JP6170400B2 - How to create a finite element model of filler compounded rubber - Google Patents

Description

  The present invention relates to a method for creating a finite element model of filler-containing rubber that can reduce creation time and labor.

  In recent years, various computer simulations using the finite element method have been performed. In these simulations, the object to be analyzed is discretized into a finite number of elements that can be handled by a computer, and a finite element model is created. The finite element model is input with characteristics indicating its rigidity and viscosity. In computer simulation, the displacement of the node of each element is calculated based on a predetermined deformation condition or the like.

  In recent years, simulations are used not only for mechanical structures but also for developing rubber materials and the like. For example, in order to improve the efficiency of the development of fillers for reinforcing rubber, a method for creating a finite element model of filler-containing rubber in which fillers are dispersed in matrix rubber using a computer Are proposed in Patent Documents 1 and 2 below.

  In Patent Documents 1 and 2, for example, the respective portions occupied by the matrix rubber and the filler are specified based on, for example, a microscopic cross-sectional photograph of the filler-containing rubber. For example, each part is modeled into a matrix rubber model and a filler model using triangular or quadrilateral elements in the case of two dimensions.

JP 2012-185733 A JP 2012-198654 A

  By the way, when the contour shape of the filler is complicated, in order to accurately model it, it is necessary to discretize with a small element. On the other hand, in order to reduce the calculation cost, it is desirable that the matrix rubber model is discretized with large elements in order to reduce the number of elements.

  However, in the conventional method, the nodes of each element are shared at the boundary between the matrix rubber model and the filler model. Therefore, there is a problem that the resolution of one model is restricted by the resolution of the other model.

  For example, when the matrix rubber model is discretized in accordance with the resolution of the filler in order to increase the calculation accuracy, the calculation cost tends to increase. Conversely, when the filler model is discretized in accordance with the resolution of the matrix rubber model discretized by a large element in order to reduce the calculation cost, the calculation accuracy tends to decrease.

  The present invention has been devised in view of the above circumstances, and has as its main object to provide a method for creating a finite element model of filler-containing rubber capable of suppressing an increase in calculation cost.

A first invention of the present invention is a method for creating a finite element model of a filler-containing rubber in which fillers are dispersedly arranged in a matrix rubber by using a computer, and the filler is limited to the computer. A first step of defining a filler model discretized using a plurality of elements, and the filler rubber model including a matrix rubber model discretized using at least a finite number of elements in the computer. A second step that is defined independently, and a model embedding step in which the computer embeds the filler model in the matrix rubber model. In the model embedding step, the matrix rubber model and the filler model Are overlapped without considering each other's sharing of nodes. In the boundary portion between Moderu and the matrix rubber model, only the nodes of the surface of the filler model, characterized in that the filler-containing rubber model giving constraints are defined.

  In the first aspect of the invention, it is desirable that the matrix rubber model has a total space including a first space occupied by the matrix rubber and a second space occupied by the filler.

A second invention of the present invention is a method for creating a finite element model of a filler-containing rubber in which fillers are dispersedly arranged in a matrix rubber by using a computer, and the filler is limited to the computer. A first step of defining a filler model discretized using a plurality of elements, and the filler rubber model including a matrix rubber model discretized using at least a finite number of elements in the computer. A second step defined independently from each other, and an interface layer model obtained by discretizing at least one interface layer surrounding the filler with a finite number of elements in the computer, the filler model and the matrix rubber model Is a third step that is defined independently, and the computer includes the matrix rubber model, A model embedding step for embedding the filler model and the interface layer model, and in the model embedding step, the matrix rubber model, the filler model, and the interface layer model consider sharing of nodes between each other. And at the first boundary between the filler model and the interface layer model, a constraint condition is given only to the nodes on the surface of the filler model , and the interface layer model and the matrix rubber model are A filler compounded rubber model is defined by giving a constraint condition only to the second boundary between the two.

  In the second invention, the matrix rubber model combines the first space occupied by the matrix rubber, the second space occupied by the filler, and the third space occupied by the interface layer. It is desirable to have a total space.

