CN112257144B - Cement-based composite material elastic-plastic constitutive model and establishment method thereof - Google Patents
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- 239000004568 cement Substances 0.000 title claims abstract description 74
- 239000002131 composite material Substances 0.000 title claims abstract description 74
- 229920003023 plastic Polymers 0.000 title claims abstract description 53
- 239000004033 plastic Substances 0.000 title claims abstract description 53
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- 238000012360 testing method Methods 0.000 claims abstract description 20
- 238000004364 calculation method Methods 0.000 claims abstract description 19
- 230000006835 compression Effects 0.000 claims description 11
- 238000007906 compression Methods 0.000 claims description 11
- 239000011182 bendable concrete Substances 0.000 abstract description 33
- 239000000463 material Substances 0.000 abstract description 19
- 238000013461 design Methods 0.000 abstract description 8
- 238000004458 analytical method Methods 0.000 abstract description 7
- 238000012669 compression test Methods 0.000 abstract description 4
- 230000000007 visual effect Effects 0.000 abstract description 4
- 239000004372 Polyvinyl alcohol Substances 0.000 description 40
- 229920002451 polyvinyl alcohol Polymers 0.000 description 40
- 238000010586 diagram Methods 0.000 description 12
- 239000004698 Polyethylene Substances 0.000 description 2
- 238000009795 derivation Methods 0.000 description 2
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- 229910000831 Steel Inorganic materials 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- -1 polyethylene Polymers 0.000 description 1
- 229920000573 polyethylene Polymers 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 239000010959 steel Substances 0.000 description 1
- 238000005482 strain hardening Methods 0.000 description 1
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Abstract
The invention discloses a cement-based composite material elastoplasticity constitutive model considering PVA fiber content and an establishment method thereof, which are based on uniaxial tension and compression test data and test phenomena of a strain hardening cement-based composite material, consider the influence of the fiber content on key points of a stress-strain relation, refer to a classical strain hardening cement-based composite material stress-strain constitutive model, and establish the cement-based composite material elastoplasticity constitutive model considering the PVA fiber content by adopting a method of mathematical analysis and data fitting. The building process of the cement-based composite material elastic-plastic constitutive model provided by the invention is scientific and strict, and the influence of PVA fiber content on the cement-based composite material constitutive model can be accurately described. In addition, the cement-based composite material elastic-plastic constitutive model provided by the invention is simple and visual, is conveniently used for the aspects of design of a strain hardening cement-based composite material structure, finite element calculation and the like, and has a very wide application prospect.
Description
Technical Field
The invention relates to the technical field of cement-based composite materials, in particular to a cement-based composite material elastic-plastic constitutive model and an establishing method thereof.
Background
For over half a century, researchers and designers have desired cement-based composites that can be strain hardened like steel under tensile loading while maintaining fracture width at a low level.
Professor Victor c.li of advanced civil engineering materials research laboratory (ACE-MRL) of michigan university and Christopher k.y.leung of the institute of civil engineering university of massachusetts issued in 1992 programmable cement-based Composites (abbreviated ECC). The fibre used first in ECC was polyethylene (abbreviated PE), which was later replaced by polyvinyl alcohol (abbreviated PVA). Although the former reinforced cement-based composite material has higher maximum strain and compressive strength than the latter, the cost is 8 times higher than that of the latter. From a combined performance-cost perspective, PVA-ECC is used more frequently in engineering today. Considering the Strain Hardening characteristics of ECC, it is more and more internationally referred to as Strain Hardening cement-based Composites (SHCC).
So far, the research on SHCC materials is mainly aimed at how to configure the mechanical properties of strain-hardened cement-based composite materials or materials with specific proportions and apply them to solve engineering problems, and is not mature enough. Although SHCC materials have been applied to the fields of high-rise buildings, bridge repair, dam repair and the like, most of the applications are based on experience or analog design, and a unified design and calculation method is lacked. Most calculation and analysis models for SHCC materials are based on macroscopic test results or theoretical derivation from a microscopic viewpoint, but a unified constitutive model or a theoretical derivation model which does not consider the influence of fiber content in a plurality of constitutive models is too complicated to be used by designers or programmed in a computer. Therefore, the SHCC simplified elastic-plastic constitutive model considering the PVA fiber content is established, is used for SHCC structural design and calculation, and has very important academic value and engineering significance.
