Phase field cohesion simulation method in fiber concrete crack three-dimensional expansion process

Abstract

The invention discloses a phase field cohesion simulation method in a fiber concrete crack three-dimensional expansion process, which comprises the following steps of: 1, respectively constructing geometric models of cement mortar, polyhedral aggregate, an aggregate-mortar interface transition area and steel fibers, and constructing a three-dimensional geometric model of fiber concrete through combined assembly; 2, based on the three-dimensional geometric model, performing finite element grid division, constructing a crack geometric function # imgabs0 # and an energy attenuation function # imgabs1 # of a cement mortar unit through a cohesion model method, and further constructing a three-dimensional physical model of the fiber concrete; 3, based on the three-dimensional physical model, calculating the interface displacement of a cement mortar unit in the three-dimensional physical model by adopting a finite element method for quantitatively representing the cracking geometric dimension and the crack extension direction of the fiber concrete; and 4, deducing the displacement and stress of the polyhedral aggregate unit, the interface transition area unit and the steel fiber unit according to the displacement deformation of the cement mortar unit by adopting a phase field method, and predicting the three-dimensional expansion process of the fiber concrete crack.

Description

Technical Field

[0001] The invention relates to the technical field of concrete numerical simulation, and in particular to a phase field cohesion simulation method for a three-dimensional crack expansion process of fiber concrete. Background Art

[0002] Fiber concrete has been widely used in the construction of infrastructure such as water conservancy and transportation. Its cracking and crack expansion problems directly affect the bearing capacity and durability of fiber concrete structures. In order to better analyze and predict the crack expansion extension path and predict the decline of the bearing and durability performance of fiber concrete structures in advance, many scholars have carried out simulation work on concrete crack expansion to achieve performance analysis and prediction of fiber concrete structures.

[0003] At present, the simulation work for concrete crack extension, whether based on the finite element method of fracture mechanics or damage mechanics, requires the pre-setting of the extension path, artificially limits the cracking range, and cannot reflect the actual stress state of the fiber reinforced concrete structure. At the same time, the above method requires a finer finite element mesh division, resulting in low calculation efficiency. Summary of the invention

[0004] The purpose of the present invention is to provide a phase-field cohesion simulation method for the three-dimensional expansion process of fiber concrete cracks, which does not require a preset crack expansion path for the fiber concrete, achieves the simulation of polyhedral aggregates, balances the simulation accuracy and computational efficiency, solves the problem of simulating the three-dimensional expansion of fiber concrete cracks, and realizes efficient simulation and accurate prediction of the three-dimensional expansion process of fiber concrete cracks.

[0005] To achieve the above object, the present invention adopts the following technical solutions: The phase field cohesion simulation method of the fiber concrete crack three-dimensional expansion process of the present invention comprises the following steps: Step 1, constructing the geometric models of cement mortar, polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber respectively, setting the mechanical property parameters of each component, and constructing the three-dimensional geometric model of fiber concrete by combining and assembling these components; Step 2: Based on the three-dimensional geometric model of the fiber concrete, a quadratic tetrahedron three-dimensional solid unit is used to perform finite element meshing to obtain cement mortar units, polyhedral aggregate units, aggregate-mortar interface transition zone units, and steel fiber units. The cohesive force model method is used to derive the constitutive equations of the interface displacement and internal force of the cement mortar unit, and the crack geometry function of the cement mortar unit is constructed. , energy decay function , used to characterize the cracking risk of cement mortar units and then construct a three-dimensional physical model of fiber concrete; Step 3, based on the three-dimensional physical model of the fiber concrete, by applying external loads and corresponding boundary conditions, using the finite element method, calculate the interface displacement of the cement mortar unit in the three-dimensional physical model of the fiber concrete to quantitatively characterize the cracking geometry and crack extension direction of the fiber concrete; Step 4, based on the displacement coordination relationship among the cement mortar unit, polyhedral aggregate unit, aggregate-mortar interface transition zone unit, and steel fiber unit, the phase field method is used to deduce the displacement and stress of the polyhedral aggregate unit, interface transition zone unit, and steel fiber unit from the displacement deformation of the cement mortar unit to predict the three-dimensional expansion process of the fiber concrete crack.

