JP6747809B2 - Material parameter estimation device, material parameter estimation method, and material parameter estimation program - Google Patents

Description

The present invention relates to a material parameter estimation device, a material parameter estimation method, and a material parameter estimation program.

"Quietness" is being demanded as one of the added values of various products such as automobiles, office automation equipment, home appliances, and homes. In order to enhance the quietness, a material having an effect of absorbing and insulating sound is often used. Such materials are called acoustic materials. The acoustic material may be a single material or a laminated material in which a plurality of materials are stacked in layers.

Here, sound absorption means that sound incident on a certain material is absorbed or transmitted by the material without being reflected. The sound absorption performance is evaluated by the value of sound absorption coefficient. Further, sound insulation means that sound incident on a material does not pass through the material. The sound insulation performance is evaluated by the value of sound transmission loss. Both sound absorption and sound transmission loss are functions of frequency. The sound absorption coefficient and the sound transmission loss are collectively called acoustic performance.

When developing an acoustic material, actually make a prototype, measure the acoustic performance of the prototype material, check whether the measurement result is desired, and perform trial and actual measurement until the desired result is obtained. It is common to repeat. However, the cost of the material is high because the trial manufacture is performed multiple times. In addition, dedicated equipment is required to measure the acoustic performance of the prototype material. Furthermore, since the trial manufacture and the actual measurement are repeated, the development period is often extended.

Therefore, instead of repeating the trial manufacture and actual measurement, a method of mathematically expressing the acoustic material as a mathematical model and calculating the acoustic performance of the acoustic material according to the mathematical model may be used. In the case of this method, the characteristics of the material to be modeled, for example, the values of material parameters such as the density and thickness of the material are determined, and the acoustic performance of the material is calculated using these values. There are several mathematical models, and the mathematical model to be used differs depending on the type of material to be modeled. Also, the types of material parameters required depend on the mathematical model. Of course, when the acoustic material is a laminated material, different mathematical models can be used for each material. Patent Document 1 describes a bio model, which is one of mathematical models.

A fibrous porous material is mentioned as an example of an acoustic material. When the fibers that form the skeleton of the fibrous porous material are viewed alone, the polymeric materials such as polyester and the fibers such as cotton are very soft. On the other hand, fibers composed of artificial mineral fibers such as glass fibers and rock wool are very hard. Therefore, the elasticity of the entire porous material is affected to a large extent by the elasticity of the skeleton.

When the elasticity of this porous material can be regarded as very soft, when a sound wave enters the porous material, the material is excited by the sound wave and vibrates in the same manner as the sound wave, and the vibration of the skeleton gives the acoustic performance of the porous material. The impact is considered to be small. On the other hand, when the elasticity of the porous material can be regarded as hard, it is considered that the skeleton does not easily vibrate even when a sound wave enters the material, and the vibration of the skeleton can be ignored.

In this way, when the skeleton of the porous material is soft or hard, the elasticity of the porous material may be ignored for modeling. In particular, the fibrous porous material often neglects elasticity. Researchers represented by Mr. Johnson, Mr. Campoux, and Mr. Allard proposed a model that ignored the elasticity of a porous material with a hard skeleton. This model ignoring elasticity is called the "JCA model" by taking the initials of the three names.

A model that ignores the elasticity of the entire porous material due to its rigid skeleton is widely called a rigid frame model. The JCA model belongs to the rigid skeleton model. A model that ignores elasticity because the skeleton is soft is called a soft skeleton model (limp frame model).

The JCA model uses five material parameters: (1) porosity, (2) flow resistance, (3) labyrinth degree, (4) viscous characteristic length, and (5) thermal characteristic length. These material parameters relate to the fluid properties of the acoustic material, ie the airborne sound. Specifically, porosity is the proportion of air in the acoustic material. The greater the percentage of voids, the greater the porosity of the acoustic material. Next, the flow resistance is a numerical value that represents the difficulty of the air flow in the acoustic material. Since sound is vibration of air, when the flow resistance of the acoustic material is large, it is difficult for air to flow in the material, that is, it can be said that the material is a material that hardly transmits sound. This flow resistance has a very large weight among the material parameters. The maze degree is a numerical value that represents the complexity of the shape of the air path created by the void. The greater the maze degree, the more sound travels through the material, and the more sound is absorbed. The viscous characteristic length and the thermal characteristic length are numerical values representing the magnitudes of the viscous loss and the heat exchange loss, respectively.

