Design method for S-chain microscopic mechanism model of magnetorheological elastomer

Abstract

The invention provides a design method of a magnetorheological elastomer S chain microscopic mechanism model. The design method comprises the following steps: applying an external magnetic field to a magnetorheological elastomer; the magnetic particle chains with different thicknesses interact to form a plurality of short chains with different thicknesses; the method comprises the following steps: uniformly assuming all attracted single or multiple suspended magnetic particles as a whole, and sequentially changing in the step 1 and the step 2 to obtain a magnetic particle chain which is of an S-chain structure provided by the invention; and applying an ideal stretching effect to the S-chain structure while considering a shearing effect, applying an ideal shearing effect to the S-chain structure while considering a stretching effect, and unifying a stretching-shearing mode and a shearing-stretching mode to obtain an S-chain micromechanism model. The invention innovatively provides a design method of an S-chain microscopic mechanism model considering a fully-coupled magnetic field, an interface expansion and contraction effect and distribution parameters, and in the design process, the combined action among complex acting forces in multiple forms of stretching, compression and shearing is emphatically considered.

Description

Technical Field

[0001] The invention relates to the technical field of intelligent magnetic material modeling and microscopic characterization, and in particular to a design method for a magnetorheological elastomer S-chain microscopic mechanism model. Background Art

[0002] In recent years, magnetorheological materials, as a new functional material that can sense environmental changes and external stimuli and respond quickly, have developed rapidly. Its research and large-scale application is a major revolution in the development of materials science. Magnetorheological elastomers, as a unique member of the magnetorheological smart material family, have the characteristics of changing stiffness with external magnetic fields, fast response speed (millimeter level) and good reversibility. In addition, due to their stable structure and easy preparation, they are widely used in structural vibration suppression, smart sensors, soft robots, biological bionics and human exoskeletons.

[0003] The research on the microscopic mechanism model based on chain structure is a hot topic in the research of magnetorheological elastomers at home and abroad. The microscopic mechanism model can not only reveal the mechanism of the change of the stiffness of magnetorheological elastomer with magnetic field from the interaction between internal materials, but also establish the analytical relationship between mechanical parameters (such as stress and modulus) and preparation parameters (such as magnetic particle size and material ratio, etc.), which is of great significance for guiding the preparation of magnetorheological elastomers. However, some microscopic mechanism models (such as the straight chain model and the cluster chain model) are based on the straight chain arrangement or oblique straight chain arrangement of magnetic particle chains, which are slightly different from the bending arrangement of magnetic particle chains inside actual magnetorheological elastomers; some microscopic mechanism models (such as the main chain adsorption model and the zigzag chain model) take the bending of magnetic particle chains into consideration, but lack systematic analysis and experimental verification of the chain formation process of magnetic particles; in addition, most microscopic mechanism models are mainly aimed at stress and modulus analysis under ideal compression, ideal tension or ideal shear, but the actual magnetorheological elastomer is a mixture of compression, tension and shear during application. Overly idealized models cannot reveal the stress conditions of the actual magnetorheological elastomer during application.

[0004] The Chinese invention patent with the announcement number "CN113515868B" and the name "A method for constructing a chain cluster model of a magnetorheological elastomer and a method for estimating its performance" discloses a method for constructing a chain cluster model of a magnetorheological elastomer and a method for estimating its performance, which includes the following steps: scanning the microstructure of the magnetorheological elastomer sample to obtain the mean particle size and mean particle distance of the magnetic particles in the magnetorheological elastomer sample; establishing a chain cluster model of the magnetorheological elastomer with the particle size and particle distance of random magnetic particles according to the set volume fraction of magnetic particles; treating the magnetic particles in the chain cluster model as magnetic dipoles of equal strength, calculating the total energy density based on the interaction between two adjacent magnetic dipoles, and then calculating the magneto-shear modulus. Based on the traditional ideal magnetorheological elastomer microscopic model, this technical solution introduces the particle size, particle distance and temperature influencing factors to correct the model, so that the constructed magnetorheological elastomer chain cluster model is more accurate and more in line with reality. However, this technical solution does not take into account the combined effects of compression, tension and shear forces on the magnetorheological elastomer, and therefore cannot reveal the actual stress conditions of the magnetorheological elastomer during actual application. Summary of the invention

[0005] In order to solve the problem that the microscopic model of magnetorheological elastomer in the above-mentioned prior art does not consider the combined effects of compression, tension and shear forces, and cannot evaluate the stress conditions of magnetorheological elastomer in actual application, the present invention proposes a design method for a magnetorheological elastomer S chain microscopic mechanism model, starting from the internal chain formation mechanism and the interaction between magnetic particles, to design a magnetorheological elastomer S chain microscopic mechanism model that is more suitable for characterization of microstructure and mechanical properties.