  In the second invention, in the second step, the space is discretized with elements having the same size, and the elements in the first step have different sizes from the elements in the second step. It is desirable that

  In the first invention of the present invention, in the first step and the second step, the filler model and the matrix rubber model can be discretized independently. Furthermore, in the first invention, the matrix rubber model and the filler model are overlapped without considering the sharing of the nodes, and a constraint condition is given to a boundary portion between the filler model and the matrix rubber. Including a model embedding step of defining the filler compounded rubber model.

  For this reason, in the first invention, the filler model and the matrix rubber model can be discretized with elements having sizes and shapes suitable for the respective shapes and accuracy requirements. Thus, in some embodiments, smaller elements may be employed for the filler model and larger and simpler shaped elements may be employed for the matrix rubber model. In this embodiment, it is possible to achieve both reduction of calculation cost by the matrix rubber model and maintenance of calculation accuracy by a filler model having a more detailed shape.

  In the second aspect of the present invention, in the first step, the second step, and the third step, the filler model, the matrix rubber model, and the interface layer model can be discretized independently. Furthermore, in the second invention, the matrix rubber model, the filler model, and the interface layer model are overlapped without considering the sharing of nodes between each other, and the matrix rubber model, the filler model, and the interface layer model are overlapped. A model embedding step of defining a filler-containing rubber model by giving a constraint condition of one boundary part and a constraint condition of a second boundary part between the interface layer model and the matrix rubber model.

  For this reason, in the second invention, the filler model, the matrix rubber model, and the interface layer model can be discretized with elements having sizes and shapes suitable for the respective shapes and accuracy requirements. Thus, in some embodiments, smaller elements may be employed for the filler model, smaller elements for the interface layer model, and larger and simpler shaped elements for the matrix rubber model. In this embodiment, it is possible to achieve both suppression of calculation cost by the matrix rubber model and maintenance of calculation accuracy by the filler model and interface layer model having a more detailed shape.

It is a partial expanded sectional view of a filler compounding rubber. It is a flowchart of embodiment of 1st invention. It is a top view of the visualized filler model. It is a top view of the visualized matrix rubber model. It is a top view of the filler compounded rubber model visualized by the 1st invention. It is the A section enlarged view of FIG. It is a diagram explaining the constraint conditions of a boundary part. It is a partial expanded sectional view of filler compounded rubber containing an interface layer. It is a flowchart of embodiment of 2nd invention. It is a top view of the visualized interface layer model. It is a top view of the filler compound rubber model visualized by the 2nd invention.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 shows a partial cross-sectional view of an example of a filler-containing rubber 1 targeted by the first invention. The filler-containing rubber 1 includes a matrix rubber 2 constituting a main part of the rubber, and a filler 3 which is a substantially circular particle disposed therein. The filler 3 is typically carbon black, but silica or other fillers may be used alone or in combination.

  In the present invention, a finite element model is created from the filler-containing rubber 1. This finite element model is also called a mesh model or the like, and is created and stored using a computer. The computer performs a numerical simulation using this finite element model. In the numerical simulation, various conditions are given to the finite element model, and physical quantities such as displacement and stress of the finite element model at that time are calculated by a computer.

  The finite element model is created according to a two-dimensional or three-dimensional coordinate system. In the following embodiment, what is defined in the two-dimensional coordinate system of xy is shown, but the present invention can be similarly applied to a three-dimensional model.

  FIG. 2 is a flowchart showing a processing procedure of a method for creating a finite element model according to the embodiment of the first invention. This processing procedure is a procedure for the computer to create a finite element model (filler-containing rubber model) of the filler-containing rubber 1 shown in FIG.

  As shown in FIG. 2, in the embodiment of the first invention, the first step S1 is performed. In the first step S1, a filler model in which the filler 3 is discretized using a finite number of elements is defined.

  In FIG. 3, one filler model 3M is visualized. The filler model 3M is obtained by dividing (discretizing) a space substantially equal to the two-dimensional space occupied by the filler 3 in the filler-containing rubber 1 with a plurality of elements 5. That is, the filler model 3M models not only the surface of the filler 3 but also the inside.

  In the case of the two-dimensional structure of the present embodiment, for example, a quadrilateral element or a triangular element is preferably used as the element 5. The filler 3 of this embodiment has a circular outline shape. A simple quadrilateral element 5a is used in the central portion of the filler model 3M. In the peripheral portion of the filler model 3M, a quadrilateral element 5a and a triangular element 5b are used. Thus, the filler model 3M having a smooth circular outline can be defined by using the elements 5 having different sizes and sides.

