process again, generate
Distortion element to result even in model unstable.Compared to the classical foundation structure based on grid model, its uncomfortable molding
Quasi- cutting network and successional cutting.And the purpose of mesh free model be overcome the problems, such as it is related to finite element model.
Compared with finite element model, mesh free model rebuilds virtual soft tissue on the basis of discrete and separation point element, and each
Relationship between point element is not associated with grid.Therefore, point element is random, and is not constrained by grid, is suitable for discontinuous
Scene.Although above-mentioned mesh free model is promising, virtual operation instrument in the cutting process of simulation soft tissue
Interaction between soft tissue becomes a problem.In order to simplify simulation process, as long as most methods all consider soft group
Knit it is inswept by analog scalpel, tissue just separated.However, result is unlike expected so simple.It, can in cutting process
Apparent deformation is likely to occur before soft tissue incision to observe.As we are to understand, different instruments with it is soft
Tissue interaction normally results in various forms of deformations.In addition, finite element model, the corresponding method of mesh free model
Calculation amount is larger, and complex.
Summary of the invention
Goal of the invention：In view of the above-mentioned drawbacks of the prior art, the present invention is intended to provide a kind of be based on being included in Kelvin
The Virtual cropping method of the grid model of viscoelastic model improves virtual deformation using the grid for being included in Kelvin's viscoelastic model
And the efficiency of cutting.
Technical solution：A kind of Virtual cropping method based on the grid model for being included in Kelvin's viscoelastic model, building are opened
The literary viscoelastic model of that, the general discrete of Kelvin's viscoelastic model are：
Wherein, KnIt is global stiffness matrix,It is global defaulted stiffness matrix；
Apply the defaulted stiffness matrix of the overall situation of defaulted function：
Wherein B, φ, Δ ∈nIn element be constant；δ is the parameter of Virtual cropping material, and b is constant,When expression
Between；
[t is solved by the parameter of Virtual cropping material and clipping timen, tn+1] displacement increment in the timeIt calculates again
The new displacement of each node, strain and stress generate simulation notch.
Further, the new displacement for calculating each node, strain and stress are specially according to [tn, tn+1] in the time
Displacement incrementIt calculates：
In tn+1When, displacement, stress, strain increment be followed successively by：
σn+1=σn+Δσn；
εn+1=εn+Δεn；
Wherein,Δ ε=∑nBiΔUi, BiWith φiIt is strain matrix：
Wherein L is constant；
Wherein, Kelvin's viscoelastic model is in [tn, tn+1] in stress increment be：Δσn=Δ εnΕk+σ0, n
；Wherein, the relationship of stress and strain is：
Wherein, ΕkIt is linear relaxation coefficient, indicates in time interval [tn, tn+1] in caused by unit step strain increment
Stress variation, c0, c1, τ1For material parameter；
tn+1When primary stress be：
Further, the constitutive equation of Kelvin's viscoelastic model is：
Wherein, σ1Indicate stress, η is the damped coefficient of damper, σ2Indicate the time-derivative of stress, Ε2And Ε1Respectively
Indicate the rigidity of two springs, ε1Indicate strain, ε2Indicate the time-derivative of strain.
Further, the constitutive relation of strain and stress is in Kelvin's viscoelastic model：
Wherein, σ indicates that stress, Ε indicate coefficient of elasticity (Young's model), and ε indicates strain, c0And c1It is material parameter, t table
Show time, τ1It is time constant.
It further, further include stress judgment step before the building Kelvin viscoelastic model：Remember that collision area is
A, given threshold f1, d1And d2If power is less than f1Or the width of A is more than or equal to d2, then only deformation occurs for the grid model；If power
More than or equal to f1, and the width of A is less than d1And be greater than 0, then belong to cutting situation one；If power is more than or equal to f1, and the width of A is big
In equal to d1And it is less than d2, then belong to cutting situation two；
The cutting situation one is specially：A is considered as straight line L1, endpoint location is read, two endpoints are set as rigid
Property core, it is fixed, replicate L1, obtain L1、L2, L will be connected in front of duplication1On grid lines and A A on left side intersection point be connected in L1
On, right side intersection point is connected in L2On, L1、L2Because force unbalance generates elastic deformation according to Hooke's law F=-k Δ x, wherein
K is device of spring stiffness coefficient, only considers horizontal direction force；
The cutting situation two is specially：A is considered as rectangular area, fixed width is motionless, the grid lines in deletion A, and two
Long side only considers horizontal direction force because force unbalance is according to Hooke's law F=-k Δ x generation elastic deformation.
