Mechanical method, device, computer and storage medium for zero-stress expansion of cylinder

Abstract

A mechanical method, device, computer and storage medium for zero-stress unfolding of a cylinder, relating to the field of mechanics. The method solves the problem that the design of flexible electronic substrate micro-nanostructures with good adhesion to spatial surfaces relies on the designer's experience, has a long cycle, high substrate processing costs and poor versatility. The method includes: constructing a mechanical model for zero-stress unfolding of a cylinder; obtaining an isometric mapping of the surface based on the mechanical model and displacement field theory; setting boundary conditions based on the isometric mapping of the surface; solving based on the boundary conditions and the isometric mapping of the surface to obtain various parameters of the unfolded surface. Setting boundary conditions based on the isometric mapping of the surface includes: setting boundary conditions of the target surface, boundary conditions of the upper and lower surfaces, and boundary conditions in the x-direction. The present invention is applied to the field of flexible electronic technology.

Description

Technical Field

[0001] The present invention relates to the field of mechanics, and in particular to a mechanical method for zero-stress expansion of a cylinder. Background Art

[0002] In recent years, with the continuous development of flexible electronics technology, it has shown promising application prospects in wearable detection systems for human physiological signals. Many researchers at home and abroad have conducted extensive research on the application of flexible wearable devices in human physiological signal monitoring; however, numerous technical bottlenecks remain. Among these, the mechanical challenges arising from the conformation of flexible wearable devices to irregularly curved body surfaces are particularly prominent. The human body surface is typically non-developable and exhibits large variations in curvature. Current mainstream flexible wearable devices are manufactured on planar substrates. This results in large and uneven stresses when these planar devices are applied to the body surface, leading to inconsistent performance between device elements and inconsistent responses to external contact force signals. To address the mechanical challenges of flexible wearable devices, large deformation design is often employed. However, this approach relies heavily on the researcher's experience, has a long design cycle, high substrate manufacturing costs, and limited versatility. Summary of the Invention

[0003] The present invention solves the problems from a mechanical point of view that the design of flexible electronic substrate micro-nanostructure with good adhesion to spatial curved surfaces relies on the designer's experience, has a long cycle, high substrate processing cost and poor versatility.

[0004] The present invention provides a mechanical method for zero-stress expansion of a cylinder, the method comprising:

[0005] Construct a mechanical model of zero-stress expansion of a cylinder;

[0006] Obtaining an isometric mapping of the surface according to the mechanical model and displacement field theory;

[0007] setting boundary conditions according to an isometric mapping of the surface;

[0008] The boundary conditions and the isometric mapping of the surface are solved to obtain various parameters of the unfolded surface.

[0009] Furthermore, a preferred embodiment is provided, wherein the construction of a mechanical model for zero-stress expansion of a cylinder includes:

[0010]

[0011] in, is a variable, is a variable, As the guideline, For the busbar, For about x function, For about x function.

[0012] Furthermore, a preferred embodiment is provided, wherein obtaining an isometric mapping of a surface according to the mechanical model and displacement field theory comprises:

[0013] ,

[0014] ,

[0015] ,

[0016] in, For x Normal stress in the direction, For y Normal stress in the direction, for xoy The tangential stress on the plane, is the thickness of the cylinder directrix before deformation, is the stress function, is the equal division of the angle, is the stress function The constant term after the trigonometric series expansion is, is the stress function The constant term after the trigonometric series expansion is, 、 、 and is the stress function The constant term after the expansion of a trigonometric series.

[0017] Furthermore, a preferred embodiment is provided, wherein setting boundary conditions according to the isometric mapping of the surface includes setting boundary conditions of the target surface, boundary conditions of the upper and lower surfaces, and boundary conditions in the x-direction.

[0018] Based on the same inventive concept, the present invention also provides a cylindrical zero-stress expansion device based on mechanics, the device comprising:

[0019] Mechanical model building unit, used to build a mechanical model of cylindrical zero-stress expansion;

[0020] A surface isometric mapping acquisition unit, configured to acquire the surface isometric mapping according to the mechanical model and displacement field theory;

[0021] a boundary condition setting unit, configured to set boundary conditions according to the isometric mapping of the surface;

[0022] The surface parameter acquisition unit is used to solve the boundary conditions and the isometric mapping of the surface to obtain the parameters of the unfolded surface.

[0023] Furthermore, a preferred embodiment is provided, wherein the structural mechanics model building unit comprises:

[0024]

[0025] in, is a variable, is a variable, As the guideline, For the busbar, For about x function, For about x function.

