A theoretical model-based dlp printing hydrogel structure control method

Abstract

The application discloses a DLP printing hydrogel structure control method based on a theoretical model and belongs to the field of intelligent additive manufacturing. The application applies a hydrogel swelling theory to DLP printing technology, and proposes a 3D printing hydrogel uneven swelling behavior prediction model based on DLP. Based on the prediction model, a post-swelling predicted shape of a hydrogel printing piece can be obtained through existing printing parameters, material attribute parameters and an original computer digital model, and the post-swelling predicted shape is compared and analyzed with the original computer digital model, the original computer digital model is reversely deformed and compensated, and a compensated digital model is obtained. Based on the compensated digital model, only printing according to a conventional process can obtain a target structure preset by the original computer digital model, so that the problem that an actual forming structure deviates from a design structure due to a swelling effect is solved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent additive manufacturing, specifically relating to a method for controlling the structure of hydrogels printed using DLP based on a theoretical model. Background Technology

[0002] Hydrogels are a class of soft polymer materials composed of a three-dimensional hydrophilic cross-linked network and water molecules, with a water content that can be as high as 90% or more. The swelling behavior of hydrogels depends on the density of the cross-linked network, the chemical potential difference between the solvent and the precursor solution, and the diffusion rate of solute molecules. Due to the difference in chemical potential between the inside and outside during the curing process, small molecules in the precursor solution migrate into the interior of the cured hydrogel, causing the hydrogel to swell. This swelling behavior usually affects the final morphology of the printed structure.

[0003] In recent years, DLP-based 3D printing technology has been widely used in the fabrication of complex hydrogel structures due to its high forming accuracy and wide material compatibility. However, the DLP printing process is characterized by layer-by-layer curing, and the cured hydrogel layers are constantly immersed in the precursor solution during subsequent printing processes. Because each layer has a different curing time, its immersion time in the liquid phase varies, leading to uneven swelling of the three-dimensional structure along its thickness. This uneven swelling behavior alters the geometric accuracy and functional performance of the printed device. For example, in hydrogel-based microfluidic devices or structures containing internal channels, channel deformation will affect fluid flow behavior, causing deviations between the actual structure and the design expectations. Therefore, accurately predicting the final shape after swelling has become a key issue in the functionalization of DLP-printed hydrogels.

[0004] Currently, although DLP printing technology has been widely used in hydrogel molding, there is still a lack of effective theoretical prediction models for the uneven swelling behavior caused by layer-by-layer curing during the printing process. How to perform reverse deformation compensation design on the digital model before printing so that the swollen structure exactly matches the target structure, thereby achieving precise manufacturing of complex hydrogel devices, is a pressing technical challenge. This technical challenge limits the functional applications of DLP-printed hydrogels. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and system for predicting and compensating the non-uniform swelling behavior of 3D printed hydrogels based on DLP. This method can accurately predict the final shape of the hydrogel printed part after swelling and obtain the target structure through reverse deformation compensation design.

[0006] To achieve the above objectives, the specific technical solution adopted by the present invention is as follows:

[0007] In a first aspect, the present invention provides a method for controlling the structure of DLP-printed hydrogels based on a theoretical model, comprising:

[0008] S1. Based on the single-layer printing thickness set for hydrogel printed parts in the current printing process, call the working curve to determine the single-layer exposure time; according to the DLP printing sequence, calculate the cumulative soaking time of each hydrogel curing layer in the precursor solution at the time of printing completion.

[0009] S2. Combining the hydrogel non-uniform swelling behavior prediction model, the swelling behavior of each hydrogel solidified layer under the corresponding cumulative immersion time is quantitatively predicted, and the predicted shape of the hydrogel printed part after swelling is determined based on the structural size of each hydrogel solidified layer after swelling.

[0010] S3. Using the original computer digital model of the hydrogel print as the target shape, compare the predicted shape of the hydrogel print after swelling with the target shape, calculate the deformation deviation of each hydrogel curing layer, and perform reverse deformation compensation design on the original computer digital model so that the hydrogel print based on the compensated digital model is close to the target shape.

[0011] As a preferred embodiment of the first aspect above, the working curve is obtained by fitting measured data of DLP printing of the same hydrogel precursor liquid system. It is in the form of a logarithmic equation with single-layer printing thickness as the dependent variable and single-layer exposure time as the independent variable, and the dependent variable is proportional to the logarithm of the independent variable.

[0012] As a preferred embodiment of the first aspect above, the cumulative soaking time of any hydrogel curing layer is the sum of the single-layer exposure times of all subsequent printed layers of that hydrogel curing layer.

