CN112287474A - Algorithm, equipment and storage medium for simulating mechanical behavior of polyvinyl alcohol fiber concrete - Google Patents
Algorithm, equipment and storage medium for simulating mechanical behavior of polyvinyl alcohol fiber concrete Download PDFInfo
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- 229910000831 Steel Inorganic materials 0.000 description 2
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- 238000009795 derivation Methods 0.000 description 1
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Abstract
The application discloses an algorithm, equipment and a storage medium for simulating mechanical behavior of polyvinyl alcohol fiber concrete, wherein the algorithm comprises the following steps: simulating the nonlinear elastic characteristics of the polyvinyl alcohol fiber concrete by using generalized Hooke's law as a basic model; on the basis of the basic model, introducing a damage factor to correct the damage influence on the concrete caused by the doping of polyvinyl alcohol fibers in the polyvinyl alcohol fiber concrete, and introducing a strain rate strengthening factor to correct the strain rate influence, thereby obtaining a constitutive model for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete; and the elastic coefficient of the basic constitutive model is in a form of an exponentiation function.
Description
Technical Field
The present disclosure relates generally to the field of civil engineering, and more particularly to an algorithm, apparatus and storage medium for simulating the mechanical behavior of polyvinyl alcohol fiber concrete.
Background
Fiber Reinforced Concrete (FRC), which is abbreviated as Fiber Concrete, is a group of composite materials composed of Concrete as a base material and various fibers as reinforcing phases, and is a novel building material which is originated in the latter half of the 20 th century. The types of common fibers include steel fibers, synthetic fibers, natural fibers, etc., and concrete can be classified into: steel fiber concrete, synthetic fiber concrete, natural fiber concrete, hybrid fiber concrete, and the like. The fibers are doped into the concrete, so that the characteristics of the concrete material cannot be influenced, the characteristics of the material can be exerted, the performance of the matrix material is improved in a micro mechanism, the defects of low tensile strength, poor toughness, low ultimate ductility and the like of the concrete are overcome, and the concrete has a series of excellent physical and mechanical properties, so that the concrete is widely applied to the field of civil engineering.
In order to accurately describe the whole damage process of the fiber concrete under the action of stress and provide parameter basis for the design of the subsequent fiber sprayed concrete, it is necessary to carry out deep research on the mechanical properties of the fiber concrete. However, in the prior art, a mechanical model capable of reflecting the whole process of the stress damage of the fiber concrete is not available.
Disclosure of Invention
In view of the above-mentioned defects or shortcomings in the prior art, it is desirable to provide a scheme for simulating the mechanical behavior of polyvinyl alcohol fiber concrete, which can reflect the whole process of the fiber concrete forced damage.
In a first aspect, the embodiments of the present application provide an algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete, including:
simulating the nonlinear elastic characteristics of the fiber concrete by using generalized Hooke's law as a basic model;
on the basis of the basic model, introducing a damage factor to correct damage influence on concrete caused by doping of fibers in the fiber concrete, and introducing a strain rate strengthening factor to correct strain rate influence, so as to obtain a constitutive model for simulating the mechanical behavior of the fiber concrete;
the expression of the constitutive model is as follows:
in the formula (I), the compound is shown in the specification,
σdthe stress of the reinforced fiber concrete is obtained;
a is a first fitting parameter;
b is a second fitting parameter;
e is the elastic modulus of the fiber concrete;
m is a shape parameter for controlling the elastic stage curve;
ε0is the initial value of the damage;
n is a first Weibull distribution parameter;
F0is a second Weibull distribution parameter;
epsilon is the fiber concrete strain;
εsis the yield strain.
Further, the algorithm is used for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete.
Further, the value range of each parameter is as follows (if there is a unit, please give the unit of each parameter):
E：108～1010；
M：1-3；
ε0：0～2×10-3；
F0：10-4～10-3；
n：0.5～2。
the embodiment of the present application further provides another algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete, including:
simulating the nonlinear elastic characteristics of the fiber concrete by using generalized Hooke's law as a basic model;
on the basis of the basic model, introducing a damage factor to correct damage influence on concrete caused by doping of fibers in the fiber concrete, and introducing a strain rate strengthening factor to correct strain rate influence, so as to obtain a constitutive model for simulating the mechanical behavior of the fiber concrete; and the elastic coefficient of the basic constitutive model is in a form of an exponentiation function.