  The numbers of the elements 5 of the filler model 3M, the position coordinates of the nodes, and the like are stored in the computer. Furthermore, physical quantities such as an elastic modulus and a damping coefficient based on the physical property values of the filler 3 are input to each element 5. These physical quantities are used for deformation calculation of each element 5.

  In the embodiment of the first invention, as shown in FIG. 2, the second step S2 is performed after the first step S1. In the second step S2, a matrix rubber model 2M is defined. However, the second step S1 may be performed before the first step S1. Furthermore, the first step S1 and the second step S2 may be performed in parallel.

  In FIG. 4, the matrix rubber model 2M is visualized. The matrix rubber model 2M is defined by discretizing at least a space occupied by the matrix rubber 2 in the filler-containing rubber 1 using a finite number of elements 6. In a preferred embodiment, in the second step, the total space including the first space occupied by the matrix rubber 2 and the second space occupied by the filler 3 is discretized as a matrix model. That is, according to this embodiment, the entire range within the contour of the analysis target portion of the filler-containing rubber 1 is discretized by the element 6.

  In the case of the two-dimensional structure of the present embodiment, for example, a quadrilateral element or a triangular element is preferably used as the element 6. Since the matrix rubber model 2M of the present embodiment has a rectangular outline shape, only a simple quadrilateral element 6a is used. In the preferred embodiment, as shown in FIG. 4, all the elements 6 of the matrix rubber model 2M have the same size. In another preferred embodiment, each element 6 of the matrix rubber model 2M is the same as or larger than the element 5 of the filler model 3M. Thereby, the matrix rubber model 2M can be easily created with a small number of elements.

  If necessary, the matrix rubber model 2M can change the length of the element 6 in the x direction or y direction. For example, when it is known from experience that that the analysis target region greatly deforms in the x direction, the length of the element 6 in the x direction can be made smaller than the length in the y direction.

  The numbers of the elements 6 of the matrix rubber model 2M, the position coordinates of the nodes, and the like are stored in the computer. Furthermore, physical quantities such as an elastic modulus and a damping coefficient based on the physical property values of the matrix rubber 2 are input to each element 6. These physical quantities are used for deformation calculation of each element 6.

  In the second step, the matrix rubber model 2M is defined independently of the filler model 3M. Here, “independently defined” means that the matrix rubber model 2M and the filler model 3M are independently defined without being associated with each other. For example, the nodes of the matrix rubber model 2M do not need to be shared with the nodes of the filler model 3M, and can be defined at arbitrary positions in order to accurately represent the shape.

  Therefore, in the first invention, the matrix rubber model 2M and the filler model 3M can be discretized with elements of sizes or shapes suitable for each. In a preferred embodiment, in order to maintain calculation accuracy, the filler model 3M can be discretized with smaller elements, and the contour and shape of the filler can be accurately reproduced. In other preferred embodiments, the matrix rubber model 2M can be discretized with larger and simpler shaped elements to reduce computational costs.

  Next, in the embodiment of the first invention, as shown in FIG. 2, a model embedding step S3 is performed. In the model embedding step S3, as shown in FIG. 5 and FIG. 6 which is an enlarged view of the A part thereof, the filler model 3M is embedded in the matrix rubber model 2M. Overlapping without any. That is, in the model embedding process, two or more models are allowed to overlap each other. The position of the filler model 3M with respect to the matrix rubber model 2M is determined based on the compounded rubber or the like of the analysis object.

In the model embedding step S3, a constraint condition for prohibiting relative deformation is further given to the boundary portion 9 between the filler model 3M and the matrix rubber model 2M. Thereby, the filler compounded rubber model 1M is defined in the computer.

  The constraint condition is a condition that constrains the translational freedom of the nodes of the models 2M and 3M, and is calculated by the computer and stored in the computer. FIG. 7 is an explanatory diagram in which the filler-containing rubber model 1M is visualized and a part thereof is extracted.

  In FIG. 7, one element 5 is shown as the matrix rubber model 2M. This element 5 has nodes i, j, k and l. Furthermore, FIG. 7 shows the element 6 of the filler model 3M embedded (overlaid) on the element 5 of the matrix rubber model 2M. In this element, the node S is located inside the element 5.