Disclosure of Invention
In order to solve the limitations and defects of the prior art, the invention provides a cement-based composite material elastic-plastic constitutive model considering PVA fiber content, which comprises the following steps:
dividing the cement-based composite material elastic-plastic constitutive model into a tensile part and a compression part for representation according to the difference of the tensile property and the compression property of the cement-based composite material and the cement-based composite material classical elastic-plastic constitutive model;
the calculation formula for obtaining the classical tensile elastic-plastic constitutive model is as follows:
wherein σ t Is a tensile stress, σ fc Is the initial tensile yield stress, ε fc Is the initial tensile yield stress σ fc Corresponding initial yield strain, σ tu Is the ultimate tensile stress, ε tu Is the ultimate tensile stress sigma tu The corresponding ultimate tensile strain;
the calculation formula for obtaining the classical compression elastic-plastic constitutive model is as follows:
wherein σ c Is the compressive stress, σ cp Is the ultimate compressive stress, ε cp Is the ultimate compressive stress sigma cp The corresponding ultimate compressive strain;
subjecting sigma in the classical elastic-plastic constitutive model of the cement-based composite material to fc 、σ tu 、ε tu Set as the fiber volume content V f The calculation formula of the cement-based composite material elastic-plastic constitutive model considering the PVA fiber content is obtained as follows:
wherein,
respectively taking into account the fiber volume content V f The initial tensile yield stress, the ultimate tensile stress and their corresponding ultimate tensile strains.
The invention also provides a method for establishing the cement-based composite material elastic-plastic constitutive model considering the PVA fiber content, wherein the cement-based composite material elastic-plastic constitutive model is the cement-based composite material elastic-plastic constitutive model, and the establishing method comprises the following steps:
analyzing and summarizing test phenomena and test data to obtain an influence rule of PVA fiber content on key points in the cement-based composite material elastic-plastic constitutive model, wherein an empirical formula of the influence rule is as follows:
wherein, a 1 、b 1 、m 1 、a 2 、b 2 、m 2 、a 3 、b 3 、m 3 Is a parameter of said empirical formula, V f Is the PVA fiber content, σ fc 、σ tu 、ε tu Key points of the cement-based composite material elastic-plastic constitutive model are set;
obtaining parameters of the empirical formula through data fitting, and when V is more than or equal to 0 f < 1.00%, a 1 ＝2.6、b 1 ＝0.55、a 2 ＝3.25、b 2 ＝1.25、a 3 ＝0.51、b 3 ＝-0.49、m 3 = 0.43; when V is more than or equal to 1.00 percent f When m is less than or equal to 2.00 percent, m 1 ＝3.15、m 2 ＝4.5、a 3 ＝-0.4、b 3 ＝0.0028、m 3 ＝3.58；
Substituting the formula (4), the formula (5) and the formula (6) into the formula (3) to obtain the cement-based composite material tensile constitutive model considering the PVA fiber content.
Optionally, only the influence of the PVA fiber content on the tensile constitutive model is considered, and the influence of the PVA fiber content on the compression constitutive model is not considered.
Optionally, the PVA fiber content V f Is taken as the percentage, the PVA fiber content V f The value range is as follows: v is more than or equal to 0 f ≤2.00％。
Optionally, the method used for fitting the data is a least squares method.
The invention has the following beneficial effects:
the invention provides a cement-based composite material elastic-plastic constitutive model considering PVA fiber content and a building method thereof, which are based on uniaxial tension and compression test data and test phenomena of a strain hardening cement-based composite material, consider the influence of the fiber content on key points of a stress-strain relation, refer to a classical strain hardening cement-based composite material stress-strain constitutive model, and build the cement-based composite material elastic-plastic constitutive model considering the PVA fiber content by adopting a method of mathematical analysis and data fitting. The cement-based composite material elastic-plastic constitutive model is scientific and rigorous in establishing process, and can accurately describe the influence of PVA fiber content on the constitutive of the cement-based composite material. The cement-based composite material elastic-plastic constitutive model is simple and visual, is conveniently used for the aspects of design, finite element calculation and the like of a strain hardening cement-based composite material structure, and has very wide application prospect. In addition, the method for establishing the cement-based composite material elastic-plastic constitutive model has very strong universality and expansibility.