[0013] As a preferred embodiment of the first aspect above, the hydrogel non-uniform swelling behavior prediction model is based on spatiotemporal distribution The corresponding nonlinear diffusion partial differential equation is used in the calculation of quantitative prediction of swelling behavior. The equation is as follows:

[0014]

[0015] In the formula: and For hydrogels in two orthogonal directions on the layer plane and The elongation ratio as a function of time t. denoted as εt, where εt is the elongation ratio of the hydrogel in the normal direction along the layer plane as a function of time t; N is the crosslinking density; and k is the Boltzmann constant. The volume of a single small molecule; It is a dimensionless parameter; denoted as the diffusion coefficient of small molecules.

[0016] As a preferred embodiment of the first aspect mentioned above, the swelling behavior of each hydrogel solidified layer under the corresponding cumulative immersion time is quantitatively predicted. Firstly, the swelling behavior of each hydrogel solidified layer is then... and Equivalent to and used as the parameter to be solved, while The elongation ratio is kept constant at 1, and the hydrogel is used to balance the swelling under constrained conditions in the plane direction where swelling needs to be controlled. As boundary conditions, and with the initial condition set to 1, the nonlinear diffusion partial differential equation is numerically solved to obtain... Then, for each hydrogel solidification layer, based on the solution obtained... And the cumulative immersion time corresponding to this hydrogel curing layer. In the direction of the layer plane where swelling needs to be controlled Moment Spatial distribution By integrating, the structural dimensions of this hydrogel solidified layer after swelling along the plane of the layer are obtained.

[0017] As a preferred embodiment of the first aspect above, steps S2 and S3 require multiple iterations. After obtaining the compensated digital model each time, the quantitative prediction needs to be re-executed to obtain the predicted shape of the hydrogel print after swelling, and then the reverse deformation compensation design is re-executed. When the deviation between the predicted shape of the hydrogel print after swelling and the target shape is within the tolerance range, the iteration terminates and the final digital model is used for actual DLP printing to obtain a hydrogel print that conforms to the target shape.

[0018] As a preferred embodiment of the first aspect mentioned above, during the DLP printing process, the light source is located below the moving platform, and the printing proceeds layer by layer from bottom to top. The moving platform moves upward layer by layer, thereby leaving space for the next layer to cure below the already printed hydrogel curing layer.

[0019] In a second aspect, the present invention provides a computer program product, including a computer program / instructions, which, when executed by a processor, can implement the DLP printing hydrogel structure control method based on a theoretical model as described in any of the first aspects above.

[0020] Thirdly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, enables the implementation of the theoretical model-based DLP printing hydrogel structure control method as described in any of the first aspects above.

[0021] Fourthly, the present invention provides a computer electronic device, which includes a memory and a processor;

[0022] The memory is used to store computer programs;

[0023] The processor is configured to, when executing the computer program, implement the theoretical model-based DLP printing hydrogel structure control method as described in any of the first aspects above.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] This invention is the first to apply hydrogel swelling theory to DLP printing technology, constructing a theoretical model that can accurately predict the non-uniform swelling behavior of hydrogels in DLP printing, filling a technological gap in this field. Based on the model's prediction results, this invention performs reverse deformation compensation design on the original digital model, ensuring that the swollen structure is exactly the target structure, thus achieving precise manufacturing of complex hydrogel devices. This invention can analyze the influence of different printing parameters on the final structure, providing theoretical guidance for optimizing process parameters. This invention is applicable to various photocurable hydrogel material systems, possessing good versatility and application value. Attached Figure Description

[0026] Figure 1 This is a schematic diagram illustrating the steps of a DLP-based method for controlling the structure of hydrogels printed using a theoretical model.

[0027] Figure 2 This is a schematic diagram of a DLP printing device.

[0028] Figure 3 This is a schematic diagram of the layering and swelling of the hydrogel during the DLP printing process.

[0029] Figure 4 The fitting results of the curing depth measurement experiment data during the working curve fitting process.

[0030] Figure 5 These are the swelling prediction and measured results in the embodiments of the present invention;

[0031] Figure 6 The predicted dimensions of hydrogel prints with three different heights (total thicknesses) after swelling are shown.

[0032] Figure 7 Digital models before and after swelling compensation and their 3D printing results Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] This invention provides a method for controlling the structure of hydrogels in DLP printing based on a theoretical model. This method includes two steps: predicting the non-uniform swelling behavior of 3D-printed hydrogels based on DLP, and compensating for the reverse deformation of 3D-printed hydrogels based on DLP. In the step of predicting the non-uniform swelling behavior of 3D-printed hydrogels based on DLP, this invention applies a hydrogel swelling theoretical model to DLP printing technology, constructing a model for predicting the non-uniform swelling behavior of hydrogels. By acquiring process and material parameters during the DLP printing process and inputting them into the prediction model, the predicted shape of the hydrogel print after swelling is output. In the step of compensating for the reverse deformation of 3D-printed hydrogels based on DLP, this invention compares the predicted shape of the hydrogel print after swelling with the actual desired target shape, calculates the deformation deviation, and designs a reverse deformation compensation for the original computer digital model. This ensures that the hydrogel print, printed according to the compensated digital model, exactly meets the target shape after swelling.