In order to estimate the acoustic performance of the porous material by the above JCA model, five appropriate material parameters are required for each. With respect to this material parameter, generally, even if the same material is used, if deformation occurs due to compression or the like such as molding, all the material parameter values change. Therefore, it is necessary to recalculate the material parameters for each state of the porous material whose acoustic performance is to be estimated, which is very laborious.

Therefore, a means for easily estimating the change in the value of the material parameter due to the deformation of the porous material is desired. Examples of such means are described in Non-Patent Documents 1 and 2. Non-Patent Document 1 attempts to estimate the case where a porous material is compressed for all five material parameters. Further, in Non-Patent Document 2, a study on flow resistance is added.

International Publication No. 2013/080993

Bernard Castagnede, Achour Aknine, Bruno Brouard, Viggo Tarnow, Effects of compression on the sound absorption of fibrous materials., Applied Acoustics, 61(2), 173-182 (2000). Viggo Tarnow, Airflow resistivity of models of fibrous acoustic materials., J. Acoust. Soc. Am. 100 (6), 3706-3713 (1996).

Non-Patent Document 2 does not mention material parameters other than the flow resistance, and it is considered that the applicable shape of the porous material is limited. Further, the estimation in Non-Patent Document 1 is also considered to have a narrow application range and insufficient verification.

It is an object of the present invention to eliminate such an inconvenience and improve the estimation accuracy when estimating the material parameter after the deformation of the porous material by using the material parameter before the deformation of the porous material.

により推定される。さらに、前記多孔質材料の変形前における流れ抵抗σ ^（１） の入力が受け付けられ、前記多孔質材料の変形後における流れ抵抗σ ^（Ｐ） が、前記変形が２次元的である場合は

により推定され、前記変形が３次元的である場合は

により推定される。 In order to achieve the above object, in the material parameter estimation according to the present invention, first, the porosity φ ⁽¹⁾ of the porous material before deformation and the volume change rate P of the porous material due to the deformation are set. Is accepted. Then, the porosity φ ^(P) of the porous material after deformation is

Estimated by. Further, when the input of the flow resistance σ ⁽¹⁾ before the deformation of the porous material is accepted and the flow resistance σ ^(P) after the deformation of the porous material is two-dimensional,

And if the deformation is three-dimensional,

Estimated by.

により推定される。 In another form of material parameter estimation, first, the porosity φ ⁽¹⁾ and the viscosity characteristic length Λ ⁽¹⁾ of the porous material before deformation and the volume change rate P of the porous material due to the deformation are Input is accepted. Then, the viscous characteristic length Λ ^(P) of the porous material after deformation is

Estimated by.

により推定される。 In another form of material parameter estimation, first, the porosity φ ⁽¹⁾ and the thermal characteristic length Λ′ ⁽¹⁾ of the porous material before deformation and the volume change rate P of the porous material due to the deformation Is accepted. Then, the thermal characteristic length Λ' ^(P) of the porous material after deformation is

Estimated by.

According to the present invention, it is possible to estimate the material parameter after the deformation of the porous material by using the material parameter before the deformation of the porous material without re-measurement of the material parameter after the deformation of the porous material. It is possible to improve the estimation accuracy.

(A) It is a cross-sectional view of a porous material. (B) It is sectional drawing of the porous material after a deformation|transformation. It is a graph showing the relationship between the porosity after deformation and the volume change rate. It is explanatory drawing which shows the functional structural example of a material parameter estimation apparatus. It is explanatory drawing which shows the computer hardware structural example of a material parameter estimation apparatus. It is a graph showing the relationship between the porosity and the maze degree after deformation. It is a graph showing the relationship between the porosity after deformation and the thermal characteristic length. It is a graph showing the relationship between the porosity after deformation and the viscosity characteristic length. It is a graph showing the relationship between porosity after deformation and flow resistance.