Drawings
Fig. 1 is a flowchart of an elastoplasticity constitutive model of a cement-based composite material considering PVA fiber content according to an embodiment of the present invention.
Fig. 2a-2b are schematic diagrams of stress-strain relationship curves of a classic cement-based composite material according to an embodiment of the present invention.
Fig. 3a-3b are graphs illustrating experimental data and empirical formulas provided in a second embodiment of the present invention.
Fig. 4 is a schematic diagram of a mechanical model of a cement-based composite material pipeline built by using an elastic-plastic constitutive model according to a second embodiment of the present invention.
Fig. 5 is a cloud diagram of the maximum principal stress distribution of the simulated three-side bearing loading according to the second embodiment of the present invention.
Fig. 6a is a schematic diagram of a test result of calculating a tube top deflection degree by using an elastic-plastic constitutive model of a cement-based composite material considering PVA fiber content, provided by the second embodiment of the present invention.
Fig. 6b is a schematic diagram of a test result of calculating a pipe waist deflection degree by using an elastic-plastic constitutive model of a cement-based composite material considering the content of PVA fibers, provided by the second embodiment of the present invention.
Fig. 6c is a schematic diagram of a test result of calculating a tube bottom deflection by using the cement-based composite material elastic-plastic constitutive model considering the content of PVA fibers according to the second embodiment of the present invention.
FIG. 7 is a schematic view of the loading and unloading curves calculated for the pipes made of the cement-based composite material with different PVA fiber contents according to the second embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the cement-based composite material elastic-plastic constitutive model and the establishment method thereof provided by the present invention are described in detail below with reference to the accompanying drawings.
Example one
The embodiment establishes a simple and visual constitutive model which is convenient for the design, calculation and analysis of the SHCC structure, and fundamentally changes the current situation of designing the SHCC structure by experience and analogy methods.
Fig. 1 is a flowchart of an elastoplasticity constitutive model of a cement-based composite material considering PVA fiber content according to an embodiment of the present invention. Fig. 2a-2b are schematic diagrams of stress-strain relationship curves of a classical cement-based composite material according to an embodiment of the present invention. The present embodiment provides a cement-based composite material elastic-plastic constitutive model considering PVA fiber content, and introduces the influence of fiber content on the basis of a classical SHCC tensile constitutive model (expressed by formula (1)) and a classical SHCC compression constitutive model (expressed by formula (2)).
The calculation formula of the classic SHCC tensile constitutive model is as follows:
wherein σ t Is the tensile stress, σ fc Is the initial tensile yield stress, ε fc Is the initial tensile yield stress σ fc Corresponding initial yield strain, σ tu Is the ultimate tensile stress, ε tu Is the ultimate tensile stress sigma tu Corresponding ultimate tensile strain.
The calculation formula of the classic SHCC compression constitutive model is as follows:
wherein σ c Is the compressive stress, σ cp Is the ultimate compressive stress, ε cp Is the ultimate compressive stress sigma cp Corresponding limitCompressive strain.
Considering that the PVA fiber content has a large influence on the SHCC tensile constitutive model and a negligible influence on the SHCC compression constitutive model, the present embodiment introduces the influence of the fiber content on the key points only in the classical tensile constitutive model, and the calculation formula is as follows:
wherein,
respectively in consideration of the fiber volume content V f The tensile stress, initial tensile yield stress, ultimate tensile stress and their corresponding ultimate tensile strain.
The embodiment provides a cement-based composite material elastic-plastic constitutive model considering PVA fiber content, which is established by taking uniaxial tension and compression test data and test phenomena of a strain hardening cement-based composite material as the basis, considering the influence of the fiber content on a stress-strain relation key point, referring to a classical strain hardening cement-based composite material stress-strain constitutive model and adopting a method of mathematical analysis and data fitting. The cement-based composite material elastic-plastic constitutive model is scientific and rigorous in establishing process, and can accurately describe the influence of PVA fiber content on the constitutive of the cement-based composite material. The cement-based composite material elastic-plastic constitutive model is simple and visual, is conveniently used for the aspects of design, finite element calculation and the like of a strain hardening cement-based composite material structure, and has very wide application prospect. In addition, the universality and expansibility of the method for establishing the cement-based composite material elastic-plastic constitutive model are very strong.