[0026] Furthermore, a preferred embodiment is provided, wherein the surface isometric mapping acquisition unit comprises:

[0027] ,

[0028] ,

[0029] ,

[0030] in, For x Normal stress in the direction, For y Normal stress in the direction, for xoy The tangential stress on the plane, is the thickness of the cylinder directrix before deformation, is the stress function, is the equal division of the angle, is the stress function The constant term after the trigonometric series expansion is, is the stress function The constant term after the trigonometric series expansion is, 、 、 and is the stress function The constant term after the expansion of a trigonometric series.

[0031] Furthermore, a preferred embodiment is provided, wherein the boundary condition setting unit includes: setting boundary conditions of the target surface, boundary conditions of the upper and lower surfaces, and boundary conditions in the x-direction.

[0032] Based on the same inventive concept, the present invention also provides a computer-readable storage medium, which is used to store a computer program, and the computer program executes any one of the mechanical methods for zero-stress expansion of a cylinder as described above.

[0033] Based on the same inventive concept, the present invention also provides a computer device, including a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a mechanical method for zero-stress expansion of a cylinder as described in any one of the above items.

[0034] The present invention is beneficial in that:

[0035] The present invention solves the problems from a mechanical point of view that the design of flexible electronic substrate micro-nanostructure with good adhesion to spatial curved surfaces relies on the designer's experience, has a long cycle, high substrate processing cost and poor versatility.

[0036] The present invention approximates the human body surface as being composed of different cylindrical surfaces, proposes a mechanical method for zero-stress expansion of cylindrical surfaces, and constructs a mechanical model for zero-stress expansion of cylindrical surfaces; obtains an isometric mapping of the surface based on the mechanical model and displacement field theory; sets boundary conditions based on the isometric mapping of the surface; solves the boundary conditions and the isometric mapping of the surface to obtain various parameters of the expanded surface, thereby achieving zero-stress expansion of the cylindrical surfaces, and using the expanded plane as a substrate for manufacturing electronic devices. Array devices are then manufactured on the plane substrate, and finally reverse lamination is performed. This research idea can solve the problems of poor precision and poor versatility in traditional manufacturing and lamination methods.

[0037] The present invention is applied to the field of flexible electronic technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of a mechanical method for zero-stress expansion of a cylinder as described in embodiment 1;

[0039] Figure 2 Schematic diagram of the mechanical model of the cylindrical zero-stress expansion according to the second embodiment;

[0040] Figure 3 This is the resultant force distribution diagram described in the eleventh embodiment;

[0041] Figure 4 A comparison diagram of the original curve and the derivative function of the solution curve described in the eleventh embodiment;

[0042] Figure 5 For the eleventh embodiment x The normal stress in the direction varies with the position;

[0043] Figure 6For the eleventh embodiment y The normal stress in the direction varies with the position;

[0044] Figure 7 This is a graph showing the shear stress changing with position in the eleventh embodiment. DETAILED DESCRIPTION

[0045] In order to make the technical solutions and advantages of the present invention more clearly described, several embodiments of the present invention are now described in further detail with reference to the accompanying drawings. However, the various embodiments described below are only a few preferred embodiments of the present invention and are not intended to limit the invention.

[0046] Implementation method 1, see Figure 1 This embodiment describes a mechanical method for zero-stress expansion of a cylinder, the method comprising:

[0047] Construct a mechanical model of zero-stress expansion of a cylinder;

[0048] Obtaining an isometric mapping of the surface according to the mechanical model and displacement field theory;

[0049] setting boundary conditions according to an isometric mapping of the surface;

[0050] The boundary conditions and the isometric mapping of the surface are solved to obtain various parameters of the unfolded surface.

[0051] Specifically, the conditions for constructing the mechanical model of cylindrical zero stress expansion are as follows:

[0052] The plane curve is used as the directrix, and the generatrix is ​​perpendicular to the cylinder of the directrix. , busbar The plane curve (here, the plane curve is relative to the space curve) is infinitely long along its length, simplifying the mechanical problem of zero-stress expansion of the cylinder to a plane stress-strain problem. Solving the problem under the condition that the plane curve has no body forces, the stress function exists, and a mechanical model of the zero-stress expansion of the cylinder can be constructed.