[0006] The present invention is achieved through the following technical solution: comprising the following steps:

[0007] Step 1, applying an external magnetic field to the magnetorheological elastomer;

[0008] Step 2: Magnetic particle chains of different thicknesses interact with each other to form several short chains of different thicknesses;

[0009] Step 3, all the attracted single or multiple suspended magnetic particles are uniformly assumed to be a whole, and the magnetic particle chain after the change in steps 1 and 2 is the S chain structure of the present invention;

[0010] Step 4, select three consecutive adjacent magnetic particles 1, 2 and 3 on the same S chain to form a microunit, apply ideal stretching to the microunit while considering the shearing effect, and obtain the magneto-stress σ1 and magneto-modulus ΔG1 in the stretching-shear mode: select a microunit composed of magnetic particles 1, 2 and 3 and add two magnetic particles 4 and 5 adjacent to the same axis of adjacent S chains to form a new microunit, apply ideal shearing effect to the new microunit while considering the stretching effect, and obtain the magneto-stress σ2 and magneto-modulus ΔG2 in the shear-stretching mode: unify the stretching-shear mode and the shear-stretching mode to obtain the S chain microscopic mechanism model.

[0011] Furthermore, the expression of the magnetic dipole magnetic moment m in step 4 is:

[0012]

[0013] Assumptions is the number of microunits in a single S chain, and there are n in total per unit volume. 2 S chains, the total interaction energy between magnetic dipoles per unit volume is:

[0014]

[0015] Magnetorheological elastomers satisfy the assumptions of constant volume and constant area. In order to further reveal the relationship between the structural parameters before and after stretching, a power series hypothesis is proposed. The power series hypothesis describes the position relationship of the magnetic dipole before and after deformation as:

[0016]

[0017] In the formula, λ is the material microstructure parameter, and const is a constant. To further characterize the relative distance between adjacent magnetic dipoles, a random variable h is introduced. The relationship between R and r can be expressed as R = (1 + h) r.

[0018] Assume that the lateral contraction of the magnetorheological elastomer is Then the distance change Δd between two adjacent S-chain magnetic dipoles is The distance between all chains is d i = total magnetic dipole interaction energy E of i(d0-Δd) d for:

[0019]

[0020] Average magnetic energy density U of magnetorheological elastomer T It can be expressed as:

[0021]

[0022] Assuming that the material is uniformly stretched macroscopically, the total magnetic energy is converted into elastic energy of tensile stress and strain, then the magneto-induced stress σ1 and magneto-induced modulus ΔG1 can be expressed as:

[0023]

[0024] Substituting the above equations (1) to (5) into (6) and (7), the expressions of the magnetostrictive stress σ1 and magnetostrictive modulus ΔG1 in the tensile-shear mode of the S chain microscopic mechanism model are obtained as follows:

[0025]

[0026] Wherein, μ0 is the vacuum magnetic permeability, μ1 is the relative magnetic permeability of the matrix material, r is the radius of the magnetic particle, φ is the volume fraction of the magnetic particle, χ is the magnetic susceptibility of the magnetic particle, H0 is the strength of the external magnetic field, ε is the tensile strain, D is the vertical distance between adjacent axis particles inside the S chain, 2R is the distance between particles on the same axis inside the S chain, λ is the material microstructure parameter, h is a random variable, d is the absolute distance between adjacent particles, d0 is the relative distance between adjacent S chains, A, B, and C are intermediate variables, n is the number of magnetic particles on a single S chain, and i is any particle on a single S chain.

[0027] Furthermore, the value of C is 1.2.

