Development of Replica Molding Processes for Hypervariable Microstructural Components

Abstract

The current study investigates the development of a replica molding process for hypervariable microstructures. Initially, the mold deformation theory for these hypervariable microstructures was derived. Based on this theory, a metal material with magnetic properties was selected as the structural material to create a negative Poisson’s ratio (NPR) geometric structure. The experimental results, obtained by fabricating the NPR geometric mold layer with a metal material with adjustable magnetic properties and controlling microstructure deformation indirectly, validate the deformation theory and its predictions. These results demonstrate that the developed molding process, integrated with the magnetic NPR regulation system, exhibits excellent stability and replication capability. In this study, at the zero height (z = 0) position on the interface between the NPR geometric structure layer and the Polydimethylsiloxane (PDMS), the variation becomes more pronounced with increasing distance from the center of the microstructure. Furthermore, the tendency of the function curve varies accordingly. The primary cause is the lack of constraints on the free ends of both sides and the excessive constraints on the intermediate parts. Under the conditions in this study, the maximum ratio of its influence on the radial diameter thickness was 2.1%. This innovative process facilitates the rapid imprinting of microstructural components and offers the advantage of efficient molding.

1. Introduction

Science and technology are advancing rapidly. Currently, various applications are seeing significant progress, including consumer electronics, opto-electro-mechanical systems, display industries [1,2], and microlens array components), optical communication components, biomedical detection microsystems, and the semiconductor industry [3,4,5,6]. These fields are actively pursuing miniaturization and integration. The design of microsystems continues to focus on high performance at the product level. Given this focus, effectively designing and manufacturing the key components of increasingly thinner and smaller microsystems [7,8,9] is crucial.

The current approach to designing and manufacturing key microsystem components often involves integrating Micro-Electro-Mechanical System (MEMS) technologies [10,11,12,13,14,15,16], semiconductor process technologies, and Micro-Opto-Electro-Mechanical Systems (MOEMS) technologies [17,18,19,20,21]. These advanced technologies collaborate and complement each other. Additionally, after selecting and implementing the original microstructural component manufacturing technology at the front end of the line, it is necessary to consider mass-produced micro-molding processes to industrialize the production of molds in the subsequent back end of the line. This approach integrates the design process with development and production.

The term “metamaterials” [22,23,24] refers to artificial materials with unique properties achieved through modifications to their material composition, geometric structure, structural size, length, and curvature. Unlike traditional materials, metamaterials do not rely on specific chemical components; their properties result from specially designed geometric structures and scales determined by researchers. As a result, metamaterials can exhibit properties that differ from traditional materials, enabling cross-disciplinary applications and functions. In 2024, Wang et al. [25] proposed a Digital-Twin (DT) framework and a comprehensive information model that demonstrated both the accurate prediction of tube and the accurate prediction effectiveness of tube cross-section deformation.

In 2022, Su et al. [26] proposed an exponential function dimensionless-method to determine residual stress. The reverse algorithm was confirmed to be excellent for determining residual stresses to guide the optimization of the manufacturing process for critical structures. In this study, auxetic metal—an example of a metamaterial characteristic—was proposed and selected to design a geometric structure pattern to effectively control the microstructural mold. The uniqueness of this pattern was geometrically simulated and derived to assess its potential as a control method for the original microstructural mold. Furthermore, it is anticipated that the auxetic geometric structure, which combines metamaterial properties with the metal’s magnetic properties, will serve as the driving force for controlling the replication and imprinting processes of the microstructural mold. Accurate control of soft materials and replica imprinting is achieved by integrating this structure with a magnetic control system and utilizing the metal auxetic structure as a flexible control material. Moreover, this study aims to analyze and understand the microstructure variations in the microstructure patterns of the hypervariable and controllable microstructural mold. Based on the geometric and mechanical mechanism from fabrication to control and prediction, the systematic experiments in this study are expected to reduce the molding time of microstructures. They are also anticipated to accelerate the imprinting speed, address issues of incomplete imprinting, and develop innovative molds and applicable process methods for the imprinting system. The research results are expected to enhance the accuracy and speed of microstructure replica molding processes while reducing costs, thereby providing effective and innovative solutions for microstructure fabrication.