In certain embodiments of the present application, the expression of the nonlinear elastic basic constitutive model of the fiber concrete is:
σ＝Eεm，
where E is the nominal modulus of elasticity and m is the shape parameter controlling the elastic phase curve.
In certain embodiments of the present application, the damage factor takes into account the randomness of the distribution of microcracks contained within the fiber concrete, establishing a statistical damage factor evolution equation.
Further, the damage factor evolution equation adopts a damage factor evolution equation which is distributed by Weibull and contains initial damage, and the expression of the damage factor evolution equation is as follows:
wherein n is the first parameter of Weibull distribution, and F0 is the second parameter of Weibull distribution.
In certain embodiments of the present application, the strain rate enhancement factor is determined from an empirical model based on experimental data analysis, the strain rate enhancement factor being expressed as:
in the formula, a and b are fitting parameters.
In a second aspect, the embodiments of the present application provide an apparatus for simulating mechanical behavior of polyvinyl alcohol fiber concrete, the apparatus comprising:
one or more processors;
a memory for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to perform the algorithm of any of the above.
In a third aspect, an embodiment of the present application provides a computer-readable storage medium storing a computer program, where the computer program is configured to implement an algorithm according to any one of the above when executed by a processor.
The algorithm for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete provided by the embodiment of the application can accurately reflect the whole process of the stress damage of the fiber concrete and provide a reference basis for the design of the subsequent fiber sprayed concrete.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
FIG. 1 shows C30PVA0.6 stress-strain curve contrast plots;
figure 2 shows a C40PVA0.6 stress-strain curve comparison.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the described embodiments are only a part, and not all, of the present invention. For convenience of description, only portions related to the invention are shown in the drawings.
It will be readily understood that the components of the embodiments of the present invention, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations without departing from the scope of the present invention. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the application provides an algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete. Concrete materials have natural defects such as holes and cracks which cannot be avoided, a test curve has an obvious compaction stage, and a linear elastic constitutive model is not suitable for describing the mechanical behavior of the stage. Therefore, a nonlinear elastic model is adopted to simulate the real deformation characteristic of the concrete according to the characteristics of the nonlinear elastic stage of the concrete, the characteristics of a fiber concrete full stress-strain curve are considered, and the strain hardening and softening effect and the strain rate enhancement effect of the concrete are described by introducing a damage factor and a strain rate enhancement factor based on a statistical strength theory, a damage theory and a strain rate effect.
(1) Nonlinear elastic constitutive model
The nonlinear elastic constitutive model is similar to the elastic constitutive model, and is divided into a full-quantity form constitutive relation and an incremental form constitutive relation, and the tensor form is used for expressing the following formulas (1) and (2):
in the formula, Dijkl sAnd Dijkl tThe elasticity tensor of the secant line and the elasticity tensor of the tangent line are respectively provided with the same expression form and are consistent with the elasticity tensor in the linear elasticity constitutive model, as shown in formula (3):
wherein G and μ are Gs、μsAnd Gt、μtInstead of the nonlinear elastic tensor in the full-volume form and the incremental form, the linear elastic tensor in which G and mu are constants is different from the linear elastic tensor in that G and mu in the two formss、μsAnd Gt、μtIs a function of the mean stress or strain.
Based on the basic relationship of the nonlinear elastic model, researchers propose a plurality of concrete compression nonlinear elastic constitutive models, including an Ottosen model, a Darwin-Pecknold model, a Saenz model, a Shenzhuang model, a Zhenhui model and the like.
The incremental constitutive model and the tangent elastic modulus proposed by Saenz are shown in formulas (4) and (5):
in the formula, E0As tangent modulus at the origin of the stress-strain curve, EcIs the secant modulus at peak stress,εcthe peak strain corresponds to the peak stress.
Converting the formula (4) into a form of the following formula,
in the formula (I), the compound is shown in the specification,
in a mathematical sense, the nonlinear elastic coefficient in the Saenz model adopts polynomial inverse fitting.