[0028] Furthermore, the expressions of A and B are respectively:

[0029]

[0030] Furthermore, in step 4, the interaction between the intermediate magnetic particles 2' and other magnetic particles is considered, and the average magnetic energy density U of the magnetorheological elastomer is s for:

[0031]

[0032]

[0033] Where θ is the angle between magnetic particles, θ 13 is the rotation angle of the magnetic particle chain, θ 2′4′ is the angle between magnetic particles 2' and 4' after the change, r 2′5′ represents the distance between magnetic particles 2' and 5' after the change, E 12’ 、E 2’3’ 、E 2’5’ and E 2’4’ They represent the energy values ​​between the magnetic particle 2' and the magnetic particles 1, 3', 5' and 4' after shearing, and the expressions corresponding to the other parameters are as follows:

[0034]

[0035] Substituting equations (1), (8) to (15) into (16) and (17), the expressions of magnetostrictive stress σ2 and magnetostrictive modulus ΔG2 in the shear-tension mode of the S chain micromechanism model are obtained as follows:

[0036]

[0037] Where γ is the external shear strain, θ is the angle between particles, and θ 13 is the particle chain rotation angle, θ 2′4′ is the angle between magnetic particles 2' and 4' after the change, r 2′5′ represents the distance between magnetic particles 2' and 5' after the change, r' 2′5′ Represents r 2′5′ Differential of shear strain γ, r″ 2′5′ Represents r′ 2′5′ Differentiation of the shear strain γ.

[0038] Furthermore, the r 2′5′ , r′ 2′5′ and r″ 2′5′ The expressions are:

[0039]

[0040] Furthermore, the expressions of the magneto-induced stress σ and magneto-induced modulus ΔG after the S chain micro-mechanism model is unified in step 4 are:

[0041]

[0042] Furthermore, the value of the random variable h is greater than or equal to 0.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. Compared with the existing chain microscopic mechanism model, the S-chain microscopic mechanism model has better accuracy in characterizing mechanical properties.

[0045] 2. The design method of the S-chain microscopic mechanism model proposed in the present invention starts from the chain-forming mechanism and magnetic interaction mechanism of the magnetic particles inside the magnetorheological elastomer, and systematically analyzes the S-chain arrangement of the magnetic particles. Taking into account that the actual magnetorheological elastomer is subjected to a mixture of compression, tension and shear during application, the unification of the tension-shear mode and the shear-stretch mode is achieved in the process of designing the S-chain microscopic mechanism model.

[0046] 3. The design method of the S-chain microscopic mechanism model proposed in the present invention also takes into account the fully coupled magnetic field, interface stretching effect and distribution parameters, further improving the accuracy of mechanical property characterization, which has important guiding significance for the subsequent preparation of magnetorheological elastomers. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the S chain formation process of the magnetorheological elastomer of the present invention.

[0048] Figure 2 Schematic diagram of the S chain microstructure of the present invention.

[0049] Figure 3 Schematic diagram of the stress condition of magnetorheological elastomer under ideal stretching conditions.

[0050] Figure 4 Schematic diagram of the stress condition of magnetorheological elastomer under ideal shear conditions.

[0051] Figure 5 Schematic diagram of the movement process of magnetic particles in shear-stretching mode.

[0052] Figure 6 It is a comparison chart of the theoretical values ​​and experimental values ​​of the S chain microscopic mechanism model of the present invention and the ideal tensile model.

[0053] Figure 7 It is a comparison chart of the theoretical values ​​and experimental values ​​of the S chain microscopic mechanism model and the ideal shear model of the present invention. DETAILED DESCRIPTION

[0054] Advantages and features of the present invention will be illustrated and explained by the following non-limiting description of preferred embodiments thereof, which are given by way of example only with reference to the accompanying drawings.

[0055] The present invention provides a design method for a magnetorheological elastomer S chain microscopic mechanism model, such as Figure 1 As shown, the following steps are included:

[0056] Step 1: applying an external magnetic field to the magnetorheological elastomer.