2. Hypervariable Microstructure Deformation Theory

2.1. Theory of the Microstructure’s Geometric Point without Any Height and Position Movements and Variations

This study utilized the cylindrical array microstructure as the primary research subject (Figure 1).

Initially, this section examines the variation in geometric position during the stretching process, specifically focusing on the zero height ($z=0$) position at the interface between the negative Poisson’s ratio (NPR) geometric structure and the PDMS. Point ${\mathsf{{\rm X}}}_1$ is designated as the initial position before stretching, while Point ${\mathsf{{\rm X}}}_2$ represents the new position of Point ${\mathsf{{\rm X}}}_1$ after stretching. The conversion formula ($\mathcal{M}$) for determining the position during the stretching process is derived, and the geometric displacement and change of ${\mathsf{{\rm X}}}_2$ are represented in Equations (1) and (2).

$${\mathsf{{\rm X}}}_2=\mathcal{M}·{\mathsf{{\rm X}}}_1$$

(1)

$$\left(\begin{array}{c}{x}_{2,i}\\ x_{2,j}\\ x_{2,k}\end{array}\right)=\left(\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right)\left(\begin{array}{c}{x}_{1,i}\\ x_{1,j}\\ x_{1,k}\end{array}\right)$$

(2)

A slight change in position ($\mathsf{\Delta }$) is observed during the stretching process. Additionally, the zero-height position ($z=0$) at the interface is considered. Thus, with $z_{1,k}=0,g=0,h=0$, Equation (2) can be expanded as Equation (3), as shown below.

$$\left\{\begin{array}{c}{\mathsf{\Delta }x}_{1,i}=a\cdot x_{1,i}+b\cdot y_{1,j}+c\cdot z_{1,k}\\ {\mathsf{\Delta }x}_{1,j}=d\cdot x_{1,i}+e\cdot y_{1,j}+f\cdot z_{1,k}\\ {\mathsf{\Delta }x}_{1,k}=g\cdot x_{1,i}+h\cdot y_{1,j}+i\cdot z_{1,k}\end{array}\right. ; \left\{\begin{array}{c}{\mathsf{\Delta }x}_{1,i}=a\cdot x_{1,i}+b\cdot y_{1,j}+c\cdot 0\\ {\mathsf{\Delta }x}_{1,j}=d\cdot x_{1,i}+e\cdot y_{1,j}+f\cdot 0\\ {\mathsf{\Delta }x}_{1,k}=0\cdot x_{1,i}+0\cdot y_{1,j}+i\cdot 0\end{array}\right.$$

(3)

Alternatively, Equation (2) can be expanded as Equation (4), as shown as follows:

$$\left\{\begin{array}{c}{x}_{2,i}=a\cdot x_{1,i}+b\cdot y_{1,j}+c\cdot z_{1,k}\\ x_{2,j}=d\cdot x_{1,i}+e\cdot y_{1,j}+f\cdot z_{1,k}\\ x_{2,k}=g\cdot x_{1,i}+h\cdot y_{1,j}+i\cdot z_{1,k}\end{array}\right. ; \left\{\begin{array}{c}{x}_{2,i}=a\cdot x_{1,i}+b\cdot y_{1,j}+c\cdot 0\\ x_{2,j}=d\cdot x_{1,i}+e\cdot y_{1,j}+f\cdot 0\\ x_{2,k}=g\cdot x_{1,i}+h\cdot y_{1,j}+i\cdot 0\end{array}\right.$$

(4)

where $a\to 1+a;e\to 1+e$, etc.