[0035] Therefore, the core of this invention is to construct a predictive model for the non-uniform swelling behavior of hydrogels using the theoretical framework of hydrogel swelling. The hydrogel swelling theoretical model needs to consider the coupling behavior of small molecule diffusion and large network deformation, including mass transport balance equations, external force balance equations, and volume constraint conditions. The free energy form of the hydrogel needs to encompass the elastic energy of the polymer network and the mixing energy between the polymer network and small molecules.

[0036] To facilitate understanding of the principle of the hydrogel non-uniform swelling behavior prediction model used in practical applications of this invention, the theoretical derivation process of the hydrogel non-uniform swelling behavior prediction model is first presented below, specifically including three parts: A), B), and C).

[0037] A) Construct a model of the curing depth of the hydrogel.

[0038] In the pre-processing stage of printing, it is necessary to determine the single-layer printing thickness and exposure time. This ensures that the single-layer hydrogel can solidify within the current exposure time and that overlapping layers can bond to form a three-dimensional structure, while preventing over-curing of previously cured layers. To more accurately determine the relationship between curing depth and time, a curing depth model needs to be constructed. This model is similar to the Jacob model commonly used in stereolithography, quantifying the light intensity attenuation law of ultraviolet light during layer-by-layer curing and the dynamic process of curing depth evolution over time. This provides key parameters for determining the single-layer thickness, exposure time, and total swelling time. Since light intensity follows the Beer-Lambert law along the thickness direction, the exposure energy at different thicknesses after the same time will vary. This same law should also be followed, namely:

[0039] (1)

[0040] In the formula, Let be the exposure energy at z=0. I0 is the constant light intensity of the UV projection equipment used in DLP printing. p The depth of light penetration in a medium is defined as the point at which the exposure energy decays to its minimum. The position at time is a specific parameter of the medium.

[0041] According to equation (1), the curing depth C of the precursor liquid is calculated. d It satisfies the following relationship:

[0042] (2)

[0043] in This is also a characteristic parameter of the medium, representing the minimum exposure energy required for the liquid to begin solidification. Therefore, the working curve equation can be derived as follows:

[0044] (3)

[0045] Equation (3) is the working curve equation corresponding to the material system of the hydrogel precursor liquid, which can be used to determine the curing of a given thickness C. d Required exposure time. For each specific hydrogel precursor, curing depth measurement experiments are required in actual DLP 3D printing, using the working light intensity of the UV projection equipment used in the actual printing. The printing thickness C under different exposure times t is compared below. d Measurements were performed, and the measured data were used as fitting data to fit equation (3) to obtain D. p and The fitting results.

[0046] B) Construct a theoretical model for hydrogel swelling.

[0047] When a hydrogel is placed in a solution, the chemical potential gradient between the two drives small molecules to migrate from a region of high chemical potential to a region of low chemical potential. As small molecules move in and out of the hydrogel surface, the volume of the hydrogel will reversibly expand or contract. It should be noted that the small molecules in this invention refer to unreacted small molecules in the hydrogel precursor solution that can enter the solidified hydrogel (including water molecules, initiator molecules, monomer molecules, etc.).

[0048] The hydrogel in its stress-free dry network state is used as a reference configuration, described by material coordinates X. When the network deforms, the material coordinate X shifts to the current configuration within time t. Therefore, the deformation gradient tensor F can be expressed as:

[0049] (4)

[0050] The mass change of hydrogels is mainly caused by the migration of small molecules on the surface. Assuming no chemical reaction occurs during this process, the number of small molecules should be conserved. Therefore, the solvent mass balance equation can be expressed as:

[0051] (5)

[0052] In the formula This represents the number of small molecules per unit volume. This represents the number of small molecules passing through a unit area per unit time.

[0053] The deformation of hydrogels caused by solvent diffusion takes place over a long timescale, much longer than the timescale related to inertia. Therefore, a quasi-static method can be used here. The equilibrium equation, neglecting the inertial term, is expressed as:

[0054] (6)

[0055] In the formula This is the first PK stress tensor.

[0056] Regarding the swelling phenomenon, the volume change of a hydrogel is caused by changes in its internal solvent content. Therefore, the volume constraint condition is related to the deformation of the hydrogel due to changes in solvent content.

[0057] (7)

[0058] In the formula The volume of a single small molecule in the hydrogel precursor solution. For volumetric deformation with respect to the reference configuration.