[0057] At the moment an external magnetic field is applied to the magnetorheological elastomer, the internal magnetic particles will aggregate along the direction of the magnetic field due to magnetization to form multiple straight chains, while some suspended magnetic particles dispersed in the matrix material that have not formed chains will be attracted by the surrounding straight chains and move closer to the straight chains, and the internal force will gradually stabilize.

[0058] Step 2: Magnetic particle chains of different thicknesses interact with each other to form several short chains of different thicknesses.

[0059] Due to the uneven distribution of local magnetic particles, the magnetic particle chains formed after chain attraction will have different thicknesses. The magnetic particles on chains of different thicknesses move in a small range due to the interaction force (following the principle that the same magnetic field attracts each other and approaches each other, and different magnetic fields repel each other and move away from each other). During the movement, the magnetic particles will also be subject to resistance from the matrix material, and eventually tend to balance in such a dynamic process, thus forming countless short chains of different thicknesses.

[0060] In step 3, all the attracted single or multiple suspended magnetic particles are uniformly assumed to be a whole, and the magnetic particle chain after the changes in steps 1 and 2 is the S chain structure of the present invention.

[0061] Idealize the actually attracted suspended magnetic particles, that is, assume that all attracted single or multiple (less than 3) suspended magnetic particles are unified as a whole. The magnetic particle chain after the changes in step 1 and step 2 can be defined as an S chain structure. The schematic diagram of the S chain structure is shown in Figure 2 As shown, d0 is the relative distance between S chains, d is the absolute distance between adjacent magnetic particles along the S chain direction, D is the vertical distance between adjacent magnetic particles on the axis inside the S chain, 2R is the distance between magnetic particles on the same axis inside the S chain, θ 67 is the relative position angle between adjacent magnetic particles on different axes inside the S chain.

[0062] Step 4, select three consecutive adjacent magnetic particles 1, 2 and 3 on the same S chain to form a microunit, apply ideal stretching to the microunit while considering the shearing effect, and obtain the magneto-stress σ1 and magneto-modulus ΔG1 in the stretching-shear mode: select a microunit composed of magnetic particles 1, 2 and 3 and add two magnetic particles 4 and 5 adjacent to the same axis of adjacent S chains to form a new microunit, apply ideal shearing effect to the new microunit while considering the stretching effect, and obtain the magneto-stress σ2 and magneto-modulus ΔG2 in the shear-stretching mode: unify the stretching-shear mode and the shear-stretching mode to obtain the S chain microscopic mechanism model.

[0063] When an ideal external tensile force is applied to the magnetorheological elastomer in the vertical direction, the magnetic particles inside a single S chain will first produce an upward and downward tensile displacement, such as Figure 3 As shown. Taking the adjacent magnetic particles 6 and 7 in the same S chain as an example, when the magnetic particle 6 is stretched upward, the magnetic particle 7 is subjected to the attractive force F1 from the magnetic particle 6. The external tensile force F needs to overcome the existing attractive force F1 and the resistance between the magnetic particles and the matrix. Since F1 has a horizontal stress component, the actual magnetorheological elastomer will have a horizontal interface contraction (i.e., a certain shear displacement σ is generated) after being subjected to a vertical tensile force. w). This interface expansion and contraction leads to a shortening of the distance between different S chains. When the distance is shortened, different S chains will have an attraction or repulsion effect, and eventually tend to be stable in this dynamic process.

[0064] When an ideal external shear force is applied to the magnetorheological elastomer, the up-and-down shear slip between different S chains plays a dominant role, such as Figure 4 As shown. Since there is an attraction F2 between magnetic particles in a single S chain, when this attraction is greater than the resistance between the magnetic particles and the matrix, the magnetic particles will produce a small horizontal deformation. From the macroscopic effect, the magnetorheological elastomer will also produce a certain compression displacement due to lateral contraction after being subjected to an ideal shear force.