In terms of position coordinates, when $a=e$, the position change can be expressed as Equation (5), as shown in Figure 2.

$$\left(\begin{array}{c}{x}_{2,i}\\ x_{2,j}\\ x_{2,k}\end{array}\right)=\left(\begin{array}{c}{x}_{1,i}\\ x_{1,j}\\ x_{1,k}\end{array}\right)+∆\left(\begin{array}{c}{x}_{1,i}\\ x_{1,j}\\ x_{1,k}\end{array}\right)$$

(5)

If position coordinates are used for positioning, then position ${\mathsf{{\rm X}}}_2$ can be expressed according to Equation (6):

$${\mathsf{{\rm X}}}_2={\mathsf{{\rm X}}}_1+\mathcal{M}·{\mathsf{{\rm X}}}_1; {\mathsf{{\rm X}}}_2=(1+\mathcal{M}){\mathsf{{\rm X}}}_1$$

(6)

It is observed that “$a\mathrm{”}$ corresponds to longitudinal stretching, while “$e\mathrm{”}$ relates to lateral variation. For general NPR materials, $a>e$ and $a\ne e$. Therefore, when $z=0$, the conversion formula $\mathcal{M}$ can be expressed by Equation (7):

$$\mathcal{M}=\left(\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right)=\left(\begin{array}{ccc}a& 0& 0\\ 0& e& 0\\ 0& 0& 0\end{array}\right)$$

(7)

2.2. Theory of the Microstructure’s Geometric Point with Height and Position Movements and Variations

Continuing from the derivation formula in the previous section, this section considers the case when $z\ne 0$ and $x_{1,k}\ne 0$, as shown in Equation (8):

$$∆{\mathsf{{\rm X}}}_1=∆\left(\begin{array}{c}{x}_{1,i}\\ x_{1,j}\\ x_{1,k}\end{array}\right)=\left(\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right)\left(\begin{array}{c}{x}_{1,i}\\ x_{1,j}\\ x_{1,k}\end{array}\right)$$

(8)

Expanding this equation obtains the following:

$$\begin{array}{c}{\mathsf{\Delta }x}_{1,i}=a\cdot x_{1,i}+b\cdot y_{1,j}+c\cdot z_{1,k}\\ {\mathsf{\Delta }x}_{1,j}=d\cdot x_{1,i}+e\cdot y_{1,j}+f\cdot z_{1,k}\\ {\mathsf{\Delta }x}_{1,k}=g\cdot x_{1,i}+h\cdot y_{1,j}+i\cdot z_{1,k}\end{array}$$

In this section, the deformation perpendicular to the non-principal deformation is considered as the secondary deformation term of impacts ($b$). This term has a functional correlation $\left(y\right)$ with the distance and is a negative value. For simplicity, it is approximated as a negative linear variation effect (e.g., $b=-\mathrm{b}\left(y\right)=-\mathrm{b}\mathrm{y}$). Furthermore, the variation in the height of the PDMS microstructure layer ($z$) can also affect the secondary deformation term. This is expressed as Equation (9):

$$-\mathrm{b}\left(y,z\right)=-\left(b_y·y+b_z·z\right)$$

(9)

where $-\left(b_y·y\right)$ represents the negative influence of the secondary deformation term ($b$) on the principal deformation direction with respect to distance, while $-\left(b_z·z\right)$ represents the negative influence of the secondary deformation term ($b$) on the principal deformation direction with respect to height variation in the PDMS microstructure layer.

Since this study primarily focuses on the micron scale, the influence of the secondary deformation term b on the height variations of the microstructure layer is minimal compared with other non-principal deformation direction terms. Therefore, in this section, it is reasonable to ignore the influence of the secondary deformation term of impacts ($b$) with respect to height, as expressed by Equation (10):

$$-\mathrm{b}\left(y,z\right)->-\mathrm{b}\left(y\right)={-b}_y·y=-\mathrm{b}\mathrm{y}$$

(10)