[0059] The free energy density of the hydrogel is considered as a state function related to F and C, denoted as . Introduce a Lagrange multiplier into the state function. Its physical meaning is that the hydrostatic pressure changes as follows:

[0060] (8)

[0061] When the deformation of the hydrogel is very small, the change in free energy is:

[0062] (9)

[0063] Since the swelling of hydrogels is a spontaneous process, the total free energy G of the system will not increase during the entire swelling process, that is:

[0064] (10)

[0065] The total free energy of the system is the free energy of the hydrogel. Potential energy of external load and the potential energy of solvent diffusion sum.

[0066] (11)

[0067] Each integral term in equation (11) represents a different energy dissipation mechanism. In order to satisfy the condition under any circumstances, each integrand must be negative or zero.

[0068] The first integral term relates to the local rearrangement of small molecules. Since the local rearrangement process is much faster than their long-distance migration, we assume local equilibrium by neglecting the viscosity associated with the local rearrangement, so this term is zero, thus yielding:

[0069] (12)

[0070] The second integral term relates to the inflow (outflow) of small molecules. Assuming a local chemical equilibrium exists between the small molecules at the hydrogel material points and the inflow (outflow) small molecules, this term is also zero, thus yielding:

[0071] (13)

[0072] The third integral term is a volume constraint, which can be eliminated according to equation (7).

[0073] The last integral term represents the long-distance migration of small molecules. The integrand of this term must be negative definite, i.e.:

[0074] (14)

[0075] Applying the laws of linear dynamics:

[0076] (15)

[0077] In the formula It is the mobility tensor, which is symmetric and positive definite, and its specific form is:

[0078] (16)

[0079] In the formula, D is the diffusion coefficient of small molecules.

[0080] The free energy of the hydrogel is mainly determined by the elastic energy W of the polymer network. e And the mixing energy W between the polymer network and small molecules m Composition, namely:

[0081] (17)

[0082] Let the two orthogonal directions of the hydrogel on the plane of the cured layer be denoted as... and The normal direction of the solidified layer plane of the hydrogel is denoted as ,by , and Representing three main directions respectively , and The elongation ratio, and the elastic energy of the polymer network caused by stretching are:

[0083] (18)

[0084] In the formula, N is the number of polymer chains per unit volume (i.e., crosslinking density), k is the Boltzmann constant, and T is the absolute temperature.

[0085] Furthermore, the free energy of mixing the polymer network with small molecules is taken as:

[0086] (19)

[0087] In the formula It is a dimensionless parameter. The first term in parentheses comes from the mixing entropy, and the second term comes from the mixing enthalpy.

[0088] Substituting equations (18) and (19) into equation (17), we obtain the total free energy of the hydrogel as follows:

[0089] (20)

[0090] Three main directions can be derived. , and Each of the above nominal stresses , and and chemical potential The specific expressions are as follows:

[0091] (twenty one)

[0092] (twenty two)

[0093] C) Applying the hydrogel swelling theory framework and free energy function to the non-uniform swelling behavior of DLP-based 3D printed hydrogels.

[0094] In DLP printing, the common practice is to position the light source below the moving platform and print layer by layer from bottom to top. The moving platform moves upwards layer by layer, leaving space for the next layer to cure below the already printed hydrogel layer. Based on this printing method and the three main directions defined earlier, in this invention, X1 and X2 can represent the material coordinates within the hydrogel layer plane, X3 can represent the material coordinates perpendicular to the layer plane and pointing downwards, and L can represent the curing length of a single hydrogel layer in the X1 direction. The influence of the horizontal constraint of the moving platform on the hydrogel swelling behavior is ignored. It is assumed that the cured hydrogel layer is unconstrained in the X1 and X2 directions and can swell freely, i.e. and However, due to the constraints of the moving platform and the substrate in the X3 direction, the elongation ratio in this direction is... .

[0095] Since the elongation ratios of the hydrogel in the X1 and X2 directions can be considered the same, the subsequent swelling of the hydrogel layer in the two-dimensional plane can be simplified to considering only the swelling in the X1 direction. After time t, the material point X1 on the solidified hydrogel moves to position... Therefore, the elongation ratio in the X1 direction is:

[0096] (twenty three)

[0097] It is not uniformly distributed in space and changes over time.

[0098] Combining equations (21) and (22), eliminate achievable The governing equations are:

[0099] (twenty four)

[0100] Considering the free swelling condition of the hydrogel, after a long period of swelling, it reaches an equilibrium swelling state. At this point... , , This is the elongation ratio under free equilibrium swelling, which can be obtained experimentally. Based on the actual printing temperature T, Boltzmann constant k, and combined with uniaxial tensile experiments, the elastic modulus E is obtained. The crosslinking density N can be calculated using the formula E = NkT, and then N is multiplied by the volume of a single small molecule. Calculate The volume of a single small molecule The volume of a water molecule can be used as an equivalent; the chemical potential of the external solution can be set to zero. The parameters can be obtained by solving equation (24). Based on the bottom-up printing method with the light source positioned below the moving platform, further consideration is given to the balanced swelling condition during DLP printing, and the elongation ratio at this point. The unknown needs to be solved, and the following settings are provided. , , and Based on the parameters already obtained under the free swelling condition of hydrogel By further solving equation (24), the elongation ratio of equilibrium swelling under constrained conditions can be obtained. .