In the early times of the last eighties, sea of townhain et al proposed a segmented constitutive model for simulating the stress-strain curve of concrete, where x and y are expressed in dimensionless strain and stress, respectively, and the specific mathematical expressions are as follows:
wherein x is ε/εc，y＝σ/σcAnd a and b are control parameters of an ascending section and a descending section, and relevant values are shown in literature requirements.
For the ascending section, the form can be changed to obtain the following formula
σ＝f(ε)ε＝(a+bε+cε2)ε (8)
Wherein, b is 3-2a, c is a-2.
The same theory shows that the nonlinear elastic constant in the sea-wrenches model is similar to the Saenz model, and a quadratic polynomial is also used for fitting.
Many nonlinear elastic constitutive models are arranged to obtain that most of the nonlinear elastic constants in the models are described by polynomials, such as first-order polynomial, second-order polynomial, and third-order polynomial (Elwinad-Murray model). Based on the relation between the nominal tangent modulus of the test curve and the strain, if the simplicity and the applicability of the model are considered, a nonlinear model which describes the deformation characteristic of the theoretical elastic stage of the concrete by a power function can be established.
The nonlinear elastic coefficient of the concrete takes the form of an exponentiation function, as shown in the following formula,
f(ε)＝Aεn (9)
wherein A and n are material parameters.
According to the generalized hooke's law, there are,
σ＝f(ε)ε＝Aεn+1 (10)
the above formula is a nonlinear constitutive model capable of reflecting the deformation characteristic of the concrete in the elastic stage. Wherein, when n is 0, the model is degraded into an ideal linear elastic model; when n is an integer, the model is similar to the prior constitutive model using polynomial fitting to nonlinear elastic constants. Analysis shows that the model can simulate the ascending section curve of the existing test result, including straight line, convex curve, concave curve and the like, and has the advantages of wide application range, less parameters and more convenient application.
The expression is transformed into a form that a more concise expression is obtained,
σ＝Eεm (11)
where E is the nominal modulus of elasticity, m is n +1, and m is the shape parameter controlling the elastic phase curve.
(2) Injury factor
Based on Lemailre equivalent strain assumption, the strain caused by the nominal stress in the damaged state is equal to the strain generated by the effective stress in the undamaged state, namely
E'＝E(1-D) (13)
Wherein, sigma and E 'are nominal stress and elastic modulus in a damage state, sigma' and E are effective stress and elastic modulus in a nondestructive state, D is a damage factor, and D is more than or equal to 0 and less than or equal to 1.
The damage factor can be explained as the weakening of material strength caused by the reduction or reduction of effective volume, area, density and even wave velocity in the material according to the original phenomenological theory, and has obvious physical significance. Later, with the development of damage mechanics, various damage definitions are proposed, including stress damage, strain damage, energy damage, and the like, and the damage definitions have only symbolic meanings.
Through analyzing the existing research results and combining the uniaxial compression test result of the fiber concrete, the objective cavities of the concrete materials after molding can be determined as initial damage, and an evolution equation of the damage factors containing the initial damage, which accords with Weibull distribution, is established.
Assuming that the infinitesimal intensity conforms to Weibull distribution, according to the probability density function, there are
In which ε is strain, n, F0Weibull distribution parameters.
The initial damage characteristic of the concrete is considered, and an initial damage value epsilon is introduced0The probability density function with initial damage is obtained as:
integrating the above formula to obtain an evolution equation of the damage factor containing the initial damage:
(3) strain rate enhancement factor
Concrete materials have obvious strain rate effect, most researches are based on objective microcracks in the materials, and the strain rate is considered to influence the initiation, development, convergence and the like of the microcracks, so that the effect of reinforcing the concrete is achieved.
The more classical of the constitutive model considering the viscous effect is the Z-W-T model, which is originally used for studying the one-dimensional mechanical behavior of epoxy resin by simulating the performance of a material by introducing a combination of a nonlinear spring and two Maxwell bodies.
fe(ε)＝E0ε+αε2+βε3 (18)
Where the first term is a nonlinear spring, the transient mechanical response of the material is simulated, and the second and third terms describe the viscous response at low and high strain rates, respectively.