Based on this simplification, it can be inferred that if all secondary deformation terms are disregarded, the impact on the deformation will be more pronounced as the distance from the zero height (z = 0) position at the interface between the NPR geometric structure and PDMS increases. The conversion matrix M is then represented as follows:

$$\mathcal{M}=\left(\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right)->\left(\begin{array}{ccc}a& 0& c\\ 0& e& f\\ 0& 0& i\end{array}\right); \left\{\begin{array}{c}c\Rightarrow c_{xi}\cdot z\Rightarrow c\cdot z\\ f\Rightarrow c_{yj}\cdot z\Rightarrow c\cdot z\\ i\Rightarrow c_{zk}\cdot z\Rightarrow c\cdot z\end{array}\right.$$

Considering that $(c_i<1$) and ($c_j<1);c_i\ne c_j->c_i\approx c_j\Rightarrow c$, the conversion formula ($\mathcal{M}$) can be simplified as shown in Equation (11):

$$\mathcal{M}=\left(\begin{array}{ccc}a& 0& c\\ 0& e& c\\ 0& 0& c\end{array}\right)$$

(11)

During the experimental process, stretching deformation prior to imprinting replication regulates the shape features of the single microstructure, as shown in Figure 3a. Considering the secondary deformation term of impacts, the conversion formula ($\mathcal{M}$) can be represented by Equation (12):

$$\mathcal{M}=\left(\begin{array}{ccc}a& -by& c\\ -dx& e& c\\ -gx& -hy& c\end{array}\right)$$

(12)

The results derived from the geometric theory suggest that the shape of the single microstructure that is regulated by stretching deformation before imprinting replication is shown in Figure 3b. In addition, at the zero height ($z=0$) position on the interface between the NPR geometric structure layer and the PDMS, the variation becomes more pronounced with increasing distance from the center of the microstructure. Furthermore, the tendency of the function curve varies accordingly.

3. Methods and Experiments

3.1. Geometric Structure Design and Mechanical Properties Simulation Analysis and Test of Magnetic Nickel Multilayer Mold

This study utilized a laminating magnetic nickel metal four-pointed star to design the geometric structure of the main intermediate layer as the regulatory pattern for NPR. A laminating magnetic nickel material was employed as the intermediate layer, with the NPR geometric structure serving as the primary control method for the microstructural mold. In this section, the mechanical properties of the magnetic nickel material were numerically simulated using the standard test scale setting (ISO6892-1 [27]) without the geometric structure, as shown in

Table 1. Stretching (stress/strain) numerical simulation analysis of the mechanical properties of the laminating magnetic nickel metal.

	Strength Length (mm)
	5	10	15
Equivalent strain (Min, mm)	4.1122 × 10−18	8.2245 × 10−18	1.2327 × 10−17
Von Mises Stress (Min, MPa)	-	-	-
Equivalent strain (Max, mm)	5.594 × 10−2	0.11188	0.16782
Von Mises Stress (Max, MPa)	4.6423 × 10−6	9.2846 × 10−6	1.3927 × 10−5
Equivalent strain (Average, mm)	3.1174 × 10−2	6.2349 × 10−2	9.3523 × 10−2
Von Mises Stress (Average, MPa)	2.5518 × 10−6	5.1035 × 10−6	7.6553 × 10−6

.

3.2. Material Composition Design and Preparation of Magnetic Nickel Multilayer Mold

3.2.1. Composition and Characteristics of Multilayer Molds

In this study, the composition setting of the magnetic nickel multilayer mold consists of two parts: the coating layer and the intermediate layer. The materials selected include a polymer and a magnetic nickel metal material. Moreover, a magnetic nickel metal auxetic structure is used as the primary control method. The magnetic nickel geometric layer in the middle of the mold exhibits magnetic properties and, within a certain range, the characteristics of a flexible plate that are atypical of thin metal. Therefore, the auxetic structure is fabricated on a magnetic nickel thin metal plate. The method controlling microstructure variation of the macromolecular microstructural mold at the coating layer is supplemented to conduct innovative research on the imprinting and replicating of the new type of microstructural mold. The composition of the magnetic nickel multilayer mold used in this study is illustrated in Figure 4.