[0101] It should be noted that, taking into account the non-uniformity, , In reality, they all exhibit spatial heterogeneity and change with time t. Essentially, it can be represented as a spatiotemporal distribution. , Essentially, it can also be represented as a spatiotemporal distribution. .

[0102] As printing time progresses, the elongation ratio of the hydrogel in the X1 direction gradually changes from the initial elongation ratio of 1 immediately after curing to... This change propagates gradually from the surface of the hydrogel inwards; therefore, the chemical potential within the hydrogel is non-uniform and changes over time. From this, we obtain information about... Partial differential governing equations:

[0103] (25)

[0104] This equation describes the non-uniform swelling behavior of 3D-printed hydrogels based on DLP. The hydrogel non-uniform swelling behavior prediction model of this invention actually participates in the quantitative prediction calculation of swelling behavior according to the above equation (25), by setting... The boundary conditions are as well as And set the initial conditions as Then, equation (25) can be solved numerically to obtain... .

[0105] Therefore, equations (1) to (25) above fully describe the theoretical derivation process of the entire hydrogel non-uniform swelling behavior prediction model and the solution method involved in the swelling behavior prediction. Based on the above description, the specific process of the DLP printing hydrogel structure control method in this invention will be further introduced below.

[0106] like Figure 1 As shown, the specific process of the DLP printing hydrogel structure control method based on the theoretical model in this invention is as follows:

[0107] S1. Based on the single-layer printing thickness set for hydrogel prints in the current printing process, call the working curve to determine the single-layer exposure time; according to the DLP printing sequence, calculate the cumulative immersion time of each hydrogel curing layer in the precursor solution at the time of printing completion.

[0108] It should be noted that the above-mentioned single-layer printing thickness is a parameter value set by the user in the current printing process and can be adjusted according to the actual process. Generally speaking, the printing thickness of each layer can be fixed in actual printing. Therefore, based on this fixed single-layer printing thickness, the single-layer exposure time of all hydrogel curing layers can be determined at once using the working curve. Of course, theoretically, if the printing thickness of each layer is different, then it is only necessary to calculate layer by layer; the principle is the same.

[0109] It should also be noted that, due to the different material systems of different hydrogel precursor liquids, their photocuring properties will also vary. Therefore, the working curve used in step S1 of this invention must be obtained by fitting actual DLP printing test data of the same hydrogel precursor liquid system, and its form is expressed as a single-layer printing thickness C. d A logarithmic equation with C as the dependent variable and the single-layer exposure time t as the independent variable, and the dependent variable C d It is proportional to the logarithm of the independent variable t. In an embodiment of the present invention, the fitting can be performed directly according to the aforementioned equation (3), wherein... The D value is fixed to the working light intensity of the UV projection equipment used in the actual printing, and the fitted value is... p and It can be used as a coefficient of the working curve.

[0110] It should also be noted that, according to the DLP printing method specified in this invention, the light source is located below the moving platform during the printing process, and ultraviolet light shines upwards for curing. Figure 2 As shown. In this invention, the DLP printing sequence requires printing layer by layer from bottom to top. The moving platform moves upwards layer by layer, leaving curing space for the next layer below the already printed hydrogel curing layer. Therefore, the cumulative immersion time of each hydrogel curing layer in the precursor solution at the time of printing completion... The calculation needs to be performed layer by layer according to the DLP printing sequence. The cumulative soaking time of any hydrogel curing layer is the sum of the single-layer exposure times of all subsequent printed layers of that hydrogel curing layer.

[0111] S2. Combining the hydrogel non-uniform swelling behavior prediction model, the swelling behavior of each hydrogel solidified layer under the corresponding cumulative immersion time is quantitatively predicted, and the predicted shape of the hydrogel printed part after swelling is determined based on the structural size of each hydrogel solidified layer after swelling.