The modeling idea of the empirical model is based on a test result, the relationship between the strain rate and the mechanical parameters of the concrete material such as strength, peak strain, elastic modulus and the like is analyzed, the constitutive model considering the strain rate effect is evolved based on the existing static constitutive model, and the constitutive model mainly comprises an HJC model, an RHT model and the like for simulating the large deformation of the concrete material under the high strain rate in consideration of damage. The empirical model is not related to complex mechanical behaviors, has simple derivation process and good fitting effect with test results, and is popular with engineering technicians.
Based on the proposed nonlinear elastic damage model, a strain rate strengthening factor is introduced to describe the mechanical behavior of the fiber concrete, as shown in the following formula:
in the formula, a and b are fitting parameters.
Substituting the formula (11) and the formula (16) into the formula (19) to obtain a constitutive model of the nonlinear elastic damage of the fiber concrete, which is shown as the following formula:
verification of nonlinear elastic damage constitutive model
Compression and splitting tensile mechanical tests under medium strain rate of fiber concrete are respectively carried out by adopting RMT-201 rock and concrete mechanical test systems. At present, in a compression strength test, a sample mainly adopts a cylindrical form, a cubic form and the like, and stress distribution of the cylindrical sample after being stressed is more uniform than that of the cubic form, so that a plurality of researchers in foreign countries commonly use a cylindrical test piece as a preferred sample shape. In consideration of large number of samples, the concrete in the test is poured and maintained by a plastic mould of 150 multiplied by 150mm, the fiber is polyvinyl alcohol fiber with the fiber length of 8mm and the diameter of 12-18 mu m, and the polyvinyl alcohol fiber concrete member is poured according to four volume ratio mixing amounts (0%, 0.2%, 0.4% and 0.6%).
Cylindrical samples of different sizes were produced by drilling sampling, and four different strain rates (10)-5/s、10-4/s、10-3S and 10-2In/s) conditions. Wherein the compression test adopts cylindrical samples with the size of phi 50 multiplied by 100mm, each group comprises 3 samples, and the total number of the samples is 48; the split draw test uses cylindrical test pieces of dimensions phi 50X 30mm, 3 pieces per set, for a total of 48 test pieces. The total number of test specimens for the two matrix strengths was 96 × 2 — 192.
Based on the nonlinear elastic damage constitutive model, an improved differential evolution algorithm in 1stoptm software is used for fitting a test curve, and the fitting result is shown in fig. 1-2. The results of curve fitting of fiber concrete tests of other doping amounts are partially given by selectivity and limited by space.
According to fitting, the model result has good matching effect with the test curve regardless of the front peak section or the rear peak section, and the nonlinear elastic injury constitutive model established in the method is reasonable and effective. The model can simulate the compaction stage and the nonlinear elasticity stage before the peak and the softening stage after the peak, and can provide reference for building a concrete full stress-strain curve model.
Because multiple factors influence the forming quality of concrete in the mixing process, the number and distribution of natural cavities and cracks in a concrete finished product have large difference, and the difference is one of main reasons for large discreteness of a stress-strain curve in the test process, so that the value range of the model parameter is provided, and the popularization and the application of the model parameter are facilitated. Aiming at the whole fitting process of the fiber concrete compression test result, the value ranges of relevant parameters are given for reference by considering the physical meanings of certain parameters and the applicability of a model, and the value ranges of main fitting parameters are shown in a table 1:
TABLE 1 main fitting parameter value ranges
As another aspect, the present application also provides an apparatus for simulating mechanical behavior of polyvinyl alcohol fiber concrete, characterized in that the apparatus comprises:
one or more processors;
a memory for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to perform the algorithms for simulating polyvinyl alcohol fiber concrete mechanical behavior of the present application.
In addition, the present application also provides a computer-readable storage medium, which may be the computer-readable storage medium included in the apparatus in the above-described embodiments; or it may be a separate computer readable storage medium not incorporated into the device. The computer readable storage medium stores one or more programs for use by one or more processors in executing the algorithms described herein for simulating the mechanical behavior of fiber concrete.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.