3.2.2. Effects of Magnetic Nickel Metal Four-Pointed Star NPR Geometric Structure and Array Number on Poisson’s Ratio and Considerations for the Design of the Magnetic Nickel Multilayer Mold

The design of the magnetic nickel metal four-pointed star NPR geometric structure and the design of different arrays of magnetic nickel metals are depicted in Figure 5.

The simulation results indicate that Poisson’s ratio increases slightly with the increase in the array number of the four-pointed star NPR structures. Additionally, Poisson’s ratio decreases slightly when the stretching displacement increases, as shown in Figure 6. In the subsequent part of this section, to determine whether die thickness affects the predetermined stretching deformation during the regulation of the intermediate layer’s stretching deformation in the magnetic nickel multilayer mold, multiple sets of conditions with varying die thicknesses are expected to be numerically analyzed. This analysis aims to preliminarily determine the optimal thickness as the basis for the inner layer thickness of the magnetic nickel multilayer mold.

3.2.3. Simulation Analysis of the Stretching Position and Bonding Mode of the Magnetic Nickel Multilayer Mold

In this study, the simulation analysis of the stretching position was conducted. The thickness of the coating layer was set to 15 mm, and the thickness of the magnetic nickel material was set to 0.1 mm. The analysis considered two scenarios: (a) both the coating layer and the intermediate layer were stretched; (b) only the intermediate layer (NPR) was stretched separately, with displacement amounts set to 1 mm, 2 mm, and 3 mm. The analysis results show that when both layers (the coating layer/the intermediate layer) are stretched with interlayer plane bonding, the average value obtained for Poisson’s ratio is 0.098. For interlayer micro-cylinder bonding, the average Poisson’s ratio is −0.9339. This indicates that under unequal interlayer bonding, Poisson’s ratio differs by nearly ten times, and the positive and negative signs are different, as shown in

Table 2. Simulation analysis results of stretching both layers (the coating layer/the intermediate layer) of the magnetic nickel multilayer mold.

Nickel (Suface Contact)
Displacement (mm)	X-Axil Original Length (mm)	X-Axis Elongation (mm)	X-Axis Strain	Z-Axil Original Length (mm)	Z-Axis Elongation (mm)	Z-Axis Strain	Poisson’s Ratio
1	26.5685	26.5240	−0.0016	48.2842	49.2004	0.0189	0.0882
2	26.5685	26.4671	−0.0038	48.2842	50.1030	0.0376	0.1012
3	26.5685	26.4103	−0.0059	48.2842	51.0058	0.0563	0.1056
Poison’s ratio (average)							0.0984
Nickel (Micro-Column Bounding)
Displacement (mm)	X-Axil Original Length (mm)	X-Axis Elongation (mm)	X-Axis Strain	Z-Axil Original Length (mm)	Z-Axis Elongation (mm)	Z-Axis Strain	Poisson’s Ratio
1	26.5685	27.0016	0.0163	48.2842	49.1261	0.0174	−0.9349
2	26.5685	27.4343	0.0325	48.2842	49.9700	0.0349	−0.9333
3	26.5685	27.8642	0.0487	48.2842	50.8072	0.0522	−0.9333
Poison’s ratio (average)							−0.9339

.

Additionally, when the force is applied only to the intermediate layer, the simulation results for the intermediate layer of the magnetic nickel multilayer mold are as follows: with interlayer plane bonding, the average Poisson’s ratio is 0.0563; and with interlayer micro-cylinder bonding, the average Poisson’s ratio is 0.0521, as shown in

Table 3. Simulation analysis results of stretching the intermediate layer of the magnetic nickel multilayer mold.