[0112] As mentioned above, the hydrogel non-uniform swelling behavior prediction model in this invention is based on spatiotemporal distribution The corresponding nonlinear diffusion partial differential equation is used in the solution calculation for quantitative prediction of swelling behavior. The equation form is shown in equation (25). Quantitative prediction of the swelling behavior of each hydrogel solidification layer under the corresponding cumulative immersion time is performed. First, the swelling behavior of each layer is quantitatively predicted. and Equivalent to and used as the parameter to be solved, while The elongation ratio is kept constant at 1, and the hydrogel is used to balance the swelling under constrained conditions in the plane direction where swelling needs to be controlled. As a boundary condition, i.e., setting as well as L represents the curing length of the monolayer hydrogel in the plane direction where swelling needs to be controlled. and These represent the coordinates of the two printed boundaries along the plane of the layer where swelling needs to be controlled, respectively, while the initial condition is set to 1, i.e., set... Based on the predefined boundary and initial conditions, the nonlinear diffusion partial differential equation shown in equation (25) is numerically solved to obtain... Then, for each hydrogel solidification layer, based on the solution obtained... And the cumulative immersion time corresponding to this hydrogel curing layer. In the direction of the layer plane where swelling needs to be controlled Moment Spatial distribution By integrating, the structural dimensions of this hydrogel solidified layer after swelling along the plane of the layer are obtained.

[0113] It should be noted that the orientation of the swelling layer plane needs to be controlled. Direction can also be The direction depends on the specific control requirements. Generally speaking, it is necessary to simultaneously... and Swelling is controlled in two directions, requiring solutions to equation (25) for both directions. Since the curing lengths in the two directions may differ, the boundary conditions must be set separately. When the boundary of the single-layer hydrogel curing layer of the hydrogel print is square, the swelling in both directions will be identical. Therefore, the solution... Direction It can be used to represent another Direction .

[0114] Based on the two distributions obtained from the solution, the swollen dimensions at any given time along both directions can be calculated using spatial integration. Specifically, the spatial integration can be performed along the plane of the layer where swelling needs to be controlled, with the actual printed boundary in that direction as the upper and lower bounds. Accumulate points. For example, for a cumulative soaking time of... Regarding the hydrogel curing layer, assuming in The coordinate range of the actual printed boundary in the direction is Therefore, the corresponding swollen size is The same principle applies to other directions; simply replace the upper and lower bounds of the integral with the upper and lower bounds of the coordinate range in that direction.

[0115] S3. Using the original computer digital model of the hydrogel print as the target shape, compare the predicted shape of the hydrogel print after swelling with the target shape, calculate the deformation deviation of each hydrogel curing layer, and perform reverse deformation compensation design on the original computer digital model so that the hydrogel print based on the compensated digital model is close to the target shape.

[0116] It should be noted that, based on the swelling characteristics of hydrogels, the predicted shape after swelling will be larger than the original target shape in space. Therefore, when calculating the deformation deviation of each hydrogel solidified layer along the plane direction where swelling needs to be controlled, the size of the hydrogel solidified layer in the predicted shape after swelling can be subtracted from the size of the hydrogel solidified layer in the target shape. The resulting size difference will be a positive value. Subtracting this size difference from the corresponding hydrogel solidified layer in the original computer digital model yields the size of the hydrogel solidified layer in the compensated digital model. Once all hydrogel solidified layers have been adjusted, the reverse deformation compensation is considered complete, resulting in the compensated digital model. When there are multiple plane directions where swelling needs to be controlled, reverse deformation compensation is performed independently for each direction.

[0117] It should also be noted that although theoretically, performing a single reverse deformation compensation design in steps S1-S3 can produce a hydrogel print based on the compensated digital model that closely approximates the target shape, in scenarios requiring high control precision, the quantitative prediction and reverse deformation compensation processes corresponding to steps S2 and S3 can be iterated multiple times. Each time a compensated digital model is obtained, the quantitative prediction needs to be re-executed to obtain the predicted shape of the hydrogel print after swelling, and then the reverse deformation compensation design is repeated. The iteration terminates when the deviation between the predicted shape of the hydrogel print after swelling and the target shape is within the tolerance range, and the final digital model is used for actual DLP printing to obtain a hydrogel print that conforms to the target shape. The specific tolerance range can be adjusted according to actual needs.

[0118] The theoretical model-based DLP printing hydrogel structure control method described in S1~S3 above will be applied to a specific embodiment to demonstrate the actual technical effect.

[0119] Example

[0120] In this embodiment, 28.43 g of AAm, 1.42 g of water-soluble TPO nanoparticles, 0.14 g of MBAA, and 2 g of food coloring were added to 72 g of deionized water and subjected to ultrasonic treatment at room temperature for 10 min to form a precursor solution. The precursor solution was stored in a low-temperature and sealed environment to avoid the influence of visible light on the solution.