  Since the filler model 3M is embedded in the matrix rubber model 2M, the computer S determines whether or not the node of the element 6 of the filler model 3M exists in the region of the element 5 of the matrix rubber model 2M. This determination is made for all the elements 5 of the matrix rubber model 2M.

  When the computer determines that the node S of the element 6 of the filler model 3M exists in the element 5 of the matrix rubber model 2M, the computer assumes the geometric position of the node S with respect to the element 5 of the matrix rubber model 2M. Based on this, the weighting coefficient of the node S is determined. The weighting coefficient is inversely proportional to the distance from the node S of the filler element 3M to each node i, j, k, and l of the element 5 of the surrounding matrix rubber model 2M. The closer to the node i, j, k, or l, the stronger the node S is constrained. In this example, the node S is strongly constrained by the node i. In this way, all the degrees of freedom (translational degrees of freedom) of the node S are constrained using the weighting factor.

  The weighting factor is calculated for all nodes of each element 6 of the filler model 3M. Thereby, the relative movement between both models can be restrained in the boundary part between the matrix rubber model 2M and the filler model 3M.

  As described above, in the first invention, since the matrix rubber model 2M and the filler model 3M are defined independently of each other, it is not necessary to consider the size of elements, sharing of nodes, and the like. Therefore, the time and labor for creating a model is reduced. In the first invention, the contour of the filler model can be accurately reproduced in the simulation while preventing the number of elements from increasing. Since the boundary portion 9 between the matrix rubber model 2M and the filler model 3M, which are defined independently, is given a constraint condition, even if the node is not shared, the force and displacement are accurate at the boundary portion. The calculation accuracy is not reduced.

Next, an embodiment of the second invention will be described.
FIG. 8 shows a partially enlarged cross-sectional view of an example of the filler-containing rubber 10 targeted by the second invention. The filler-containing rubber 10 of this embodiment is expressed in a more detailed configuration than the filler-containing rubber 1 of FIG. The filler-containing rubber 10 includes a matrix rubber 2, a filler 3, and an interface layer 4 between the filler 3 and the matrix rubber 2.

  As a result of various experiments, it is known that a thin layer (sometimes referred to as a glass layer) showing mechanical properties different from the bulk portion of the matrix rubber 2 is formed around the filler 3. . The second invention is suitable for creating a finite element model (filler compounded rubber model) including such an interface layer 4.

  FIG. 9 is a flowchart showing a processing procedure of a method for creating a finite element model according to the embodiment of the second invention. This processing procedure is a procedure for the computer to create a finite element model (filler compound rubber model) of the filler compound rubber 10 of FIG.

  As shown in FIG. 9, the second embodiment also includes the first step S1 and the second step S2. The contents of these steps are as described in the embodiment of the first invention.

  In the embodiment of the second invention, the third step S30 is further performed. In the third step S30, an interface layer model 4M is defined in which at least one interface layer 4 surrounding the filler 3 is discretized with a finite number of elements.

  In FIG. 10, the interface layer model 4M is visualized. The interface layer model 4M is obtained by dividing (discretizing) a space substantially equal to the two-dimensional space occupied by the interface layer 4 in the filler-containing rubber 10 with a plurality of elements 7.

  In the case of the two-dimensional structure of the present embodiment, for example, a quadrilateral element or a triangular element is preferably used as the element 7. The interface layer 4 of the present embodiment has an annular circular contour shape. The interface layer model 4M uses quadrilateral elements 7a and triangular elements 7b. Thus, by using the elements 7 having different sizes and the number of sides, the interface layer model 4M having a smooth circular contour can be defined.

  The numbers of the elements 7 of the interface layer model 4M, the position coordinates of the nodes, and the like are stored in the computer. Furthermore, physical quantities such as an elastic modulus and a damping coefficient based on physical property values of the interface layer 4 (for example, physical property values harder than the matrix rubber) are input to each element 7. These physical quantities are used for deformation calculation of each element 7.

  In the third step, the interface layer model 4M is defined independently of the filler model 3M and the matrix rubber model 2M.

  In the third step, “independently defined” means that the interface layer model 4M is uniquely defined without being associated with the matrix rubber model 2M and the filler model 3M. Therefore, each node of the interface layer model 4M does not need to be shared with any of the nodes of the matrix rubber model 2M and the filler model 3M, and can be defined at an arbitrary position. Therefore, the degree of freedom of model creation is improved.