Nickel (Suface Contact)
Displacement (mm)	X-Axis Original Length (mm)	X-Axis Elongation (mm)	X-Axis Strain	Z-Axis Original Length (mm)	Z-Axis Elongation (mm)	Z-Axis Strain	Poisson’s Ratio
1	28.2843	28.2643	−0.0007	50	50.5926	0.0118	0.0593
2	28.2843	28.2448	−0.0013	50	51.2696	0.0253	0.0548
3	28.2843	28.2254	−0.0020	50	51.9044	0.03808	0.0546
Poisson’s ratio (average)							0.0563
Nickel (Micro-Column Bounding)
Displacement (mm)	X-Axis Original Length (mm)	X-Axis Elongation (mm)	X-Axis Strain	Z-Axis Original Length (mm)	Z-Axis Elongation (mm)	Z-Axis Strain	Poisson’s Ratio
1	28.2843	28.1549	−0.0045	50	50.4804	0.0096	0.4759
2	28.2843	28.0255	−0.0091	50	50.9610	0.0192	0.4759
3	28.2843	27.8962	−0.0137	50	51.4414	0.0288	0.4758
Poisson’s ratio (average)							0.0521

. These results indicate that under the condition of stretching of only the intermediate layer, all the average Poisson’s ratios of the mold are positive. The primary reason is that the thickness of the coating layer (microstructural mold layer) is too large, leading to a positive Poisson’s ratio greater than that of the intermediate layer. Therefore, selecting and using the appropriate thickness for the coating and intermediate layers is necessary to achieve the negative Poisson’s ratio required for the study.

Furthermore, this study simulated and analyzed the influence of the relative position of the microstructure (PDMS) layer and the magnetic nickel metal layer upon fabrication on Poisson’s ratio. In this scenario, a 5 × 3 magnetic nickel array was used, with bonding configured between the upper and lower layers of the PDMS. The variations in Poisson’s ratio for different stretching lengths under the condition of penetrating the holes of the magnetic nickel metal geometric layer (immersion) and only close contact without bonding (non-immersion) were compared and discussed. The results show that the average Poisson’s ratio for the immersion type is −0.609, which is slightly higher than that for the non-immersion type (−0.604), with both values being similar. In the follow-up research, the immersion type will be used as the primary research method, as shown in

Table 4. Discussion on the influence of different stretching lengths of the magnetic nickel layer of the mold on the variation of Poisson’s ratio for both the immersion and the non-immersion types.

	Strength Length (mm)
	0.1	0.2	0.3	1	2	3
Immersion	−0.609	−0.610	−0.609	−0.609	−0.609	−0.609
Poison’s ratio (average)	−0.609
Non-Immersion	−0.604	−0.605	−0.604	−0.604	−0.604	−0.604
Poison’s ratio (average)	−0.604

and Figure 7.

3.3. Establishment of the Replication System and Preparation of the Magnetic Nickel Multilayer Mold Microstructure

The system’s main components in this research include the electromagnetic plate system with magnetic attraction force, power supply unit (voltage control unit), UV-LED light, spring with adjustable force, and other components. A voltage-controlled electromagnetic plate provides the magnetic attraction force to the microstructural mold with the NPR magnetic nickel layer, which drives the imprinting action. The system in this research is illustrated in Figure 8. In this study, the precise intermediate layer of the NPR structure was obtained via precision cutting. The original microstructure plate was placed on the bottom layer using a custom molding box to achieve the shape-complementary microstructure after the molding process. An adjustable precision angle device suspended the magnetic nickel intermediate layer in the appropriate position. The PDMS coating layer that covers the magnetic nickel intermediate layer was obtained via precision molding, and the magnetic nickel multilayer mold was finalized after curing.