FIG. 1 shows a cross section of a fibrous porous material. The porous material 1 has a skeleton 2 and a void 3 between the skeletons 2. When the porous material 1 is deformed by compression or expansion due to molding or the like, the voids 3 between the skeletons 2 are often deformed, and the skeleton 2 itself is rarely deformed. Therefore, it is assumed that only the voids are deformed as the porous material is deformed.

When the volume occupied by the skeleton of the porous material before deformation is V _f , the volume occupied by voids is V _a , and the total volume is V _T , the following relationships are established.
V _T =V _f +V _a

Then, the total volume V _T ^(P) of the porous material after the deformation is expressed as follows.
^{_{V T (P): = PV}} T = V f + PV a
However, P is a volume change rate of the porous material due to deformation. When P>1, the volume increases, and when P<1, the volume decreases. In addition, the volume V _a ^(P) of the void after deformation is expressed as follows.
V _a ^(P) := PV _a

An embodiment of the present invention based on the above will be described below. However, the present invention is not limited to the following embodiments.

である。そして、多孔質材料の変形後における多孔度φ^（Ｐ）は、以下のように表される。

[Porosity]
From its definition, the porosity φ ⁽¹⁾ of the porous material before deformation is expressed as follows.

Is. Then, the porosity φ ^(P) after the deformation of the porous material is expressed as follows.

In this way, the post-deformation porosity φ ^(P) can be obtained from the pre-deformation porosity φ ⁽¹⁾ and the volume change rate P associated with the deformation. When the volume change rate P is unknown and the pre-deformation porosity φ ⁽¹⁾ and the post-deformation porosity φ ^(P) are given, the following formula (2) is obtained. The volume change rate P can be obtained.

FIG. 2 shows the relationship between the post-deformation porosity φ ^(P) and the volume change rate P when the pre-deformation porosity φ ⁽¹⁾ =0.99.

FIG. 3 shows an example of the functional configuration of the material parameter estimation device 5 that estimates the value of a material parameter including porosity after deformation. The material parameter estimation device 5 includes a reception unit 51 and an estimation unit 52. The functions of the reception unit 51 and the estimation unit 52 will be described later.

FIG. 4 shows a computer hardware configuration example of the material parameter estimation device 5. The material parameter estimation device 5 includes a CPU 510, an interface device 520, a display device 530, an input device 540, a drive device 550, an auxiliary storage device 560, and a memory device 570, which are connected by a bus 580. Connected to each other.

A program that realizes the function of the material parameter estimation device 5 is provided by a recording medium 590 such as a CD-ROM. When the recording medium 590 recording the program is set in the drive device 550, the program is installed in the auxiliary storage device 560 from the recording medium 590 via the drive device 550. Alternatively, the program does not necessarily have to be installed on the recording medium 590, and can be downloaded from another computer via a network. The auxiliary storage device 560 stores the installed program and also stores necessary files and data.

The memory device 570 reads the program from the auxiliary storage device 560 and stores the program when an instruction to activate the program is given. The CPU 510 realizes the function of the material parameter estimation device 5 according to the program stored in the memory device 570. The interface device 520 is used as an interface for connecting to another computer through a network. The display device 530 displays a GUI (Graphical User Interface) or the like according to the program. The input device 540 is a keyboard and a mouse.

In estimating the porosity, the reception unit 51 in the material parameter estimation device 5 receives an input of the pre-deformation porosity φ ^{(1) and} an input of the volume change rate P due to the deformation. Then, the estimation unit 52 estimates the post-deformation porosity φ ^(P) by the equation (2).

The porosity φ ⁽¹⁾ before deformation may be either an actually measured value or a calculated value.

ただし、α_∞ ^（１）は、変形前の多孔度である。 [Maze degree]
The inventor previously performed a computational fluid dynamics analysis (hereinafter referred to as a two-dimensional CFD) by a computer. Specifically, a two-dimensional ideal fluid steady flow analysis of an incompressible inviscid fluid was performed using the complex variable boundary element method (CVBEM). As a result, it was found that the deformed maze degree α _∞ ^(P) can be expressed by a linear expression with respect to the deformed porosity φ ^(P) . If the slope of this linear equation is set to a and Equation (1) is also used, the degree of maze α _∞ ^(P) after deformation can be obtained as follows.