Beneficial effect：The present invention is that grid incorporates Kelvin's viscoelastic model, and viscoplasticity is the basic of biologic soft tissue
Characteristic makes soft tissue that there is viscoplasticity to carry out simulating cut and is more in line with reality, and is more advantageous to the setting of the feedback of subsequent power.
The method of the present invention bases oneself upon the grid model of high quality, replaces approximate calculation with stress deformation, solves the net in finite element model
In the problem of lattice distortion, continuous cutting and mesh free model the problem of related different distortion form.And grid proposed by the present invention
Model replaces the calculating of the position of partial dot with the balance of power, greatly reduces calculation amount, optimizes performance.By this model,
For deformation, the position of force time point need to be only calculated, and after removing power, since the balance of power is broken, grid restores automatically, reduces
Calculation amount；For cutting, rejecting between being open has viscoelastic grid lines, breaks the equilibrium state of power, keeps grid automatic
Deformation, compared to traditional approximate opening shape, size, more meets reality, and easy to operate.Since deformation and cutting more accord with
Close the modelling effect brilliance practical, later rendering obtains.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is Kelvin's viscoelastic model；
Fig. 3 is grid model；
Fig. 4 is the schematic diagram for cutting situation one；
Fig. 5 is the schematic diagram for cutting situation two.
Specific embodiment
The technical program is described in detail below by a most preferred embodiment and in conjunction with attached drawing.
As shown in Figure 1, a kind of Virtual cropping method based on the grid model for being included in Kelvin's viscoelastic model, main
Step includes being included in Kelvin's viscoelastic model, viscoelastic combination, stress for grid and judging correlated condition, cutting, specifically
It is as follows：
Step 1：Kelvin's viscoelastic model is included in for grid.
Real-life soft tissue has lag, loose and creep property, these properties are referred to as viscoplasticity.The viscoelastic
Property Mechanism Model can describe the viscoplasticity of soft tissue, this is extremely important in biological characteristics.It can be by modifying in vivo
The relevant parameter that can be obtained in experiment describes the biomechanical characterizations of different soft tissues.Kelvin's viscoplasticity used herein
Model is a kind of standard linear model, and structure is as shown in Fig. 2；
Spring in model indicates the linear elastic characteristics of soft tissue, and damper indicates damping spy when software interrup
Property.Geometry in the geometry and the equation of motion and Elasticity of Viscous Elastic Mechanics is identical as the equation of motion.Visco-spring Boundary value
Solution can be by solving the equation of motion, and the constitutive equation of geometric equation, boundary condition and primary condition obtains；
The constitutive equation of Kelvin's viscoelastic model is：
Wherein, σ1Indicate stress, η is the damped coefficient of damper, σ2Indicate the time-derivative of stress, Ε2And Ε1Respectively
Indicate the rigidity of two springs, ε1Indicate strain, ε2Indicate the time-derivative of strain；
The constitutive relation of strain and stress is：
Wherein, σ indicates that stress, Ε indicate coefficient of elasticity (Young's model), and ε indicates strain, c0And c1It is material parameter, t table
Show time, τ1It is time constant；
Step 2：Viscoelastic combination.