[0006] Furthermore, the geometric modeling process of the cement mortar, polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber comprises the following steps: Step 1.1, the geometric model building process of the cement mortar: according to the geometric models of the polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber constructed above, geometric body Boolean operations are used to calculate the spatial distribution of the cement mortar in the three-dimensional geometric model of the fiber concrete, and to construct a geometric model of the cement mortar of the remaining part of the fiber concrete; Step 1.2, the geometric modeling process of the polyhedral aggregate: setting the three-dimensional geometric dimension length of the fiber concrete ,width ,high , Maximum particle size of aggregate , minimum particle size , construct the random vertex generation function of polyhedral aggregate , adjacent random vertices are connected into line segments, and adjacent multiple line segments form planes to form polyhedral aggregates, and then the polyhedral aggregate collision discrimination function is constructed , calculate the distance between polyhedral aggregates to ensure that the polyhedral aggregates do not collide with each other; Step 1.3, the geometric modeling process of the aggregate-mortar interface transition zone: setting the thickness of the interface transition zone , based on the constructed polyhedral aggregate geometric model, the thickness of the transition zone is increased on the surface of the polyhedral aggregate to form a geometric model of the aggregate-mortar interface transition zone; Step 1.4, the geometric modeling process of the steel fiber: setting the steel fiber length , Steel fiber radius , construct the collision discrimination function between steel fibers , collision discrimination function between steel fiber and polyhedral aggregate , calculate the random spatial positions of the steel fibers.

[0007] Furthermore, the three-dimensional physical modeling process of the fiber concrete includes: Based on the three-dimensional geometric model of fiber concrete, a ten-node quadratic tetrahedron three-dimensional solid unit is used for finite element meshing. The constitutive equation of interface displacement and cracking of cement mortar unit is derived through the cohesive force model method, and the crack geometry function of cement mortar unit is constructed. , energy decay function , forming a three-dimensional physical model of fiber concrete as shown below: in, is the crack parameter, , used to characterize the finite distribution of cracks, is an exponential parameter used to characterize the ultimate crack opening displacement, Indicates the cracking state of concrete, 0 means no cracking, 1 means cracking, represents the characteristic length of brittle fracture of concrete, represents the crack size parameter, The destructive strength of concrete. represents the fracture energy of concrete, represents the elastic modulus of concrete, and Represents the constitutive relationship parameters of concrete.

[0008] Furthermore, the external load, the corresponding boundary conditions and the finite element calculation method include: Based on the 3D physical model of the fiber reinforced concrete, external loads were applied. With the corresponding boundary constraints, the finite element method is used to calculate the local displacement and stress of the cement mortar unit, the polyhedral aggregate unit, the interface transition zone unit, and the steel fiber unit; First, the shape function of the quadratic tetrahedron three-dimensional solid element is derived as follows: in, They represent the shape functions of the ten nodes of the tetrahedral element, , , They represent the three-dimensional axes of the local coordinate system of the tetrahedral element respectively; Based on the shape function derived above, the displacement-strain coordination matrices of cement mortar unit, polyhedral aggregate unit, interface transition zone unit and steel fiber unit are derived respectively: , used to calculate the strain of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external load , whose vector form is , the calculation formula is as follows: in, , , They represent the three-dimensional axes of the unit's global coordinate system, , , Respectively represent the unit as a whole , , The positive strain in the direction, , , Respectively represent the unit as a whole , , The shear strain in the direction , , Respectively represent the local unit at its ten nodes , , Direction displacement, represents the displacement-strain compatibility matrix; Based on the above calculation, the strains of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external loads , derive the strain-stress relationship matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit, which is used to calculate the stress of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit , whose vector form is , the calculation formula is as follows: in, , , Respectively represent the units in , , The normal stress in the direction, , , Respectively represent the units in , , Shear stress in the direction , They represent the elastic modulus and Poisson’s ratio of fiber concrete respectively. represents the strain-stress relationship matrix; Based on the above-established unit shape function, unit displacement-strain coordination matrix, and unit strain-stress relationship matrix, according to the applied external loads and boundary constraints, the stress of each unit under the external load is calculated through the external force-displacement-strain-stress calculation path.

[0009] Furthermore, the phase field method solves the three-dimensional crack expansion process of fiber concrete, including: Based on the above calculation, the stress of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external load , respectively into the crack geometry function , energy decay function , the equilibrium equations of cracks and displacements of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit are derived as follows: in, is the external load applied to the concrete mass. represents the fracture energy of concrete, represents the elastic modulus of concrete, represents the crack size, represents the model parameters, are the stresses of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit obtained by the above calculations; The crack propagation direction and size of the fiber concrete are output through the displacement and stress of the fiber concrete finite element unit calculated above.

