CN112016200B - Construction method of skin nonlinear constitutive model under compression load - Google Patents
Construction method of skin nonlinear constitutive model under compression load Download PDFInfo
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- CN112016200B CN112016200B CN202010867589.0A CN202010867589A CN112016200B CN 112016200 B CN112016200 B CN 112016200B CN 202010867589 A CN202010867589 A CN 202010867589A CN 112016200 B CN112016200 B CN 112016200B
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- 230000006835 compression Effects 0.000 title claims abstract description 20
- 238000007906 compression Methods 0.000 title claims abstract description 20
- 238000010276 construction Methods 0.000 title claims abstract description 7
- 239000007787 solid Substances 0.000 claims abstract description 9
- 230000002040 relaxant effect Effects 0.000 claims 1
- 239000000463 material Substances 0.000 abstract description 6
- 230000035945 sensitivity Effects 0.000 abstract description 4
- 238000004088 simulation Methods 0.000 abstract description 3
- 210000003491 skin Anatomy 0.000 description 35
- 238000002474 experimental method Methods 0.000 description 4
- 238000000034 method Methods 0.000 description 3
- 210000004207 dermis Anatomy 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 230000004075 alteration Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000012620 biological material Substances 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 210000002615 epidermis Anatomy 0.000 description 1
- 230000001747 exhibiting effect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000035515 penetration Effects 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 238000005482 strain hardening Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract
The invention discloses a construction method of a skin nonlinear constitutive model under the action of compression load, which comprises the following steps: establishing a modified Odgen model as a skin superelastic portion model; establishing a Maxwell model as a relaxation unit to describe relaxation phenomena caused by skin viscoelasticity; establishing a standard three-parameter solid model as a creep unit to describe the creep phenomenon caused by skin viscoelasticity; by introducing a strain rate function, a specific model capable of describing skin mechanical behavior at a strain rate of 10 ‑4/s～103/s is established; the strain rate sensitivity of the pigskin and the relaxation and creep phenomena caused by the viscoelasticity of the pigskin can be captured by using the nonlinear constitutive model of the pigskin, and a foundation is laid for the modeling and simulation of the subsequent skin material.
Description
Technical Field
The invention relates to the technical field of computational mechanics and experimental mechanics, in particular to a construction method of a skin nonlinear constitutive model under the action of compression load.
Background
Skin is a biomaterial consisting of epidermis, papillary dermis and reticular dermis, exhibiting high nonlinearity, strain rate sensitivity, superelasticity and relaxation, creep properties due to viscoelasticity. Under compression load, the mechanical property of the internal structure of the material is continuously changed, and research on constitutive relation of skin is always one of the key points of skin mechanical research, so that the material is an important basis for establishing a real human finite element model in the penetration process. The mechanical properties of the skin material can be accurately described, and the constitutive model has high reliability, so that the constitutive model is an urgent requirement in engineering and scientific research.
Currently, a superelastic or viscoelastic model is mainly used as a constitutive model of skin, but the superelastic model cannot describe the skin's viscoelasticity; the viscoelastic constitutive model is divided into two models under low strain rate and high strain rate, and only the relaxation property of skin can be described, and the creep property of skin is ignored. Thus, the skin material lacks a complete and compact constitutive model.
Disclosure of Invention
The invention aims to provide a construction method of a skin nonlinear constitutive model under the action of compression load, so as to solve the problem that the existing skin constitutive model cannot fit skin compression experimental curves under different strain rates well (namely, fitting accuracy is low) at the same time, and model reliability is low.
In order to achieve the above purpose, the present invention provides the following technical solutions: the construction method of the skin nonlinear constitutive model under the action of compression load comprises the following steps:
step 1: establishing a Maxwell model as a relaxation unit of the constitutive model;
step 2: establishing a standard three-parameter solid model as a creep unit of the constitutive model;
step 3: the Odgen model is modified as the superelastic part of the constitutive model;
step 4: introducing a function related to the strain rate, and establishing a whole constitutive model.