In order to bring viscoplasticity in distorted pattern into, the viscoelastic model of incremental form is used.Firstly, by deformation simulative
Time T point is n timeslice t1, t2..., tn.Each time intervalReferred to as increment.The stress at each moment, strain
It is respectively σ with displacement1, σ2..., σn, ε1, ε2..., εn,From tnTo tn+1, displacement, stress and strain
Increment is respectivelyΔσnWith Δ εn.The body force generated by acceleration is not considered during deformation simulative, soft tissue is not
It is compressible, constancy of volume.Therefore body force b will not change, it is assumed that the external force on the Γ of boundaryIt is constant；
In Kelvin's viscoelastic model, the slackness that soft tissue is in the situation under external force this structure can be closed by relaxation
System indicates：
When in tnWith tn+1, and when Δ t → 0, stress increment is：
Wherein, Ε indicates the rigidity of spring, and τ indicates time constant；
The stress and strain relationship of Kelvin's viscoelastic model is indicated by (2), is obtained in conjunction with (4)：
Wherein ΕkIt is linear relaxation coefficient, indicates in time interval [tn, tn+1] in as caused by unit step strain increment
Stress variation.c0, c1, τ1For material parameter.T is obtained by following formulan+1When stress σ0, n：
Kelvin's viscoelastic model is obtained in [t by following formulan, tn+1] in stress increment：
Δσn=Δ εnΕk+σ0, n (7)
In tn+1When, it is displaced, the increment of stress, strain is respectively：
σn+1=σn+Δσn (9)
εn+1=εn+Δεn (10)
Wherein,Δ ε=∑nBiΔUi, BiWith φiIt is strain matrix, form is：Stress and strain can be calculated according to (8)：
Wherein L is constant.During Soft Tissue Deformation, stress, physical strength and external force meet equilibrium condition, i.e., according to deformation
Virtual work principle, total dummy activity is zero, and the general discrete of viscoelastic model can be obtained：
Wherein, KnIt is global stiffness matrix,It is global defaulted stiffness matrix, the combining form class with global stiffness matrix
Seemingly.Global stiffness matrix can be expressed as with the defaulted stiffness matrix of the overall situation for applying defaulted function：
Wherein, material is homogeneous, B, φ, Δ ∈nIn element be constant.δ is material parameter, and b is constant,Table
Show the time.Corresponding material parameter and time are provided, [t can be solved according to (12)n, tn+1] in displacement incrementFinally
Calculate the new displacement of each node, strain and stress；
Step 3：Stress simultaneously judges correlated condition.
Grid model such as Fig. 3, note collision area are A, given threshold f1, d1And d2If power is less than f1Or the width of A is greater than
Equal to d2, then only deformation occurs for the grid model；If power is more than or equal to f1, and the width of A is less than d1And be greater than 0, then belong to cutting
Situation one (such as Fig. 4)；If power is more than or equal to f1, and the width of A is more than or equal to d1And it is less than d2, then belong to cutting situation two (such as
Fig. 5)；
Step 4：Deformation.
According to stress condition, the algorithm of viscoplasticity bound fraction is completed, calculates displacement；
Step 5：Cutting.
When situation belongs to situation 1 or situation 2, which will generate notch；
5-1：Situation one is cut, A is considered as straight line L1, endpoint location is read, two endpoints are set as rigid nuclear, Gu
It is fixed motionless, replicate L1, obtain L1、L2, L will be connected in front of duplication1On grid lines and A A on left side intersection point be connected in L1On,
Right side intersection point is connected in L2On, in this way, L1、L2Because force unbalance is according to Hooke's law F=-k Δ x, (wherein k is spring stiffness
Coefficient), elastic deformation is generated, horizontal direction force is only considered, is finally reached force balance state, to generate notch；
5-2：Situation two is cut, A is considered as rectangular area, fixed width is motionless, the grid lines in A is deleted, so that two long
Because force unbalance generates elastic deformation according to Hooke's law, only considers horizontal direction force, is finally reached force balance state,
To generate notch.
Claims (5)
1. a kind of Virtual cropping method based on the grid model for being included in Kelvin's viscoelastic model, which is characterized in that building is opened
The literary viscoelastic model of that, the general discrete of Kelvin's viscoelastic model are：
Wherein, KnIt is global stiffness matrix,It is global defaulted stiffness matrix；
Apply the defaulted stiffness matrix of the overall situation of defaulted function：
Wherein B, φ, Δ ∈nIn element be constant；δ is the parameter of Virtual cropping material, and b is constant,Indicate the time；
[t is solved by the parameter of Virtual cropping material and clipping timen, tn+1] displacement increment in the timeIt calculates again each
The new displacement of node, strain and stress generate simulation notch.