However, α _∞ ⁽¹⁾ is the porosity before deformation.

FIG. 5 shows the relationship between the labyrinth degree α _∞ ^(P) after deformation and the porosity φ ^(P) after deformation for porous materials having four fiber diameters. The fiber diameter is the diameter of the skeleton 2 having a circular cross section, as indicated by reference numeral D in FIG. 1(A).

In FIG. 5, a circle (∘) represents a maze degree obtained by the two-dimensional CFD when the fiber diameter is 10 μm. The square (□) points represent the degree of maze obtained by two-dimensional CFD when the fiber diameter is 5 μm. The points of triangles (Δ) represent the degree of maze obtained by two-dimensional CFD when the fiber diameter is 2.5 μm. The diamond points (⋄) represent the degree of maze obtained by two-dimensional CFD for a fiber diameter of 1 μm. Note that, in the figure, the circled points, the quadrangular points, and the triangular points are not clearly shown because they overlap the diamond-shaped points.

Similarly, in FIG. 5, a graph G11 represents the estimated value of the maze degree using the equation (4) when the fiber diameter is 10 μm. The graph G12 represents the estimated value of the maze degree using the equation (4) when the fiber diameter is 5 μm. The graph G13 represents the estimated value of the maze degree using the equation (4) when the fiber diameter is 2.5 μm. The graph G14 represents the estimated value of the maze degree using the equation (4) when the fiber diameter is 1 μm.

In this way, the deformed maze degree α _∞ ^(P) can be expressed by a linear expression with respect to the deformed porosity φ ^(P) . It can be seen that the estimation accuracy is particularly high when the post-deformation porosity φ ^(P) is 0.9 or more.

In estimating the degree of maze, the accepting unit 51 in the material parameter estimating apparatus 5 accepts the input of the degree of maze α _∞ ⁽¹⁾ before deformation and the input of the volume change rate P due to deformation. Then, the estimation unit 52 estimates the deformed labyrinth degree α _∞ ^(P) by the equation (4).

The labyrinth degree α _∞ ⁽¹⁾ before deformation may be either an actually measured value or a calculated value.

ただし、Ｓ_ｆは骨格の表面積を表しているとともに、Ｖ_Ｔ ^（１）＝Ｖ_Ｔである。つまり、熱的特性長とは、空隙の体積と骨格の表面積の比の２倍である。変形後の多孔質材料の熱的特性長Λ’^（Ｐ）は、式（２）と式（５）から、以下のように表すことができる。

[Thermal characteristic length]
From the definition, the thermal characteristic length Λ′ ⁽¹⁾ before deformation is expressed as follows.

However, S _f represents the surface area of the skeleton, and V _T ⁽¹⁾ =V _T. That is, the thermal characteristic length is twice the ratio of the void volume to the skeleton surface area. The thermal characteristic length Λ' ^(P) of the deformed porous material can be expressed by the following equation (2) and equation (5).

Thus, if the thermal characteristic length Λ′ ⁽¹⁾ before deformation is known, the thermal characteristic length Λ′ ^(P) after deformation can be calculated from the volume change rate P and the porosity φ ⁽¹⁾ before deformation. Can be asked.

FIG. 6 shows the relationship between the deformed thermal characteristic length Λ′ ^(P) and the deformed porosity φ ^(P) in a porous material having four fiber diameters with a circular cross section. A circle (∘) represents a thermal characteristic length of a fiber diameter of 10 μm obtained by two-dimensional CFD. The square (□) points represent the thermal characteristic length of the fiber diameter of 5 μm obtained by the two-dimensional CFD. The triangle (Δ) points represent the thermal characteristic length of the fiber diameter of 2.5 μm, which was obtained by the two-dimensional CFD. The diamond (⋄) points represent the thermal characteristic length of the fiber diameter of 1 μm obtained by the two-dimensional CFD. In the two-dimensional CFD, a two-dimensional ideal fluid steady flow analysis of an incompressible inviscid fluid was performed using the complex variable boundary element method (CVBEM) as in the case of the maze degree.