[0010] Compared with the prior art, the present invention has the following significant improvements: 1) The three-dimensional crack propagation calculation of the fiber concrete of the present invention does not require artificial pre-selection of the crack propagation path and range of the fiber concrete; 2) The finite element of the present invention adopts a ten-node quadratic tetrahedron element, which greatly improves the calculation accuracy of the existing four-node first-order tetrahedron element; 3) The present invention adopts the cohesive force model and phase field method to simulate the expansion and extension process of three-dimensional cracks in fiber concrete under external loads; 4) The fiber concrete three-dimensional crack extension calculation method of the present invention has low grid sensitivity, high calculation efficiency and high calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention.

[0012] Figure 2 It is a schematic diagram of the geometric model of the cement mortar described in the embodiment of the present invention.

[0013] Figure 3 It is a schematic diagram of the geometric model of the polyhedral aggregate described in the embodiment of the present invention.

[0014] Figure 4 It is a schematic diagram of the geometric model of the aggregate-mortar interface transition zone described in an embodiment of the present invention.

[0015] Figure 5 Schematic diagram of the geometric model of the steel fiber described in the embodiment of the present invention.

[0016] Figure 6 It is a schematic diagram of a three-dimensional geometric model of the fiber concrete described in an embodiment of the present invention.

[0017] Figure 7 It is a schematic diagram of a three-dimensional physical model of the fiber concrete described in an embodiment of the present invention.

[0018] Figure 8 It is a schematic diagram of a three-dimensional finite element of a ten-node quadratic tetrahedron according to an embodiment of the present invention.

[0019] Figure 9a-9f It is a schematic diagram of the change of crack initiation and expansion over time of the three-dimensional physical model of the fiber concrete under the action of external loads according to the embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention is further described in detail below in conjunction with specific embodiments: like Figure 1 As shown, the phase field cohesion simulation method of the three-dimensional expansion process of fiber concrete cracks of the present invention comprises the following steps: Step 1: Set the geometric size of fiber concrete to 150 mm × 150 mm × 150 mm. Within this boundary, construct the geometric models of cement mortar, polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber, respectively. Figure 2-Figure 5 shown; specifically: Step 1.1, the process of modeling the geometric model of cement mortar: according to the geometric models of polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber constructed above, geometric body Boolean operation is used to calculate the spatial distribution of cement mortar in the three-dimensional geometric model of the fiber concrete, and the geometric model of cement mortar in the remaining part of the fiber concrete is constructed; Step 1.2, the geometric modeling process of the polyhedral aggregate: setting the three-dimensional geometric dimension length of the fiber concrete ,width ,high , Maximum particle size of aggregate , minimum particle size , construct the random vertex generation function of polyhedral aggregate , adjacent random vertices are connected into line segments, and adjacent multiple line segments form planes to form polyhedral aggregates, and then the polyhedral aggregate collision discrimination function is constructed , calculate the distance between polyhedral aggregates to ensure that the polyhedral aggregates do not collide with each other; Step 1.3, the geometric modeling process of the aggregate-mortar interface transition zone: setting the thickness of the interface transition zone , based on the constructed polyhedral aggregate geometric model, the thickness of the transition zone is increased on the surface of the polyhedral aggregate to form a geometric model of the aggregate-mortar interface transition zone; Step 1.4, the geometric modeling process of the steel fiber: setting the steel fiber length , Steel fiber radius , construct the collision discrimination function between steel fibers , collision discrimination function between steel fiber and polyhedral aggregate , calculate the random spatial positions of the steel fibers.

[0021] By combining and assembling these geometric models, a three-dimensional geometric model of fiber concrete is constructed, such as Figure 6 shown.

[0022] Step 2: Based on the three-dimensional geometric model of fiber reinforced concrete, a ten-node quadratic tetrahedron three-dimensional solid element (such as Figure 8 As shown in the figure), three-dimensional finite element meshing is performed to construct the crack geometry function of cement mortar unit. , energy decay function , forming a three-dimensional physical model of fiber concrete (such as Figure 7 As shown), the calculation formula is as follows: Among them, the elastic modulus of concrete The value is 2800 MPa, the fracture energy The value is 0.5 N / mm, the breaking strength The value is 20 MPa, the characteristic length The value is 3.5 mm, and the crack parameter Value 1, crack size The value is 1.0 mm. For the linear softening relation of concrete constitutive law, and The value is 1. The value is 2. The value is -0.5. The value is 0.