Example two
The embodiment provides a method for establishing a cement-based composite material elastic-plastic constitutive model considering PVA fiber content, wherein the cement-based composite material elastic-plastic constitutive model is the cement-based composite material elastic-plastic constitutive model provided in the first embodiment, and the establishing method comprises the following steps:
step 1): and the influence rule of the PVA fiber content on key points in the constitutive model is proved by analyzing the test phenomenon and summarizing test data.
Step 2): through mathematical analysis, the PVA fiber content V is provided f For the key point (sigma) in the constitutive model fc 、σ tu 、ε tu ) An empirical formula for influencing the rule is described by a piecewise function respectively, and the fiber content V f The value range of (A) is as follows: v is more than or equal to 0 f Less than or equal to 2.00 percent. The empirical formula is as follows:
wherein, a 1 、b 1 、m 1 、a 2 、b 2 、m 2 、a 3 、b 3 、m 3 Is a parameter of said empirical formula, V f Is the PVA fiber content, σ fc 、σ tu 、ε tu Is a key point of the cement-based composite material elastic-plastic constitutive model.
And step 3): the parameters in the empirical formula were obtained by data fitting (least squares method), as shown in table 1:
TABLE 1 parameters of empirical formula
Fig. 3a-3b are graphs illustrating experimental data and empirical formulas provided in a second embodiment of the present invention.
Step 4): will be provided withSubstituting the obtained formulas (4) - (6) into the formula (3) to obtain the PVA fiber content V f The SHCC material tensile constitutive model and the formula (2) jointly form the SHCC material constitutive model considering PVA fiber content.
Fig. 4 is a schematic diagram of a mechanical model of a cement-based composite material pipeline built by using an elastic-plastic constitutive model according to a second embodiment of the present invention. Fig. 5 is a cloud diagram of the maximum principal stress distribution of the simulated three-side bearing loading according to the second embodiment of the present invention. Fig. 6a is a schematic diagram of a test result of calculating a tube top deflection degree by using an elastic-plastic constitutive model of a cement-based composite material considering PVA fiber content, provided by the second embodiment of the present invention. Fig. 6b is a schematic diagram of a test result of calculating a pipe waist deflection degree by using an elastic-plastic constitutive model of a cement-based composite material considering the content of PVA fibers, provided by the second embodiment of the present invention. Fig. 6c is a schematic diagram of a test result of calculating a tube bottom deflection by using the cement-based composite material elastic-plastic constitutive model considering the content of PVA fibers according to the second embodiment of the present invention. FIG. 7 is a schematic view of the loading and unloading curves calculated for the pipes made of the cement-based composite material with different PVA fiber contents according to the second embodiment of the present invention. The constitutive model provided by the embodiment is used for pipeline numerical simulation verification: the constitutive model provided in this embodiment is programmed in finite element software, and a mechanical calculation model of the SHCC pipeline is established, where the size of the SHCC pipeline is: inner diameter 680mm by wall thickness 100mm by tube length 2800mm. The three-side bearing loading test of the simulated pipeline is shown in fig. 4, the maximum main stress distribution cloud chart is shown in fig. 5, and the region with larger stress distribution is consistent with the failure position monitored in the test. Fig. 6a to 6c show the strain at the tube top, the tube waist and the tube bottom calculated by the constitutive model provided in this embodiment, and it can be seen that the calculation result of the constitutive model provided in this embodiment is very close to the test monitoring result. Fig. 7 is a loading and unloading curve of the SHCC pipeline calculated by using constitutive models of different PVA fiber contents, and it can be seen that the change trends of the SHCC pipeline under different fiber contents are obviously different, and as the fiber content increases, the impact resistance of the pipeline (the area enclosed by the curve and the X axis represents the absorbed energy) is obviously increased.