Similarly, in FIG. 6, a graph G21 represents an estimated value of the thermal characteristic length using the equation (6) when the fiber diameter is 10 μm. The graph G22 represents the estimated value of the thermal characteristic length using the equation (6) when the fiber diameter is 5 μm. The graph G23 represents the estimated value of the thermal characteristic length using the equation (6) when the fiber diameter is 2.5 μm. The graph G24 represents the estimated value of the thermal characteristic length using the equation (6) when the fiber diameter is 1 μm.

Thus, it is understood that the thermal characteristic length after deformation can be accurately estimated by the equation (6) for any of the four fiber diameters.

In estimating the thermal characteristic length, the reception unit 51 in the material parameter estimation device 5 inputs the thermal characteristic length Λ′ ⁽¹⁾ before deformation, the porosity φ ⁽¹⁾ before deformation, and the deformation. And the input of the volume change rate P associated with. Then, the estimation unit 52 estimates the thermal characteristic length Λ' ^(P) after the deformation by the equation (6).

The thermal characteristic length Λ′ ⁽¹⁾ and the porosity φ ⁽¹⁾ before deformation may be either actual measured values or calculated values.

ただし、Λ^（１）は、変形前の粘性特性長である。 [Viscosity characteristic length]
As a result of the two-dimensional CFD, the inventor found that the deformed viscous characteristic length Λ ^(P) changes almost the same as the thermal characteristic length with respect to the deformed porosity φ ^(P) . Therefore, referring to the equation (6), the viscosity characteristic length Λ ^(P) after deformation is expressed as follows.

However, Λ ⁽¹⁾ is the viscosity characteristic length before deformation.

Thus, if the viscosity characteristic length Λ ⁽¹⁾ before deformation is known, the viscosity characteristic length Λ ^(P) after deformation can be obtained from the volume change rate P and the porosity φ ⁽¹⁾ before deformation. it can.

FIG. 7 shows the relationship between the post-deformation viscosity characteristic length Λ ^(P) and the post-deformation porosity φ ^(P) in a porous material having four fiber diameters with a circular cross section. A circle (∘) represents a viscous characteristic length of a fiber diameter of 10 μm obtained by two-dimensional CFD. The square (□) points represent the viscous characteristic length of the fiber diameter of 5 μm obtained by the two-dimensional CFD. The points of triangles (Δ) represent the viscous characteristic length of the fiber diameter of 2.5 μm obtained by the two-dimensional CFD. The diamond (⋄) points represent the viscous characteristic length of the fiber diameter of 1 μm obtained by the two-dimensional CFD.

Similarly, in FIG. 7, a graph G31 represents an estimated value of the viscosity characteristic length using the equation (7) when the fiber diameter is 10 μm. The graph G32 represents the estimated value of the viscosity characteristic length using the equation (7) when the fiber diameter is 5 μm. The graph G33 represents the estimated value of the viscosity characteristic length using the equation (7) when the fiber diameter is 2.5 μm. The graph G34 represents the estimated value of the viscosity characteristic length using the equation (7) when the fiber diameter is 1 μm.

Thus, for any of the four fiber diameters, the viscous characteristic length after deformation can be accurately estimated by the equation (7).

In estimating the viscosity characteristic length, the reception unit 51 in the material parameter estimation device 5 inputs the viscosity characteristic length Λ ⁽¹⁾ before deformation, the porosity φ ⁽¹⁾ before deformation, and the volume accompanying deformation. The input of the rate of change P is accepted. Then, the estimation unit 52 estimates the viscous characteristic length Λ ^(P) after the deformation by the equation (7).

The viscosity characteristic length Λ ⁽¹⁾ and the porosity φ ⁽¹⁾ before deformation may be either actually measured values or calculated values.

[Flow resistance]
The flow velocity of the air flowing through the porous material when measuring the flow resistance is extremely low, and the Reynolds number at that time is sufficiently smaller than 1. Therefore, the Stokes approximation in which the inertial term in the Navier-Stokes equation is ignored is adopted as an equation expressing the flow of air in the porous material. The Stokes equation in this approximation is expressed as follows.