3.4. Replication Methods of the NPR Magnetic Hypervariable Microstructure Replication System

In this system, the voltage-controlled magnetic electromagnetic plate provides a magnetic attraction force to assist the multilayer magnetic nickel NPR geometric structure in driving the PDMS mold for imprinting. A curing method was also employed for curing and molding with a photoresist. The operating steps of the process include: (a) controlling the stretching strength and length of the magnetic nickel multilayer mold to achieve the microstructure of the required characteristic scale; (b) applying an appropriate thickness of SU8 photoresist on the PC via spin coating on a quartz transparent glass platform, and applying a voltage to adjust and control the magnetic attraction force; (c) imprinting the magnetic nickel NPR multilayer microstructural mold onto the photoresist with the magnetic attraction force, maintaining the pressure, and using UV-LED light for curing and molding; (d) turning off the UV-LED light, stopping the magnetic attraction force, and releasing the mold to obtain the complementary microstructure product after imprinting replication, as shown in Figure 9.

4. Results and Discussion

4.1. Simulation Analysis and Discussion of the Influence of Microstructural Mold Thickness on the Poisson’s Ratio of the Magnetic Nickel Multilayer Mold

In this section, different thicknesses (3 mm, 4 mm, and 6 mm) of the microstructural mold (under the conditional parameters of the PDMS base agent: curing agent = 10:1, Young’s modulus: 1.74 MPa; density: 963 kg/m³; Poisson’s ratio: 0.49) were set to investigate the influence of the magnetic nickel multilayer mold in this study on the Poisson’s ratio values. The simulation results show that under the stretching numerical simulation of the NPR layer of a 5 × 3 array (with each single geometric structure measuring 30 mm × 30 mm), the overall negative Poisson’s ratio decreases as the mold microstructure thickness increases. When the microstructural mold thickness is 3 mm, 4 mm, and 6 mm, the overall average Poisson’s ratio of the mold is −0.6, −0.59, and −0.52, respectively. This indicates that the microstructural mold thickness may affect the overall Poisson’s ratio performance of the mold, as shown in Figure 10.

4.2. Influence of Stretching Displacement of the Magnetic Nickel Multilayer Mold on the Bevel Angle of the Edge Side of the Microstructural Mold Layer

In this section, the possible influence of the stretching process of the magnetic nickel NPR geometric layer on the bevel angle (ψ) of the edge side of the mold was simulated and analyzed. The study set the NPR structure layer as a 5 × 5 array (with each single geometric structure measuring 30 mm × 30 mm). The microstructural mold layer with a coating thickness of 4 mm was used for the stretching numerical simulation. The simulation results show that with the increase in stretching displacement, the bevel angle coating on the edge side of the microstructural mold layer tends to increase. However, the value of the increase is relatively small (e.g., a stretching of 1 mm may increase the angle by about 0.002 degrees), and it exhibits a near-linear performance, as shown in Figure 11. In this study, one-fifth of the middle region of the mold (the total length range of the mold) was taken as the main research scope of the experiment to avoid the influence of marginal effects.

4.3. Influence of Stretching Regulation on the Microstructure Shape of the Mold

4.3.1. Influence of Stretching Force (Length) on the Morphological Characteristic Scale of the Microstructural Mold

In this section, the magnetic nickel multilayer mold was set up on the stretching test machine (Instron 5965 system (Instron, Canton, MA, USA)) to explore the influence of different stretching forces (lengths) on the morphological characteristic scale of the microstructural mold used in this study. The experimental results show that within the elastic stretching range of the mold, an increase in stretching length causes a micro-angle variation and a slight increase.

4.3.2. Influence of Stretching Force (Length) on the Variation of the Microstructure Height

In this section, the magnetic nickel multilayer mold was set up on the stretching test machine to explore the influence of different stretching forces (lengths) on the height variation of the microstructural mold used in this study. The actual measurement results within the elastic stretching range of the mold show that an increase in the stretching length leads to a shortening tendency in the microstructure height.

4.4. Influence on the Replica Moldability and Microstructure Deformation Verification

4.4.1. Influence on the Replica Moldability

In this study, the self-developed system and the regulation of the intermediate layer of the magnetic nickel multilayer mold were used to control the microstructure. After regulation, the whole mold was driven to conduct the imprinting replication with the magnetic attraction force as the main driving mode through the magnetic intermediate layer. The experimental results show that with the increase in voltage of the electronic control system, the imprinting replication of the microstructure can be enhanced by increasing the magnetic attraction force. The greater the force, the better its height replica moldability, as shown in Figure 12.