[0023] Step 3: Based on the above three-dimensional physical model of fiber concrete, a uniformly distributed load is applied to the top surface of a 150 mm × 150 mm × 150 mm cube of fiber concrete. Taking the value of 20 kN and applying fixed boundary conditions to the bottom surface, the shape function of the quadratic tetrahedron three-dimensional solid element is derived as follows: in, They represent the shape functions of the ten nodes of the tetrahedral element, , , They represent the three-dimensional axes of the local coordinate system of the tetrahedral element respectively; Based on the shape function derived above, the displacement-strain coordination matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit is derived as follows: in, , , They represent the three-dimensional axial direction of the overall coordinate system of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit, respectively. , , They represent the cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit as a whole. , , The positive strain in the direction, , , They represent the cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit as a whole. , , The shear strain in the direction , , They represent cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit locally at their ten nodes. , , Directional displacement; Based on the displacement-strain coordination matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit derived above, the strain-stress relationship matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit is derived as follows: in, , , They represent cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit respectively. , , The normal stress in the direction, , , They represent cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit respectively. , , Shear stress in the direction, elastic modulus of fiber concrete The value is 2800MPa, Poisson's ratio The value is 0.38; Based on the above-established shape functions of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, steel fiber unit, displacement-strain coordination matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, steel fiber unit, strain-stress relationship matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, steel fiber unit, according to the applied external load and boundary constraints, through the calculation path of external force-displacement-strain-stress, calculate the stress of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, steel fiber unit under the action of external load; Step 4: Based on the above calculated stresses of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external load, the crack geometry function is introduced. , energy decay function , derive the equilibrium equation of unit crack and displacement, and use the phase field method to solve the three-dimensional crack expansion process of fiber concrete, mainly including: Among them, the external load The value is 20 kN, and the fracture energy of fiber reinforced concrete is The value is 0.5 N / mm, elastic modulus The value is 2800MPa, the crack size The value is 1.0 mm, and the model parameters Value ; Through the above calculation process, the three-dimensional crack expansion process of fiber concrete under external load changes with time (such as Figures 9a-9f ), which provides a calculation method for the efficient and accurate prediction of the three-dimensional crack propagation process of fiber concrete, and also provides a scientific analysis platform for the quantitative study of the crack resistance of fiber concrete structures.

Claims

1. A phase field cohesion simulation method for the three-dimensional expansion process of fiber concrete cracks, characterized in that: The steps include: Step 1, constructing the geometric models of cement mortar, polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber respectively, setting the mechanical property parameters of each component, and constructing the three-dimensional geometric model of fiber concrete by combining and assembling these components; Step 2: Based on the three-dimensional geometric model of the fiber concrete, a quadratic tetrahedron three-dimensional solid unit is used to perform finite element meshing to obtain cement mortar units, polyhedral aggregate units, aggregate-mortar interface transition zone units, and steel fiber units. The cohesive force model method is used to derive the constitutive equations of the interface displacement and internal force of the cement mortar unit, and the crack geometry function of the cement mortar unit is constructed. , energy decay function , used to characterize the cracking risk of cement mortar units and then construct a three-dimensional physical model of fiber concrete; Step 3, based on the three-dimensional physical model of the fiber concrete, by applying external loads and corresponding boundary conditions, using the finite element method to calculate the interface displacement of the cement mortar unit in the three-dimensional physical model of the fiber concrete; Step 4, based on the displacement coordination relationship among the cement mortar unit, polyhedral aggregate unit, aggregate-mortar interface transition zone unit, and steel fiber unit, the phase field method is used to deduce the displacement and stress of the polyhedral aggregate unit, interface transition zone unit, and steel fiber unit from the displacement deformation of the cement mortar unit to predict the three-dimensional expansion process of the fiber concrete crack.