ただし、Ｐ_１は多孔質材料の表面における圧力を表し、Ｐ_２は多孔質材料の裏面における圧力を表し、Ｌは多孔質材料の表面から裏面までの長さである。 Here, μ is the viscosity of air, and u is the flow velocity of air flowing from the front surface to the back surface of the porous material in the porous material. U=U/φ can be expressed as U, where U is the given velocity before infiltration into the porous material and φ is the porosity of the porous material. Further, p represents pressure, and grad is directional differentiation. Therefore, the directional differential (grad p) of the pressure p can be considered to represent the pressure difference between the front and back surfaces of the porous material. That is, it is as follows.

However, P ₁ represents the pressure on the surface of the porous material, P ₂ represents the pressure on the back surface of the porous material, and L is the length from the front surface to the back surface of the porous material.

Further, Δ in Expression (8) represents the second derivative of the direction. Therefore, the expression (8) shows that the pressure difference grad p is proportional to the flow velocity u in the porous material and inversely proportional to the square of the length L. That is, it is as follows.

On the other hand, the flow resistance σ ⁽¹⁾ before deformation is expressed as follows, considering the expression (9) from its definition.

Next, considering the flow resistance after deformation, the fact that the volume increases P times with deformation means that the length of one side of a square porous material is √P times, considering two-dimensional deformation. Becomes Therefore, the flow resistance σ ^(P) after the deformation is expressed as follows with reference to the equation (10).

In the case of three-dimensional deformation (force is applied from the front, rear, left, right, and bottom), the length of one side of the cubic porous material is the cube root of P. Therefore, the flow resistance σ ^(P) after three-dimensional deformation is expressed as follows.

That is, considering the equation (2), if the flow resistance σ ⁽¹⁾ before deformation is known, the flow resistance σ ^(P after deformation is calculated from the volume change rate P and the porosity φ ⁽¹⁾ before deformation. ⁾ Can be asked.

FIG. 8 shows the relationship between the flow resistance σ ^(P) after deformation and the porosity φ ^(P) after deformation in a porous material having four fiber diameters with a circular cross section. The circle (∘) represents the flow resistance of the fiber diameter of 10 μm obtained by the two-dimensional CFD. The square (□) points represent the flow resistance of the fiber diameter of 5 μm obtained by the two-dimensional CFD. The points of triangles (Δ) represent the flow resistance of the fiber diameter of 2.5 μm obtained by the two-dimensional CFD. The diamond points (⋄) represent the flow resistance of the fiber diameter of 1 μm obtained by the two-dimensional CFD. In the two-dimensional CFD, a two-dimensional steady flow analysis of an incompressible viscous fluid was performed.

Similarly, in FIG. 8, a graph G41 represents an estimated value of the flow resistance using the equation (11) when the fiber diameter is 10 μm. The graph G42 represents the estimated value of the flow resistance using the equation (11) when the fiber diameter is 5 μm. The graph G43 represents the estimated value of the flow resistance using the equation (11) when the fiber diameter is 2.5 μm. The graph G44 represents the estimated value of the flow resistance using the equation (11) when the fiber diameter is 1 μm.

Thus, for any of the four fiber diameters, the flow resistance after deformation can be accurately estimated by the equation (11). The estimation accuracy is particularly high when the deformed porosity φ ^(P) is 0.9 or more.

In estimating the flow resistance, the reception unit 51 in the material parameter estimation device 5 inputs the flow resistance σ ⁽¹⁾ before deformation, the porosity φ ⁽¹⁾ before deformation, and the volume change rate due to deformation. Input of P is accepted. Then, the estimation unit 52 estimates the post-deformation porosity φ ^(P ) by the equation (2) and also estimates the post-deformation flow resistance σ ^(P) by the equation (11).

The flow resistance σ ⁽¹⁾ and the porosity φ ⁽¹⁾ before deformation may be either actually measured values or calculated values.

According to the method for estimating the material parameters as described above, the material parameters before the deformation of the porous material are used without re-measurement of the material parameters after the deformation of the porous material. The material parameter can be estimated, and the estimation accuracy can be improved.

[Other]
The above five material parameters are used not only in the JCA model but also in other mathematical models such as a rigid skeleton model, a soft skeleton model, and a bio model. The above-mentioned material parameter estimation method can be applied to any mathematical model using five material parameters. Further, the acoustic material targeted by the present method can be any porous material including a fibrous porous material. This method can be used regardless of the distribution state of the skeleton in the porous material and whether or not the cross-sectional shape of the skeleton is circular.