[0053] Implementation method 2, see Figure 2 This embodiment further defines the mechanical method for zero-stress expansion of a cylinder described in Embodiment 1. The mechanical model for zero-stress expansion of a cylinder includes:

[0054]

[0055] in, is a variable, is a variable, As the guideline, For the busbar, For aboutx function, For about x function.

[0056] Specifically, the cylinder is composed of Point on a plane The surface equation is mapped to . Let the initial length of the cylinder directrix before deformation be , thickness is ,exist The width of the direction is .

[0057] Implementation method 3: This implementation method further limits the mechanical method of cylindrical zero-stress expansion described in implementation method 1. The isometric mapping of the surface obtained according to the mechanical model and displacement field theory includes:

[0058] ,

[0059] ,

[0060] ,

[0061] For the stress function , satisfying the compatibility equation According to the separation of variables method, = f ( x ) g ( y ), and f ( x ) is expanded into a trigonometric series, we can get .

[0062] Specifically, obtaining the isometric mapping of the surface according to the mechanical model and displacement field theory includes: calculating the displacement field according to the formula:

[0063] (1)

[0064] in, are the variables in the expanded plane, is the plane variable within the expansion, is the plane variable within the expansion, For about x function, For about x function.

[0065] The strain of the surface model only occurs In the plane, it conforms to the definition of plane strain problem. That is, the strain component in the region is only function, and It is irrelevant. According to the isometric mapping relationship of the cylinder, the directrix is ​​a plane curve (Formula 2), that is:

[0066] (2)

[0067] The positive strain can be obtained:

[0068] (3)

[0069] in, for x Direction positive strain, for y Direction positive strain, for z Direction positive strain.

[0070] The shear strain can be obtained:

[0071] (4)

[0072] in, for xy In-plane shear strain, for yz In-plane shear strain, for xz In-plane shear strain.

[0073] The generalized Hooke's law of isotropic materials is used as the constitutive equation. When the elastic modulus of the material is known to be , Poisson's ratio is Under the condition of , the stress can be calculated as follows:

[0074] (5)

[0075] (6)

[0076] in, for yz In-plane shear strength, for zx In-plane shear strength, for xy In-plane shear strength, is the elastic modulus of the material.

[0077] For the stress function , satisfying the compatibility equation:

[0078] (7)

[0079] According to the separation of variables method: , and Expanding with trigonometric series, we get:

[0080] (8)

[0081] The solution is:

[0082] (9)

[0083] Bringing it back to the stress function expression, we can get:

[0084] (10)

[0085] According to the relationship between stress function and stress component, and noting that n =0, . So we can get:

[0086] (11)

[0087] (12)

[0088]

[0089] in, For x Normal stress in the direction, For y Normal stress in the direction, is the tangential stress on the xoy plane, is the thickness of the cylinder directrix before deformation, is the stress function, = n π / l (in, l is the initial base length of the alignment line before deformation), is the equal division of the angle, is the stress function The constant term after the trigonometric series expansion is, is the stress function The constant term after the trigonometric series expansion is, 、 、 and is the stress function The constant term after the expansion of a trigonometric series.

[0090] Implementation method 4. This implementation method further limits the mechanical method of cylindrical zero stress expansion described in implementation method 1. The boundary conditions set according to the isometric mapping of the surface include: setting the boundary conditions of the target surface, the boundary conditions of the upper and lower surfaces, and the x-direction boundary conditions.

[0091] Specifically, setting boundary conditions includes:

[0092] (1) Setting the boundary conditions of the target surface includes:

[0093] (14)

[0094] (15)

[0095] (16)

[0096] in, .

[0097] Therefore, formula (16) must satisfy the The coefficient of this expansion term is 0, that is:

[0098] (17)

[0099] That is, in the above results For other terms, according to the expansion results, the coefficients can be obtained :

[0100] (18)

[0101]

[0102] (2) Set the upper and lower surface boundary conditions as follows:

[0103] For upper and lower surfaces , which corresponds to the surface normal vector , so that the shear stress on the surface is zero. Therefore, the boundary condition is:

[0104] (20)

[0105]

[0106] Simplifying, we can get: .

[0107] (twenty one)

[0108] As an additional condition to close the equation. Combining (20) and (21) we can solve ; According to (18) (19), we can solve , so far all the solutions have been completed.

[0109] (3) Settings x Directional boundary conditions:

[0110] (twenty two)

[0111]

[0112] in, for Figure 2 The shear stress at the far left, for Figure 2 Shear stress at the far right.