2. the Virtual cropping method according to claim 1 based on the grid model for being included in Kelvin's viscoelastic model,
It is characterized in that, the new displacement for calculating each node, strain and stress are specially according to [tn, tn+1] displacement in the time increases
AmountIt calculates：
In tn+1When, displacement, stress, strain increment be followed successively by：
σn+1=σn+Δσn；
εn+1=εn+Δεn；
Wherein,BiWith φiIt is strain matrix：
Wherein L is constant；
Wherein, Kelvin's viscoelastic model is in [tn, tn+1] in stress increment be：Δσn=Δ εnΕk+σ0, n；Wherein, stress with
The relationship of strain is：
Wherein, ΕkIt is linear relaxation coefficient, indicates in time interval [tn, tn+1] in answered as caused by unit step strain increment
Power variation, c0, c1, τ1For material parameter；
tn+1When primary stress be：
3. the Virtual cropping method according to claim 1 based on the grid model for being included in Kelvin's viscoelastic model,
It is characterized in that, the constitutive equation of Kelvin's viscoelastic model is：
Wherein, σ1Indicate stress, η is the damped coefficient of damper, σ2Indicate the time-derivative of stress, Ε2And Ε1Respectively indicate two
The rigidity of a spring, ε1Indicate strain, ε2Indicate the time-derivative of strain.
4. the Virtual cropping method according to claim 1 based on the grid model for being included in Kelvin's viscoelastic model,
It is characterized in that, the constitutive relation of strain and stress is in Kelvin's viscoelastic model：
Wherein, σ indicates that stress, Ε indicate coefficient of elasticity (Young's model), and ε indicates strain, c0And c1It is material parameter, when t is indicated
Between, τ1It is time constant.
5. the Virtual cropping method according to claim 1 based on the grid model for being included in Kelvin's viscoelastic model,
It is characterized in that, further includes stress judgment step before the building Kelvin viscoelastic model：Note collision area is A, sets threshold
Value f1, d1And d2If power is less than f1Or the width of A is more than or equal to d2, then only deformation occurs for the grid model；If power is more than or equal to
f1, and the width of A is less than d1And be greater than 0, then belong to cutting situation one；If power is more than or equal to f1, and the width of A is more than or equal to d1
And it is less than d2, then belong to cutting situation two；
The cutting situation one is specially：A is considered as straight line L1, endpoint location is read, two endpoints are set as rigid nuclear,
It is fixed, replicate L1, obtain L1、L2, L will be connected in front of duplication1On grid lines and A A on left side intersection point be connected in L1On,
Right side intersection point is connected in L2On, L1、L2Because force unbalance generates elastic deformation according to Hooke's law F=-k Δ x, wherein k is bullet
Spring stiffness factor, only considers horizontal direction force；
The cutting situation two is specially：A is considered as rectangular area, fixed width is motionless, deletes the grid lines in A, two long sides
Because force unbalance generates elastic deformation according to Hooke's law F=-k Δ x, horizontal direction force is only considered.
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| CN113052975A (en) * | 2020-09-23 | 2021-06-29 | 视伴科技(北京)有限公司 | Model optimizing method and device |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102044086A (en) * | 2010-11-30 | 2011-05-04 | 华北水利水电学院 | Soft tissue deformation simulation method |
| CN102262699A (en) * | 2011-07-27 | 2011-11-30 | 华北水利水电学院 | Soft tissue deformation simulation method based on coupling of mesh-free Galerkin and mass spring |
| CN105559887A (en) * | 2015-12-11 | 2016-05-11 | 哈尔滨工业大学 | Operation cutting training system and method based on force feedback and used for surgical robot |
| CN106570201A (en) * | 2015-10-12 | 2017-04-19 | 中国石油化工股份有限公司 | Numerical simulation method and system for viscoelastic medium |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102044086A (en) * | 2010-11-30 | 2011-05-04 | 华北水利水电学院 | Soft tissue deformation simulation method |
| CN102262699A (en) * | 2011-07-27 | 2011-11-30 | 华北水利水电学院 | Soft tissue deformation simulation method based on coupling of mesh-free Galerkin and mass spring |
| CN106570201A (en) * | 2015-10-12 | 2017-04-19 | 中国石油化工股份有限公司 | Numerical simulation method and system for viscoelastic medium |
| CN105559887A (en) * | 2015-12-11 | 2016-05-11 | 哈尔滨工业大学 | Operation cutting training system and method based on force feedback and used for surgical robot |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113052975A (en) * | 2020-09-23 | 2021-06-29 | 视伴科技(北京)有限公司 | Model optimizing method and device |
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