The above-described material parameter estimation method has not only an aspect as a material parameter estimation device but also an aspect as a material parameter estimation method and a material parameter estimation program.

The functional configuration and the physical configuration of the material parameter estimation device described above are not limited to the above-described aspects, and for example, the functions and physical resources are integrated and mounted, or conversely, further distributed and mounted. It is also possible.

1 Porous Material 2 Skeleton 3 Void

5 Material Parameter Estimating Device 51 Receiving Section 52 Estimating Section

Claims (9)

A receiving unit that receives inputs of the porosity φ ⁽¹⁾ of the porous material before deformation and the volume change rate P of the porous material due to the deformation;
The porosity φ ^(P) of the porous material after deformation is

And a estimation unit that estimates by,
The reception unit further receives an input of the flow resistance σ ⁽¹⁾ before the deformation of the porous material ,
When the deformation is two-dimensional, the estimating unit further calculates a flow resistance σ ^(P) after the deformation of the porous material.

If the deformation is three-dimensional,

A material parameter estimating device for estimating a material parameter. A receiving unit that receives inputs of the porosity φ ⁽¹⁾ and the viscosity characteristic length Λ ⁽¹⁾ of the porous material before deformation, and the volume change rate P of the porous material due to the deformation.
The viscous characteristic length Λ ^(P) of the porous material after deformation is

And a material parameter estimation device comprising: A receiving unit that receives inputs of the porosity φ ⁽¹⁾ and the thermal characteristic length Λ′ ⁽¹⁾ of the porous material before deformation, and the volume change rate P of the porous material due to the deformation;
The thermal characteristic length Λ′ ^(P) of the porous material after deformation is

And a material parameter estimation device comprising: A receiving step of receiving inputs of the porosity φ ⁽¹⁾ of the porous material before deformation and the volume change rate P of the porous material due to the deformation;
The porosity φ ^(P) of the porous material after deformation is

Only including the estimated step be estimated by,
Further, in the receiving step, the input of the flow resistance σ ⁽¹⁾ before the deformation of the porous material is received,
Further, in the estimating step, when the flow resistance σ ^(P) after the deformation of the porous material is two-dimensional,

And if the deformation is three-dimensional,

Material parameter estimation method estimated by. A step of receiving an input of the porosity φ ⁽¹⁾ and the viscosity characteristic length Λ ⁽¹⁾ before the deformation of the porous material and the volume change rate P of the porous material due to the deformation;
The viscous characteristic length Λ ^(P) of the porous material after deformation is

And a material parameter estimation method comprising: A receiving step of receiving inputs of the porosity φ ⁽¹⁾ and the thermal characteristic length Λ′ ⁽¹⁾ of the porous material before deformation, and the volume change rate P of the porous material due to the deformation;
The thermal characteristic length Λ′ ^(P) of the porous material after deformation is

And a material parameter estimation method comprising: A receiving step of receiving inputs of the porosity φ ⁽¹⁾ of the porous material before deformation and the volume change rate P of the porous material due to the deformation;
The porosity φ ^(P) of the porous material after deformation is

Let the computer execute the estimation step and
Further, in the receiving step, the input of the flow resistance σ ⁽¹⁾ before the deformation of the porous material is received,
Further, in the estimating step, when the flow resistance σ ^(P) after the deformation of the porous material is two-dimensional,

And if the deformation is three-dimensional,

Material parameter estimation program estimated by. A step of receiving an input of the porosity φ ⁽¹⁾ and the viscosity characteristic length Λ ⁽¹⁾ before the deformation of the porous material and the volume change rate P of the porous material due to the deformation;
The viscous characteristic length Λ ^(P) of the porous material after deformation is

A material parameter estimation program that causes a computer to execute the estimation step and A receiving step of receiving inputs of the porosity φ ⁽¹⁾ and the thermal characteristic length Λ′ ⁽¹⁾ of the porous material before deformation, and the volume change rate P of the porous material due to the deformation;
The thermal characteristic length Λ′ ^(P) of the porous material after deformation is

A material parameter estimation program that causes a computer to execute the estimation step and

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