2. The phase field cohesion simulation method for the three-dimensional crack expansion process of fiber concrete according to claim 1 is characterized in that: The geometric modeling process of the cement mortar, polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber comprises the following steps: Step 1.1, the geometric model building process of the cement mortar: according to the geometric models of the polyhedral aggregate, aggregate-mortar interface transition zone, and steel fiber constructed above, geometric body Boolean operations are used to calculate the spatial distribution of the cement mortar in the three-dimensional geometric model of the fiber concrete, and to construct a geometric model of the cement mortar of the remaining part of the fiber concrete; Step 1.2, the geometric modeling process of the polyhedral aggregate: setting the three-dimensional geometric dimension length of the fiber concrete ,width ,high , Maximum particle size of aggregate , minimum particle size , construct the random vertex generation function of polyhedral aggregate , adjacent random vertices are connected into line segments, and adjacent multiple line segments form planes to form polyhedral aggregates, and then the polyhedral aggregate collision discrimination function is constructed , calculate the distance between polyhedral aggregates to ensure that the polyhedral aggregates do not collide with each other; Step 1.3, the geometric modeling process of the aggregate-mortar interface transition zone: setting the thickness of the interface transition zone , based on the constructed polyhedral aggregate geometric model, the thickness of the transition zone is increased on the surface of the polyhedral aggregate to form a geometric model of the aggregate-mortar interface transition zone; Step 1.4, the geometric modeling process of the steel fiber: setting the steel fiber length , Steel fiber radius , construct the collision discrimination function between steel fibers , collision discrimination function between steel fiber and polyhedral aggregate , calculate the random spatial positions of the steel fibers.

3. The phase field cohesion simulation method for the three-dimensional crack expansion process of fiber concrete according to claim 1 is characterized in that: The three-dimensional physical model building process of the fiber concrete includes: Based on the three-dimensional geometric model of fiber concrete, the cohesive force model method is used to derive the constitutive equation of interface displacement and cracking of cement mortar unit, and construct the crack geometry function of cement mortar unit. , energy decay function , forming a three-dimensional physical model of fiber concrete as shown below: in, is the crack parameter, , used to characterize the finite distribution of cracks, is an exponential parameter used to characterize the ultimate crack opening displacement, Indicates the cracking state of concrete, 0 means no cracking, 1 means cracking, represents the characteristic length of brittle fracture of concrete, represents the crack size parameter, The destructive strength of concrete. represents the fracture energy of concrete, represents the elastic modulus of concrete, and Represents the constitutive relationship parameters of concrete.

4. The phase field cohesion simulation method for the three-dimensional crack expansion process of fiber concrete according to claim 1 is characterized in that: The external loads, corresponding boundary conditions and finite element calculation method include: Based on the 3D physical model of the fiber reinforced concrete, external loads were applied. With the corresponding boundary constraints, the finite element method is used to calculate the local displacement and stress of the cement mortar unit, the polyhedral aggregate unit, the interface transition zone unit, and the steel fiber unit; First, the shape function of the quadratic tetrahedron three-dimensional solid element is derived as follows: in, They represent the shape functions of the ten nodes of the tetrahedral element, , , They represent the three-dimensional axes of the local coordinate system of the tetrahedral element respectively; Based on the shape function derived above, the displacement-strain coordination matrices of cement mortar unit, polyhedral aggregate unit, interface transition zone unit and steel fiber unit are derived respectively: , used to calculate the strain of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external load , whose vector form is , the calculation formula is as follows: in, , , They represent the three-dimensional axes of the unit's global coordinate system, , , Respectively represent the unit as a whole , , The positive strain in the direction, , , Respectively represent the unit as a whole , , Shear strain in the direction, , , Respectively represent the local unit at its ten nodes , , Direction displacement, represents the displacement-strain compatibility matrix; Based on the above calculation, the strains of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external loads , derive the strain-stress relationship matrix of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit, which is used to calculate the stress of each unit , whose vector form is , the calculation formula is as follows: in, , , Respectively represent the units in , , The normal stress in the direction, , , Respectively represent the units in , , Shear stress in the direction , They represent the elastic modulus and Poisson’s ratio of fiber concrete respectively. represents the strain-stress relationship matrix; Based on the above-established unit shape function, unit displacement-strain coordination matrix, and unit strain-stress relationship matrix, according to the applied external loads and boundary constraints, the stress of each unit under the external load is calculated through the external force-displacement-strain-stress calculation path.

5. The phase field cohesion simulation method for the three-dimensional crack expansion process of fiber concrete according to claim 1 is characterized in that: The phase field method for solving the three-dimensional crack expansion process of fiber concrete includes: Based on the above calculation, the stress of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit under external load , respectively into the crack geometry function , energy decay function , the equilibrium equations of cracks and displacements of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit are derived as follows: in, is the external load applied to the concrete mass. represents the fracture energy of concrete, represents the elastic modulus of concrete, represents the crack size, represents the model parameters, are the stresses of cement mortar unit, polyhedral aggregate unit, interface transition zone unit, and steel fiber unit obtained by the above calculations; The crack propagation direction and size of the fiber concrete are output through the displacement and stress of the fiber concrete finite element unit calculated above.

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