Claims (10)
1. An algorithm for simulating the mechanical behavior of polyvinyl alcohol fiber concrete, comprising:
simulating the nonlinear elastic characteristics of the polyvinyl alcohol fiber concrete by using generalized Hooke's law as a basic model;
on the basis of the basic model, introducing a damage factor to correct the damage influence on the concrete caused by the doping of polyvinyl alcohol fibers in the polyvinyl alcohol fiber concrete, and introducing a strain rate strengthening factor to correct the strain rate influence, thereby obtaining a constitutive model for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete;
the expression of the constitutive model is as follows:
in the formula (I), the compound is shown in the specification,
σdthe stress of the polyvinyl alcohol fiber concrete after being strengthened;
a is a first fitting parameter;
b is a second fitting parameter;
e is the elastic modulus of the polyvinyl alcohol fiber concrete;
m is a shape parameter for controlling the elastic stage curve;
ε0is the initial value of the damage;
n is a first Weibull distribution parameter;
F0is a second Weibull distribution parameter;
epsilon is the strain of polyvinyl alcohol fiber concrete;
εsis the yield strain.
2. The algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete according to claim 1, wherein the algorithm is used for simulating mechanical behavior of polyvinyl alcohol fiber concrete.
3. The algorithm for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete according to claim 2, wherein the value ranges of the parameters are as follows:
E：108-1010Mpa；
m：1-3；
ε0：0-2×10-3；
F0：10-4-10-3；
n：0.5-2。
4. an algorithm for simulating the mechanical behavior of polyvinyl alcohol fiber concrete, comprising:
simulating the nonlinear elastic characteristics of the polyvinyl alcohol fiber concrete by using generalized Hooke's law as a basic model;
on the basis of the basic model, introducing a damage factor to correct the damage influence on the concrete caused by the doping of polyvinyl alcohol fibers in the polyvinyl alcohol fiber concrete, and introducing a strain rate strengthening factor to correct the strain rate influence, thereby obtaining a constitutive model for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete; and the elastic coefficient of the basic constitutive model is in a form of an exponentiation function.
5. The algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete according to claim 4, wherein the expression of the nonlinear elastic basic constitutive model of the polyvinyl alcohol fiber concrete is as follows:
σ＝Eεm，
where E is the nominal modulus of elasticity and m is the shape parameter controlling the elastic phase curve.
6. The algorithm for simulating the mechanical behavior of the polyvinyl alcohol fiber concrete according to claim 4, wherein the damage factor takes into account the randomness of the distribution of micro-cracks contained in the polyvinyl alcohol fiber concrete to establish the evolution equation of the statistical damage factor.
7. The algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete according to claim 6, wherein the damage factor evolution equation adopts a Weibull distributed damage factor evolution equation with initial damage, and the expression of the damage factor evolution equation is as follows:
wherein n is the first parameter of Weibull distribution, and F0 is the second parameter of Weibull distribution.
8. The algorithm for simulating mechanical behavior of polyvinyl alcohol fiber concrete according to claim 4, wherein the strain rate enhancement factor is determined according to an empirical model based on experimental data analysis, and the expression of the strain rate enhancement factor is as follows:
in the formula, a and b are fitting parameters.
9. An apparatus for simulating the mechanical behavior of polyvinyl alcohol fiber concrete, the apparatus comprising:
one or more processors;
a memory for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to perform the method recited in any of claims 1-8.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1-8.
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Cited By (2)
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| CN113742943A (en) * | 2021-09-26 | 2021-12-03 | 江西科技学院 | Algorithm, system and readable storage medium for simulating mechanical behavior of polyvinyl alcohol fiber concrete |
| CN113987763A (en) * | 2021-10-12 | 2022-01-28 | 广州特种承压设备检测研究院 | Construction method and application of polyethylene hyperbolic constitutive model |
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| CN113987763B (en) * | 2021-10-12 | 2024-04-12 | 广州特种设备检测研究院(广州市特种设备事故调查技术中心、广州市电梯安全运行监控中心) | Construction method and application of polyethylene hyperbola constitutive model |
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