[0121] Hydrogel samples were prepared using a self-built DLP 3D printing system. This system mainly includes a moving platform, a transparent tank for containing the precursor solution, an electrically driven lifting stage, and a precision UV projection device (PRO6500, Wintech, China), with a UV wavelength of 405 nm and a constant light intensity of 27.35 mW / cm². 2 During the printing process, a precision UV projection device is placed below the moving platform to irradiate ultraviolet light. The hydrogel is printed layer by layer from bottom to top. Under the control of an electric lifting displacement stage, the moving platform moves upwards layer by layer, thus leaving space for the next layer to cure beneath the already printed hydrogel layer. Figure 3 As shown in (a) of the diagram. To simplify the process, all hydrogel cured layers were printed with the same single-layer thickness. A pre-fitted working curve equation based on experimental data and the current hydrogel precursor solution formulation was used to determine the single-layer exposure time corresponding to that thickness. After UV irradiation for the set single-layer exposure time, one layer was cured. The moving platform then moved upwards to perform the next layer's UV curing operation. To prevent the impact of water loss on its mechanical properties, all samples were tested immediately after printing.

[0122] like Figure 3 As shown in (b) of this embodiment, the original computer digital model of the hydrogel print is a 15mm × 15mm × 7mm cuboid, and the plane of each hydrogel curing layer is a 15mm × 15mm square. Therefore, the ideal target shape of the hydrogel print is a 15mm × 15mm × 7mm cuboid. After printing layer by layer according to conventional methods without swelling control, the side of the sample is photographed using a Nikon Z5 camera, and the resulting sample image is shown below. Figure 3 As shown in (c), what should have been a 15mm x 7mm side surface actually forms an inverted trapezoid with a larger top and a smaller bottom due to swelling.

[0123] Therefore, in this embodiment, the predicted shape of the hydrogel printed part after swelling was predicted according to the aforementioned steps S1 and S2. Wherein, Figure 4 This paper presents the fitting results of the curing depth measurement experimental data during the working curve fitting process, showing the curing depth C. d With exposure energy The fitting relationship between them depends on the working light intensity. A constant light intensity of 27.35 mW / cm was used. 2 Therefore, based on this data, equation (3) can be fitted to obtain D. p and The fitting results.

[0124] To ensure generalizability, this embodiment further introduces three hydrogel printed parts with different heights (8mm, 10mm, and 15mm). Original computer digital models of the hydrogel printed parts are constructed using cuboids with dimensions of 15mm×15mm×8mm, 15mm×15mm×10mm, and 15mm×15mm×15mm, respectively, as the target shapes. After dividing the three target shapes into layers according to a fixed single-layer printing thickness, the single-layer exposure time is calculated using the fitted working curve. Then, following the DLP printing sequence, the cumulative immersion time of each hydrogel cured layer in the precursor solution at the time of printing completion is calculated sequentially.

[0125] Then, we first consider the free swelling condition of the hydrogel, which reaches an equilibrium swelling state after a long period of swelling. , , It is the elongation ratio under free equilibrium swelling, obtained experimentally. Let kT be 4 × 10 -21 J, Take the volume of a single water molecule as 3 × 10 -29 m 3 Based on the uniaxial tensile test, the elastic modulus E = NkT = 15.96 kPa. From this, we can calculate... And set the chemical potential of the external solution to zero. The parameters can be obtained by solving equation (24). Based on the bottom-up printing method with the light source below the moving platform, and considering the balanced swelling conditions during the DLP printing process, at this point... , , and The elongation ratio of equilibrium swelling under constrained conditions can be obtained by solving equation (24). .

[0126] As printing time progresses, the elongation ratio of the hydrogel in the X1 direction gradually changes from the initial elongation ratio of 1 immediately after curing to... In this embodiment, since the plane of the hydrogel solidified layer is square, the swelling in the X1 and X2 directions can be considered equivalent. Therefore, the solution to equation (25) regarding the... The partial differential governing equations can be obtained. In this embodiment, the equation is solved in MATLAB. According to the requirements of PDE solving in MATLAB, the two-dimensional space and height direction of the layer plane need to be discretized by mesh, and the time dimension also needs to be discretized. The boundary conditions are as well as And set the initial conditions as However, to avoid the singularity problem at the start of the computation, MATLAB sets the initial conditions to... , where eps is a small quantity. The program automatically solves equation (25) numerically to obtain... Theoretically It is a continuous distribution, and the size of the solidified hydrogel layer after swelling can be obtained by integration at a specified time. However, since X1 and t are discretized in advance in MATLAB, the obtained value is different. The solution is a matrix, where each element corresponds to a specific spatiotemporal coordinate. elongation ratio at the point .

[0127] Taking a target shape with a height of 10mm as an example, based on its The solution results in the elongation ratio of the hydrogel layer in the X1 direction. The distribution at different swelling times was visualized, and the results are as follows: Figure 5 As shown, (a), (b), and (c) respectively demonstrate the normalized coordinate position (X1 / L) and elongation ratio at different times. The change curve, time and elongation ratio corresponding to different normalized coordinate positions (X1 / L) Change curves, predicted shape of the hydrogel printed parts after swelling, and such as Figure 5 (d) shows an actual sample image obtained by taking a picture of the side of the sample with a camera. The comparison shows that the predicted shape after swelling in this invention matches the actual swelling situation very well.