Preferably, the step 1 includes: the Maxwell model describes the relaxation phenomenon that occurs in the skin under pressure load, and the formula of the Maxwell model is as follows:
Wherein k 1 represents the elastic coefficient of the 1 st elastic element in the model, k i represents the elastic coefficient of the i st elastic element in the model, τ represents the shear stress, t represents time, e represents the natural constant, dt represents the independent variable of the integrand, σ v represents the stress to which the relaxation unit is subjected in the viscoelastic part, η 1 represents the viscosity coefficient of the 1 st viscous pot in the model, η i represents the viscosity coefficient of the i st viscous pot in the model.
Preferably, the step 2 includes: the standard three-parameter solid model describes the creep phenomenon of skin under the conditions of large stress and large strain, and the formula of the standard three-parameter solid model is as follows:
wherein σ c represents the stress to which the creep unit is subjected in the viscoelastic portion, ε represents the strain that the skin develops under compressive load, Indicating the strain rate.
Preferably, the step 3 includes: the Odgen model describes the superelasticity of the skin and the Odgen model is formulated as follows:
Wherein μ, α are superelastic model parameters in Odgen model, σ represents stress, λ represents elongation.
Preferably, by introducing a function on the strain rate, a nonlinear constitutive model of skin under compressive load is derived, the formula of which is as follows:
wherein A 1、B1 is the model parameter to be solved.
Compared with the prior art, the invention has the beneficial effects that:
The skin nonlinear constitutive model under the compression load provided by the invention can describe the strain rate sensitivity of the skin under the action of the compression load and the relaxation and creep phenomena caused by viscoelasticity, and also forms a compact unified model. The skin constitutive model can quantitatively determine the relationship between the stress and the strain of the skin under the compression load, and lays a foundation for numerical simulation calculation and engineering application of skin stress analysis under different compression conditions.
Drawings
FIG. 1 is a flow chart of a skin nonlinear constitutive model under compressive load;
FIG. 2 is a schematic diagram of a relaxation unit;
FIG. 3 is a schematic view of a creep cell;
FIG. 4 is a schematic diagram of a constitutive model;
FIG. 5 shows the results of static skin compression experiments (0.01/s and 0.1/s) and model predictions;
FIG. 6 shows the results of skin dynamic compression experiments (2000/s, 3000/s and 4000/s) and model predictions.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a technical scheme that: in order to solve the problems of the existing skin constitutive model, the invention establishes the specific constitutive model capable of describing the mechanical characteristics of the skin under the compression load, and the model can capture the strain rate sensitivity of the skin and the relaxation and creep phenomena caused by viscoelasticity, thereby providing basis for modeling and simulation of the subsequent skin material.
The technical scheme provided by the invention comprises the following specific steps:
step 1, a Maxwell model is established as a relaxation unit of the constitutive model, as shown in fig. 2:
In the Maxwell viscoelastic model, the relaxation time θ is an important parameter, satisfying the following conditions:
η1＝k1θ (2)
Wherein: k i represents the elastic coefficient of the i-th elastic element in the model, σ v represents the stress to which the relaxation unit is subjected in the viscoelastic portion, η i represents the viscosity coefficient of the i-th visco-pot in the model.
Combining formulas (1) and (2) to obtain a Maxwell model:
Step 2, establishing a standard three-parameter solid model as a creep unit of the constitutive model, as shown in fig. 3:
σc＝k2ε1＝k3ε2+η2ε2′(t) (4)
ε＝ε1+ε2 (5)
ε′(t)＝ε′1(t)+ε2′(t) (6)
The following formulas (4) to (6) can be used:
Where σ c denotes the stress to which the creep unit is subjected in the viscoelastic portion, ε i is the strain in the ith direction of the skin under compressive load, Indicating the strain rate.
The standard three-parameter solid model is given by:
step 3, improving Odgen the model to serve as a super-elastic part of the constitutive model;
The strain potential of Odgen model is written as:
Where μ i is the shear modulus in the i-th direction and α i is the compressive strain hardening index in the i-th direction. N is the total number of directions, lambda i is the elongation in the i-th direction, and sigma i is the stress in the i-th direction.