[0113] The missing resultant couple due to the relaxation of the stress in the x-direction:

[0114] (twenty four)

[0115] The above resultant moment is applied as Figure 2 For the force system shown, we can obtain:

[0116] (25)

[0117] Finally, given the analytical method of the target curve, it can be analyzed that for the target surface, the directrix equation on the given surface is given as According to the above analysis, we can get , combined with the conditions of (2), we can get:

[0118] .

[0119] Embodiment 5: A cylindrical zero-stress expansion device based on mechanics described in this embodiment includes:

[0120] Mechanical model building unit, used to build a mechanical model of cylindrical zero-stress expansion;

[0121] A surface isometric mapping acquisition unit, configured to acquire the surface isometric mapping according to the mechanical model and displacement field theory;

[0122] a boundary condition setting unit, configured to set boundary conditions according to the isometric mapping of the surface;

[0123] The surface parameter acquisition unit is used to solve the boundary conditions and the isometric mapping of the surface to obtain the parameters of the unfolded surface.

[0124] Implementation 6: This implementation is a further limitation of the cylindrical zero-stress expansion device based on mechanics described in Implementation 5. The mechanics model building unit includes:

[0125]

[0126] in, is a variable, is a variable, As the guideline, For the busbar, For about x function, For about x function.

[0127] Embodiment 7: This embodiment further limits the cylindrical zero-stress expansion device based on mechanics described in Embodiment 5. The surface isometric mapping acquisition unit includes:

[0128] ,

[0129] ,

[0130] ,

[0131] in, For x Normal stress in the direction, For y Normal stress in the direction, is the tangential stress on the xoy plane, is the thickness of the cylinder directrix before deformation, is the stress function, = n π / l (in l is the initial base length of the alignment line before deformation), so is the equal division of the angle, is the stress function The constant term after the trigonometric series expansion is, is the stress function The constant term after the trigonometric series expansion is, 、 、 and is the stress function The constant term after the trigonometric series expansion.

[0132] Implementation 8. This implementation further limits the mechanics-based cylindrical zero-stress expansion device described in Implementation 5. The boundary condition setting unit includes: setting boundary conditions of the target surface, boundary conditions of the upper and lower surfaces, and boundary conditions in the x-direction.

[0133] Implementation method 9. A computer-readable storage medium described in this implementation method is used to store a computer program, and the computer program executes a mechanical method for zero-stress expansion of a cylinder described in any one of implementation methods 1 to 4.

[0134] Implementation method 10. A computer device described in this implementation method includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a mechanical method for zero-stress expansion of a cylinder described in any one of implementation methods 1 to 4.

[0135] Implementation method 11, see Figures 3 to 7 This embodiment provides a specific implementation method for the mechanical method of zero-stress expansion of a cylinder described in the first embodiment, and is also used to explain the second to fourth embodiments. Specifically:

[0136] The initial length of the cylinder directrix before deformation is , thickness is ,in, l =10mm, h =0.5mm. The differential form of the given curve is , and give the initial conditions f (0)=0.

[0137] Natural rubber is selected as the material, and its elastic modulus E =6.1MPa, Poisson's ratio μ =0.49.

[0138] when m When I was very young, ≈1. At this point, the curve can be roughly approximated as a parabola. In actual calculations, take m =0.001. The following solution is obtained through theoretical analysis and numerical simulation calculation.

[0139] Obviously, the differential function of the given curve is an even function, Figure 2 As shown in q ( x )and q 1( x ) is symmetrical about the y-axis, the resultant force R 2= R 1; At this point, the torque is automatically balanced and there is no need to apply a resultant couple M. The solution is given below.

[0140] After the above steps, we can get the resultant force R 2= R 1=0.6791N, distributed force q ( x )=- q 1( x ), and its distribution results are as follows Figure 3 shown.

[0141] By using numerical results calculated curve and compare it with Figure 3 The curve comparison in Figure 4 The degree of fit between the two curves (very good) proves the accuracy of the calculation results of the mechanical method for zero-stress expansion of a cylinder described in this embodiment.

[0142] On this basis, the results of stress solution are displayed , can be obtained from Figure 5 and Figure 6 See, in y = 0 surface does not have normal stress, such as Figure 7 As shown in the figure, the shear stress is also very small, which basically achieves the goal of near-zero stress. In addition, the shear stress on the upper and lower surfaces is zero, which is the same as the boundary setting.