[0065] Select three consecutive adjacent magnetic particles 1, 2 and 3 on the S chain to form a microunit, and the magnetic particles are equivalent to ideal magnetic dipoles. When tensile strain ε occurs, under the action of an external magnetic field H, the interaction energy value between magnetic dipoles in the microunit is:

[0066]

[0067] In the formula, E 12 、E 23 and E 13 are the energy values ​​between magnetic particles 1 and 2, magnetic particles 2 and 3, and magnetic particles 1 and 3, respectively; μ0 is the vacuum magnetic permeability; μ1 is the relative magnetic permeability of the matrix material; d′ is the absolute distance between adjacent magnetic particles along the S chain after stretching; R′ is half the distance between magnetic particles on the same axis inside the S chain after stretching; and D′ is the vertical distance between magnetic particles on adjacent axes inside the S chain after stretching. m is the magnetic dipole moment, and its expression is:

[0068]

[0069] Where μ0 is the vacuum magnetic permeability, μ1 is the relative magnetic permeability of the matrix material, r is the radius of the magnetic particle, χ is the magnetic susceptibility of the magnetic particle, H0 is the strength of the external magnetic field, and C is an intermediate variable generally taken as 1.2.

[0070] Assumptions is the number of microunits in a single S chain, and there are n in total per unit volume. 2 S chains, the total interaction energy between magnetic dipoles per unit volume is

[0071]

[0072] Magnetorheological elastomers satisfy the assumptions of constant volume and constant area. To further reveal the relationship between structural parameters before and after stretching, a power series hypothesis is proposed. The power series hypothesis describes the position relationship of the magnetic dipole before and after deformation as:

[0073]

[0074] In the formula, λ is the material microstructure parameter, and const is a constant. To further characterize the relative distance between adjacent magnetic dipoles, a random variable h (h ≥ 0) is introduced, and the relationship between R and r can be expressed as R = (1 + h) r.

[0075] Assume that the lateral contraction of the magnetorheological elastomer is Then the distance change Δd between two adjacent S-chain magnetic dipoles is The distance between all chains is d i = total magnetic dipole interaction energy E of i(d0-Δd) d for:

[0076]

[0077] Average magnetic energy density U of magnetorheological elastomer T It can be expressed as

[0078]

[0079] Where V is the total volume of the magnetorheological elastomer. Assuming that the material is uniformly stretched macroscopically, the total magnetic energy is converted into the elastic energy of tensile stress and strain. The magnetostrictive stress σ1 and magnetostrictive modulus ΔG1 can be expressed as:

[0080]

[0081] Substituting equations (3) to (7) into equations (8) and (9) above, we can obtain the magneto-induced stress σ1 and magneto-induced modulus ΔG1 in the tensile-shear mode of the S chain micro-mechanism model:

[0082]

[0083]

[0084] In the formula, A and B are intermediate variables, and the corresponding expressions are as follows:

[0085]

[0086] On the basis of the microunit composed of magnetic particles 1, 2 and 3, two magnetic particles 4 and 5 adjacent to the same axis of adjacent S chains are added to form a new microunit. The specific force conditions and position changes when subjected to shear force are shown in the following figure. Figure 5 shown. Figure 5In the figure, the numbers 1, 2', 3', 4' and 5' are obtained after the magnetic particles 1, 2, 3, 4 and 5 are subjected to shear force. When there is external shear force, the magnetic particles at the inflection point of the S chain (magnetic particle 2) and the adjacent S chains have a shear strain γ in one direction, and the angle θ between the magnetic particles becomes larger; however, the interaction between the magnetic particles is not stable, and the attraction between the magnetic particles needs to overcome the resistance between the magnetic particles and the matrix, which will cause the overall chain to rotate θ 13 According to the change process of magnetic particles, the following three model assumptions are proposed:

[0087] 1) The spatial relative relationship between the magnetic particles 1, 2', and 3' remains unchanged after rotation;

[0088] 2) Δd is the change in distance between S chains. For ease of analysis, let Δd = kγ (k is a constant);

[0089] 3) After rotation, the magnetic particle 2' is perpendicular to the direction of the right chain.