Due to the adoption of a uniaxial compression experiment, the following steps can be obtained:
σ1＝σ,σ2＝σ3＝0,λ2＝λ3 (12)
due to the almost incompressibility of the skin, we get:
I3＝(λ1λ2λ3)2＝1 (13)
combining formulas (11) to (13) to obtain a stress model of the superelastic portion:
Step 4, introducing a function related to the strain rate, and establishing a whole constitutive model, as shown in fig. 4:
Under compressive loading, the skin constitutive equation consists of a superelastic portion and a viscoelastic portion in parallel, as shown in fig. 4. Wherein the skin superelastic portion uses a modified Odgen model; the viscoelastic portion is obtained by a parallel connection of a relaxation unit and a creep unit. The parallel constitutive model can be expressed as:
Wherein, sigma hσvσc is shown in the formula (14), the formula (3) and the formula (10) respectively,
Wherein A n、Bn is the model parameter to be solved, and n is the term number of the polynomial.
Assuming that both equations (16) and (17) are first order polynomials, the complete constitutive model that can be obtained is:
For further understanding of the present invention, the present invention will be described in detail with reference to the accompanying drawings and examples, wherein the specific process of using the present structural model of the present example is as follows:
1) Performing quasi-static and dynamic compression experiments on the pigskin to obtain compression mechanical characteristic curves of the pigskin at strain rates of 0.01/s, 0.1/s, 2000/s, 3000/s and 4000/s respectively;
2) All parameters of the skin constitutive model (equation (18)) were determined using the iterative parameter estimation method in Matlab, as shown in table 1.
TABLE 1 constitutive model parameters under compression load
3) Comparing the experimental result with the prediction result of the constitutive model, the matching degree of the experimental result and the prediction result of the constitutive model can be seen to be higher, and the constitutive model can accurately describe the mechanical behavior of the skin, as shown in fig. 5 and 6.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (1)
1. The construction method of the skin nonlinear constitutive model under the action of the compression load is characterized by comprising the following steps of:
step 1: establishing a Maxwell model as a relaxation unit of the constitutive model;
step 2: establishing a standard three-parameter solid model as a creep unit of the constitutive model;
step 3: the Odgen model is modified as the superelastic part of the constitutive model;
step 4: introducing a function related to the strain rate, and establishing a whole constitutive model;
The step 1 comprises the following steps: the Maxwell model describes the relaxation phenomenon that occurs in the skin under pressure load, and the formula of the Maxwell model is as follows:
Wherein k 1 represents the elastic coefficient of the 1 st elastic element in the model, k i represents the elastic coefficient of the i st elastic element in the model, τ represents the shear stress, t represents time, e represents the natural constant, dt represents the independent variable of the integrand, σ v represents the stress to which the relaxing unit is subjected in the viscoelastic part, η 1 represents the viscosity coefficient of the 1 st viscous pot in the model, η i represents the viscosity coefficient of the i st viscous pot in the model;
The step 2 comprises the following steps: the standard three-parameter solid model describes the skin-induced creep phenomenon, and the formula of the standard three-parameter solid model is as follows:
wherein σ c represents the stress to which the creep unit is subjected in the viscoelastic portion, ε represents the strain that the skin develops under compressive load, Indicating the strain rate;
The step 3 comprises the following steps: the Odgen model describes the superelasticity of the skin and the Odgen model is formulated as follows:
wherein μ, α are superelastic model parameters in Odgen model, σ represents stress, λ represents elongation;
By introducing a function on strain rate, a nonlinear constitutive model of skin under compressive load is derived, the formula of which is as follows:
wherein A 1、B1 is the model parameter to be solved.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106953582A (en) * | 2017-04-13 | 2017-07-14 | 南通大学 | A kind of alternating-current variable frequency motor drags two dimensional surface position control method |
| CN109829231A (en) * | 2019-01-24 | 2019-05-31 | 北京理工大学 | A kind of propellant mechanics prediction technique based on CMDB propellant damage process |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106953582A (en) * | 2017-04-13 | 2017-07-14 | 南通大学 | A kind of alternating-current variable frequency motor drags two dimensional surface position control method |
| CN109829231A (en) * | 2019-01-24 | 2019-05-31 | 北京理工大学 | A kind of propellant mechanics prediction technique based on CMDB propellant damage process |
Non-Patent Citations (1)
| Title |
|---|
| 猪皮生物材料的力学特性研究;王志超;《中国优秀硕士学位论文全文数据库 医药卫生科技辑》;第36-51页 * |
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