[0143] The above proves from the mechanical theory that the method proposed in this embodiment is effective for zero-stress expansion of the cylinder. The following finite element simulation technology is carried out on the above specific embodiment to further confirm that the method of the present invention can achieve zero-stress expansion of the cylinder.

[0144] First, a finite element model of a portion of the cylinder is established. The model is configured based on the cylinder's geometric dimensions and material properties, including the selected calculation equations, boundary conditions, and calculation termination conditions. The core of this model is the edge zero displacement constraint.

[0145] Next, the model is calculated.

[0146] Although the preferred embodiments of the present disclosure have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present disclosure.

[0147] Obviously, those skilled in the art may make various changes and modifications to the present disclosure without departing from the spirit and scope of the present disclosure. Thus, if these modifications and variations of the present disclosure fall within the scope of the claims of the present disclosure and their equivalents, the present disclosure is intended to include these modifications and variations.

[0148] Those skilled in the art will appreciate that the embodiments of the present disclosure may be provided as methods, systems, or computer program products. Therefore, the present disclosure may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present disclosure may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or box in the flowcharts and / or block diagrams, as well as the combination of processes and / or boxes in the flowcharts and / or block diagrams, may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing one or more processes and / or boxes in the flowchart. Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including the instruction device, which implements the function specified in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0149] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present disclosure and are not intended to limit its scope of protection. Although the present disclosure has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that after reading the present disclosure, those skilled in the art may still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the disclosed claims.

Claims

1. A mechanical method for zero-stress expansion of a cylinder, characterized in that: The method comprises: Construct a mechanical model of zero-stress expansion of a cylinder; Obtaining an isometric mapping of the surface according to the mechanical model and displacement field theory; setting boundary conditions according to an isometric mapping of the surface; Solving the boundary conditions and the isometric mapping of the surface to obtain various parameters of the unfolded surface; The mechanical model for constructing the cylindrical zero-stress expansion includes: in, is a variable, is a variable, As the guideline, For the busbar, For about x function, For about x function; The step of obtaining an isometric mapping of a surface according to the mechanical model and displacement field theory includes: ， ， ， in, For x Normal stress in the direction, For y Normal stress in the direction, is the tangential stress on the xoy plane, is the thickness of the cylinder directrix before deformation, is the stress function, is the equal division of the angle, is the stress function The constant term after the trigonometric series expansion is, is the stress function The constant term after the trigonometric series expansion is, 、 、 and is the stress function The constant term after the trigonometric series expansion.

2. A mechanical method for zero-stress expansion of a cylinder according to claim 1, characterized in that: The setting of boundary conditions according to the isometric mapping of the surface includes: setting boundary conditions of the target surface, boundary conditions of the upper and lower surfaces, and boundary conditions in the x-direction.

3. A mechanical device for zero-stress expansion of a cylinder, characterized in that: The device comprises: Mechanical model building unit, used to build a mechanical model of cylindrical zero-stress expansion; A surface isometric mapping acquisition unit, configured to acquire the surface isometric mapping according to the mechanical model and displacement field theory; a boundary condition setting unit, configured to set boundary conditions according to the isometric mapping of the surface; A surface parameter acquisition unit, configured to obtain various parameters of the developed surface by solving the boundary conditions and the isometric mapping of the surface; The mechanical model building unit includes: in, is a variable, is a variable, As the guideline, For the busbar, is a function of x, For about x function; The surface isometric mapping acquisition unit includes: ， ， ， in, For x Normal stress in the direction, For y Normal stress in the direction, for xoy The tangential stress on the plane, is the thickness of the cylinder directrix before deformation, is the stress function, is the equal division of the angle, is the stress function The constant term after the trigonometric series expansion is, is the stress function The constant term after the trigonometric series expansion is, 、 、 and is the stress function The constant term after the trigonometric series expansion.

4. A mechanical device for zero-stress expansion of a cylinder according to claim 3, characterized in that: The boundary condition setting unit includes: setting the boundary conditions of the target surface, the boundary conditions of the upper and lower surfaces and x Directional boundary conditions.

5. A computer-readable storage medium, characterized in that The computer-readable storage medium is used to store a computer program, and the computer program executes the mechanical method for zero-stress expansion of a cylinder according to any one of claims 1-2.

6. A computer device, characterized in that: The invention comprises a memory and a processor, wherein a computer program is stored in the memory, and when the processor runs the computer program stored in the memory, the processor executes a mechanical method for zero-stress expansion of a cylinder as described in any one of claims 1-2.

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