[0090] Considering the interaction between the intermediate magnetic particles 2 and other magnetic particles, the average magnetic energy density U of the magnetorheological elastomer is s for:

[0091]

[0092]

[0093] Where θ is the angle between magnetic particles, θ 13 is the rotation angle of the magnetic particle chain, θ 2′4′ is the angle between magnetic particles 2' and 4' after the change, r 2′5′ represents the distance between magnetic particles 2' and 5' after the change, E 12’ 、E 2’3’ 、E 2’5’ and E 2’4’ They represent the energy values ​​between the magnetic particle 2' and the magnetic particles 1, 3', 5' and 4' after shearing, and the expressions corresponding to the other parameters are as follows:

[0094]

[0095] Substituting equations (3), (14) to (21) into equations (22) and (23), we can obtain the magnetostrictive stress σ2 and magnetostrictive modulus ΔG2 in the shear-tension mode of the S chain microscopic mechanism model:

[0096]

[0097]

[0098] Where U12′ , U 2′3′ , U 2′5′ and U 2′4′ are the average magnetic energy density between magnetic particles 1 and 2', 2' and 3', 2' and 5', 2' and 4', σ 12′ , σ 2′3′ , σ 2′5′ and σ 2′4′ are the magnetostrictive stresses between magnetic particles 1 and 2', 2' and 3', 2' and 5', and 2' and 4', respectively. 2′5′ represents the distance between magnetic particles 2' and 5' after the change, r' 2′5′ Represents r 2′5′ Differential of shear strain γ, r″ 2′5′ Represents r′ 2′5′ Differential of shear strain γ, r′ 2′5′ and r″ 2′5′ The expressions are

[0099]

[0100] In step 4, the expressions of magneto-stress σ and magneto-modulus ΔG after the S-chain micro-mechanism model is unified are:

[0101]

[0102] like Figure 6 As shown, the theoretical value of the S chain micro-mechanism model of the magnetorheological elastomer designed by the present invention under the stretching-shear mode is compared with the theoretical values ​​of the stretching experiment and the ideal stretching model. When the volume fraction of the magnetic particles is 15%, the theoretical value of the S chain micro-mechanism model under the stretching-shear mode is greater than the stretching test result, and less than the theoretical value of the ideal stretching model. When the strain is less than 5%, the theoretical value of the S chain micro-mechanism model is closer to the stretching test result; when the volume fraction of the magnetic particles is 25%, the theoretical value of the S chain micro-mechanism model under the stretching-shear mode is closer to the stretching test result than the theoretical value of the ideal stretching model, and has higher accuracy.

[0103] like Figure 7 As shown, the theoretical value of the shear-stretch mode of the S-chain micro-mechanism model of the magnetorheological elastomer designed by the present invention is compared with the theoretical values ​​of the shear experiment and the ideal shear model. As the strength of the applied magnetic field increases, the magneto-modulus shows a nonlinear change, and the theoretical value of the stretch-shear mode of the S-chain micro-mechanism model is closer to the experimental result than the ideal shear model, and has higher accuracy.

[0104] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solutions formed by equivalent replacement or equivalent transformation shall fall within the protection scope required by the present invention.

Claims

1. A design method for a magnetorheological elastomer S chain microscopic mechanism model, characterized in that: The following steps are involved: Step 1, applying an external magnetic field to the magnetorheological elastomer; Step 2: Magnetic particle chains of different thicknesses interact with each other to form several short chains of different thicknesses; Step 3, all the attracted single or multiple suspended magnetic particles are uniformly assumed to be a whole, and the magnetic particle chain after the change in steps 1 and 2 is the S chain structure of the present invention; Step 4, select three consecutive adjacent magnetic particles 1, 2 and 3 on the same S chain to form a microunit, apply ideal stretching to the microunit while considering the shearing effect, and obtain the magneto-stress σ1 and magneto-modulus ΔG1 in the stretching-shear mode: select a microunit composed of magnetic particles 1, 2 and 3 and add two magnetic particles 4 and 5 adjacent to the same axis of adjacent S chains to form a new microunit, apply ideal shearing effect to the new microunit while considering the stretching effect, and obtain the magneto-stress σ2 and magneto-modulus ΔG2 in the shear-stretching mode: unify the stretching-shear mode and the shear-stretching mode to obtain the S chain microscopic mechanism model.