4.4.2. Microstructure Deformation Verification

The results derived from the geometric theory suggest that the shape of the single microstructure is regulated by stretching deformation before imprinting replication. In this section, in terms of the influence of different stretching control forces (lengths) on the magnetic nickel multilayer mold, an increase in the stretching length of the intermediate layer may cause the microstructural mold to take the shape of a micro-pyramid. The actual imprinting replication results show that under different control voltages of magnetic pressure, the vertical and radial thickness relative to the molding height may also decrease, as shown in Figure 13.

Furthermore, this section demonstrates that cylindrical holes may develop a small cylindrical bevel after stretching and imprinting replication. The study found that under a fixed stretching control force and magnetic pressure force conditions, the radial length obtained from different microstructural heights tends to increase gradually and shows an approximate linear tendency compared with the original radial length of the microstructure. This is consistent with the derivation of the theory of the microstructure’s geometric point with height and position displacements and changes discussed in this study, as shown in Figure 14.

Since the intermediate layer is a metal material with a small elastic stretching range, the cylindrical bevel is relatively small compared to the radial diameter thickness. Additionally, at the interface between the NPR geometric structure layer and the PDMS at zero height (z = 0), the variation intensifies with the increasing distance from the center of the microstructure. Moreover, the function curve’s tendency changes in correlation. Under the conditions outlined in this study, the maximum ratio of its influence on the radial diameter thickness is 2.1%.

5. Conclusions

This study primarily focused on developing a replica molding process for the preparation of hypervariable microstructures. The research was based on two main theories: the microstructure’s geometric point without any height and position displacements and changes, and the microstructure’s geometric point with height and position displacements and changes. The cylindrical array microstructure was the primary focus of this study. Additionally, it was explained that at the zero height ($z=0$) position on the interface between the NPR geometric structure layer and the PDMS, the farther (higher) the distance to the center of the microstructure, the more pronounced the variation would be. Moreover, the tendency of the function curve varies.

In this study, a laminating magnetic nickel metal four-pointed star was used to design the geometric structure of the main intermediate layer to discuss and optimize the design considerations of the magnetic nickel multilayer mold. The establishment of the replication system and the preparation of the magnetic nickel multilayer mold microstructure were completed, and replication methods of the magnetic hypervariable microstructure replication system were proposed. Through simulation analysis, it was found that when the microstructural mold thickness was 3 mm, 4 mm, and 6 mm, the overall average Poisson’s ratio of the mold was −0.6, −0.59, and −0.52, respectively, indicating that the microstructural mold thickness may affect the overall Poisson’s ratio performance of the mold.

The findings were mainly because the free end of both sides of the mold were unrestrained, and with the increase in displacement, the bevel angle coating on the edge side of the microstructural mold layer tends to increase, with a 1 mm stretching increasing the angle by about 0.002 degrees. The imprinting replication of the microstructure can be obtained by increasing the magnetic attraction force, and the greater the force, the better its height replica moldability. Additionally, the vertical and radial thickness relative to the molding height may decrease under different control voltages of magnetic pressure. This is consistent with the derivation of the theory of the microstructure’s geometric point with height and position displacements and changes in this study. In this study, at the zero height ($z=0$) position on the interface between the NPR geometric structure layer and the PDMS, the variation became more pronounced with increasing distance from the center of the microstructure. Furthermore, the tendency of the function curve varied accordingly. The primary cause is the lack of constraints on the free ends of both sides of the molds and the excessive constraints on the intermediate parts. Under the conditions used in this study, the maximum ratio of its influence on the radial diameter thickness was 2.1%.

In the future, we plan to design and evaluate various geometric structures with negative Poisson’s ratios to identify opportunities for actual application and their potential applications in micromechanical engineering and microsystem technology.