  In the embodiment of the second invention, as shown in FIG. 9, the model embedding step S40 is further performed. In the model embedding step S40, as shown in FIG. 11, the filler model 3M and the interface layer model 4M are embedded in the matrix rubber model 2M. In the model embedding step S40, the matrix rubber model 2M, the filler model 3M, and the interface layer model 4M are overlapped at positions based on the filler-containing rubber 10.

  In the model embedding step S40, the constraint condition of the first boundary portion 13 between the filler model 3M and the interface layer model 4M and the second boundary portion 14 between the interface layer model 4M and the matrix rubber model 2M are further included. Each constraint condition is given. Thereby, the said filler compounded rubber model 10M is defined. The method for defining the constraint condition is the same as in the above-described embodiment.

  Also in the second invention, since the matrix rubber model 2M, the filler model 3M, and the interface layer model 4M are defined independently of each other, the trouble of sharing the nodes is reduced. In the second invention, the contours of the filler model 3M and the interface layer model 4M can be accurately reproduced in the simulation while preventing an increase in the number of elements. In addition, since each boundary portion of the matrix rubber model 2M, the filler model 3M, and the interface layer model 4M, which are independently defined, is given a constraint condition, Force and displacement are reliably transmitted at the boundary portions 13 and 14, and the calculation accuracy is not impaired.

  As mentioned above, although especially preferable embodiment of this invention was explained in full detail, this invention is not limited to embodiment of illustration, It can deform | transform and implement in a various aspect.

1, 10 Filler compound rubber 1M, 10M Filler compound rubber model 2 Matrix rubber 2M Matrix rubber model 3 Filler 3M Filler model 4 Interface layer 4M Interface layer model 5, 6, 7 Element 9 Boundary part 13 First boundary part 14 Second boundary Part

Claims (5)

A method for creating, using a computer, a finite element model of filler-containing rubber in which fillers are dispersed in matrix rubber,
Defining a filler model in which the filler is discretized using a finite number of elements in the computer;
A second step of defining, in the computer, a matrix rubber model obtained by discretizing at least a space occupied by the matrix rubber by using a finite number of elements independently of the filler model;
The computer includes a model embedding step of embedding the filler model in the matrix rubber model,
In the model embedding step, the matrix rubber model and the filler model are overlaid without considering the sharing of nodes between each other, and at the boundary between the filler model and the matrix rubber model, the filler model A method for creating a finite element model of filler-containing rubber , wherein a filler-containing rubber model is defined by giving constraint conditions only to the nodes on the surface .   2. The finite element model of filler-containing rubber according to claim 1, wherein the matrix rubber model has a total space in which a first space occupied by the matrix rubber and a second space occupied by the filler are combined. How to create A method for creating, using a computer, a finite element model of filler-containing rubber in which fillers are dispersed in matrix rubber,
Defining a filler model in which the filler is discretized using a finite number of elements in the computer;
A second step of defining, in the computer, a matrix rubber model obtained by discretizing at least a space occupied by the matrix rubber by using a finite number of elements independently of the filler model;
A third step of defining, in the computer, an interface layer model obtained by discretizing at least one interface layer surrounding the filler with a finite number of elements independently from the filler model and the matrix rubber model;
The computer includes a model embedding step of embedding the filler model and the interface layer model in the matrix rubber model,
In the model embedding step, the matrix rubber model, the filler model, and the interface layer model are overlaid without considering mutual node sharing,
In the first boundary part between the filler model and the interface layer model, a constraint condition is given only to the nodes on the surface of the filler model , and a second between the interface layer model and the matrix rubber model. A method for creating a finite element model of a filler-blended rubber, wherein a filler-blended rubber model is defined by giving a constraint condition only to a boundary portion.   The matrix rubber model has a total space including a first space occupied by the matrix rubber, a second space occupied by the filler, and a third space occupied by the interface layer. A method for creating a finite element model of filler-containing rubber according to claim 3. In the second step, the space is discretized with elements of the same size,
The method for creating a finite element model of filler-containing rubber according to any one of claims 1 to 4, wherein the element in the first step has a size different from that of the element in the second step.

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