2. The design method of a magnetorheological elastomer S chain microscopic mechanism model according to claim 1, characterized in that: The expression of the magnetic dipole magnetic moment m in step 4 is: Assumptions is the number of microunits in a single S chain, and there are n in total per unit volume. 2 S chains, the total interaction energy between magnetic dipoles per unit volume is: Magnetorheological elastomers satisfy the assumptions of constant volume and constant area. In order to further reveal the relationship between the structural parameters before and after stretching, a power series hypothesis is proposed. The power series hypothesis describes the position relationship of the magnetic dipole before and after deformation as: In the formula, λ is the material microstructure parameter, and const is a constant. To further characterize the relative distance between adjacent magnetic dipoles, a random variable h is introduced. The relationship between R and r can be expressed as R = (1 + h) r. Assume that the lateral contraction of the magnetorheological elastomer is Then the distance change Δd between two adjacent S-chain magnetic dipoles is The distance between all chains is d i = total magnetic dipole interaction energy E of i(d0-Δd) d for: Average magnetic energy density U of magnetorheological elastomer T It can be expressed as: Assuming that the material is uniformly stretched macroscopically, the total magnetic energy is converted into elastic energy of tensile stress and strain, then the magneto-induced stress σ1 and magneto-induced modulus ΔG1 can be expressed as: Substituting the above equations (1) to (5) into (6) and (7), the expressions of the magnetostrictive stress σ1 and magnetostrictive modulus ΔG1 in the tensile-shear mode of the S chain microscopic mechanism model are obtained as follows: Wherein, μ0 is the vacuum magnetic permeability, μ1 is the relative magnetic permeability of the matrix material, r is the radius of the magnetic particle, φ is the volume fraction of the magnetic particle, χ is the magnetic susceptibility of the magnetic particle, H0 is the strength of the external magnetic field, ε is the tensile strain, D is the vertical distance between adjacent axis particles inside the S chain, 2R is the distance between particles on the same axis inside the S chain, λ is the material microstructure parameter, h is a random variable, d is the absolute distance between adjacent particles, d0 is the relative distance between adjacent S chains, A, B, and C are intermediate variables, n is the number of magnetic particles on a single S chain, and i is any particle on a single S chain.

3. The design method of a magnetorheological elastomer S chain microscopic mechanism model according to claim 2, characterized in that: The value of C is 1.

2.

4. The design method of a magnetorheological elastomer S chain microscopic mechanism model according to claim 3, characterized in that: The expressions of A and B are:

5. The design method of a magnetorheological elastomer S chain microscopic mechanism model according to claim 4, characterized in that: In step 4, the interaction between the intermediate magnetic particles 2' and other magnetic particles is considered, and the average magnetic energy density U of the magnetorheological elastomer is s for: Where θ is the angle between magnetic particles, θ 13 is the rotation angle of the magnetic particle chain, θ 2′4′ is the angle between magnetic particles 2' and 4' after the change, r 2′5′ represents the distance between magnetic particles 2' and 5' after the change, E 12’ 、E 2’3’ 、E 2’5’ and E 2’4’ They represent the energy values ​​between the magnetic particle 2' and the magnetic particles 1, 3', 5' and 4' after shearing, and the expressions corresponding to the other parameters are as follows: Substituting equations (1), (8) to (15) into (16) and (17), the expressions of magnetostrictive stress σ2 and magnetostrictive modulus ΔG2 in the shear-tension mode of the S chain micromechanism model are obtained as follows: Where γ is the external shear strain, θ is the angle between particles, and θ 13 is the particle chain rotation angle, θ 2′4′ is the angle between magnetic particles 2' and 4' after the change, r 2′5′ represents the distance between magnetic particles 2' and 5' after the change, r' 2′5′ Represents r 2′5′ Differential of shear strain γ, r″ 2′5′ Represents r′ 2′5′ Differentiation of the shear strain γ.

6. The design method of a magnetorheological elastomer S chain microscopic mechanism model according to claim 5, characterized in that: The r 2′5′ , r′ 2′5′ and r″ 2′5′ The expressions are:

7. The design method of a magnetorheological elastomer S chain microscopic mechanism model according to claim 6, characterized in that: The expressions of the magneto-stress σ and magneto-modulus ΔG after the S chain micro-mechanism model is unified in step 4 are:

8. The method for designing a microscopic mechanism model of an S chain of a magnetorheological elastomer according to any one of claims 2 to 7, characterized in that: The value of the random variable h is greater than or equal to 0.

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