The embodiment provides a method for establishing a cement-based composite material elastic-plastic constitutive model considering PVA fiber content, which is based on uniaxial tension and compression test data and test phenomena of a strain hardening cement-based composite material, considers the influence of the fiber content on key points of a stress-strain relation, refers to a classical strain hardening cement-based composite material stress-strain constitutive model, and establishes the cement-based composite material elastic-plastic constitutive model considering the PVA fiber content by adopting a method of mathematical analysis and data fitting. The building process of the cement-based composite material elastic-plastic constitutive model is scientific and strict, and the influence of PVA fiber content on the cement-based composite material constitutive model can be accurately described. The cement-based composite material elastic-plastic constitutive model is concise and intuitive, is conveniently used for the aspects of design, finite element calculation and the like of a strain hardening cement-based composite material structure, and has very wide application prospect. In addition, the method for establishing the cement-based composite material elastic-plastic constitutive model has very strong universality and expansibility.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be noted that the above-mentioned preferred embodiments are described in detail, and therefore should not be considered as limiting the scope of the invention, and those skilled in the art will be able to make substitutions and modifications within the scope of the invention without departing from the scope of the invention as defined by the appended claims.
Claims (4)
1. A method for establishing an elastoplasticity constitutive model of a cement-based composite material considering PVA fiber content is characterized by comprising the following steps:
according to the difference of the tensile property and the compression property of the cement-based composite material and a classical elastoplasticity constitutive model of the cement-based composite material, dividing the elastoplasticity constitutive model of the cement-based composite material into a tensile part and a compression part for representation;
the calculation formula for obtaining the classical tensile elastic-plastic constitutive model is as follows:
wherein σ t Is the tensile stress, σ fc Is the initial tensile yield stress, ε fc Is the initial tensile yield stress σ fc Corresponding initial yield strain, σ tu Is the ultimate tensile stress, ε tu Is the ultimate tensile stress sigma tu The corresponding ultimate tensile strain;
the calculation formula for obtaining the classical compression elastic-plastic constitutive model is as follows:
wherein σ c Is the compressive stress, σ cp Is the ultimate compressive stress, ε cp Is the ultimate compressive stress sigma cp The corresponding ultimate compressive strain;
subjecting sigma in the classical elastic-plastic constitutive model of the cement-based composite material to fc 、σ tu 、ε tu Set as the fiber volume content V f The calculation formula of the cement-based composite material elastic-plastic constitutive model considering the PVA fiber content is obtained as follows:
wherein,
respectively taking into account the fiber volume content V f The tensile stress, initial tensile yield stress, ultimate tensile stress and their corresponding ultimate tensile strain;
the establishing method comprises the following steps:
analyzing and summarizing test phenomena and test data to obtain an influence rule of PVA fiber content on key points in the cement-based composite material elastic-plastic constitutive model, wherein an empirical formula of the influence rule is as follows:
wherein, a 1 、b 1 、m 1 、a 2 、b 2 、m 2 、a 3 、b 3 、m 3 Is a parameter of said empirical formula, V f Is the PVA fiber content, σ fc 、σ tu 、ε tu Key points of the cement-based composite material elastic-plastic constitutive model are set;
obtaining parameters of the empirical formula through data fitting, and when V is more than or equal to 0 f When the content is less than or equal to 1.00 percent, a 1 ＝2.6、b 1 ＝0.55、a 2 ＝3.25、b 2 ＝1.25、a 3 ＝0.51、b 3 ＝-0.49、m 3 = -0.43; when 1.00% < V f When m is less than or equal to 2.00 percent, m 1 ＝3.15、m 2 ＝4.5、a 3 ＝-0.4、b 3 ＝0.0028、m 3 ＝3.58；
Substituting the formula (4), the formula (5) and the formula (6) into the formula (3) to obtain the cement-based composite material tensile constitutive model considering the PVA fiber content.
2. The method for establishing the elastic-plastic constitutive model of the cement-based composite material with the PVA fiber content taken into consideration as claimed in claim 1, wherein only the influence of the PVA fiber content on the tensile constitutive model is considered, and the influence of the PVA fiber content on the compression constitutive model is not considered.
3. According to claimThe method for establishing the elastoplasticity constitutive model of the cement-based composite material considering the PVA fiber content in claim 1, wherein the PVA fiber content V is f Is counted as percentage, the PVA fiber content V f The value range is as follows: v is more than or equal to 0 f ≤2.00％。
4. The method for building the elastoplasticity constitutive model of the cement-based composite material with the PVA fiber content taken into consideration in the claim 1 is characterized in that the method used for data fitting is a least square method.
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