[0128] In addition, for three target shapes with different heights, actual sample images captured by the camera were imported into Photoshop image processing software. The width of each layer was measured, and the measurement results were normalized to obtain the swelling deformation distribution of the sample along the thickness direction. This was then compared with the predicted swelling shape of the side of the hydrogel printed part calculated by a theoretical model. The results are as follows: Figure 6 As shown. Among them. Figure 6 (a) shows the X1 direction length at different layer heights in the predicted shape after swelling of hydrogel prints with three different heights (8mm, 10mm, and 15mm). (b), (c), and (d) show the comparison between experimental data and theoretical calculations of the X1 direction length of hydrogel prints with three different heights (8mm, 10mm, and 15mm) at different layer heights. The experimental data were obtained by Photoshop measurement, and the theoretical calculations were obtained by integration from the predicted shape after swelling.

[0129] Finally, referring to step S3 above, based on the predicted shape after swelling calculated by the theoretical model, and using the original computer digital model of the hydrogel print as the target shape, the predicted shape after swelling of the hydrogel print is compared with the target shape. The deformation deviation of each hydrogel curing layer is calculated, and a reverse deformation compensation design is performed on the original computer digital model. The single compensation process is as follows: Figure 7 As shown in (a) of the diagram. In this embodiment, multiple rounds of iterative compensation are required until the final compensated digital model conforms to the target shape. Subsequently, a DLP 3D printing device is used to solidify and shape the model layer by layer according to the compensated digital model to obtain the corrected hydrogel print. The hydrogel print before correction is shown in the diagram. Figure 7 As shown in (b) above, the corrected hydrogel print is as follows: Figure 7 As shown in (c), the hydrogel print based on the compensated digital model closely approximates the target shape. Furthermore, taking a target shape with a total height of 10mm as an example, the X1 direction lengths of the hydrogel print without swelling control (experimental - uncorrected), the hydrogel print based on the compensated digital model (experimental - corrected), the predicted shape after swelling calculated by the theoretical model (theoretical - uncorrected), and the compensated digital model (theoretical - corrected) at different layer heights are superimposed and displayed. The results are as follows: Figure 7 As shown in (d), it can be seen that the present invention can significantly correct the swelling deformation during the hydrogel printing process.

[0130] The embodiments described above are merely some preferred implementations of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for controlling the structure of DLP-printed hydrogels based on a theoretical model, characterized in that, include: S1. Based on the single-layer printing thickness set for hydrogel printed parts in the current printing process, call the working curve to determine the single-layer exposure time; According to the DLP printing sequence, calculate the cumulative soaking time of each hydrogel curing layer in the precursor solution at the time of printing completion. S2. Combining the hydrogel non-uniform swelling behavior prediction model, the swelling behavior of each hydrogel solidified layer under the corresponding cumulative immersion time is quantitatively predicted, and the predicted shape of the hydrogel printed part after swelling is determined based on the structural size of each hydrogel solidified layer after swelling. S3. Using the original computer digital model of the hydrogel print as the target shape, compare the predicted shape of the hydrogel print after swelling with the target shape, calculate the deformation deviation of each hydrogel curing layer, and perform reverse deformation compensation design on the original computer digital model so that the hydrogel print based on the compensated digital model is close to the target shape.

2. The method for controlling the structure of DLP-printed hydrogels based on a theoretical model as described in claim 1, characterized in that, The working curve is obtained by fitting the measured data of DLP printing of the same hydrogel precursor liquid system. It is in the form of a logarithmic equation with the single-layer printing thickness as the dependent variable and the single-layer exposure time as the independent variable, and the dependent variable is proportional to the logarithm of the independent variable.

3. The method for controlling the structure of DLP-printed hydrogels based on a theoretical model as described in claim 1, characterized in that, The cumulative soaking time of any hydrogel curing layer is the sum of the single-layer exposure times of all subsequent printed layers of that hydrogel curing layer.

4. The method for controlling the structure of DLP-printed hydrogels based on a theoretical model as described in claim 1, characterized in that, The hydrogel non-uniform swelling behavior prediction model. spatiotemporal distribution The corresponding nonlinear diffusion partial differential equation is used in the calculation of quantitative prediction of swelling behavior. The equation is as follows: ； In the formula: and For hydrogels in two orthogonal directions on the layer plane and The elongation ratio as a function of time t. denoted as εt, where εt is the elongation ratio of the hydrogel in the normal direction along the layer plane as a function of time t; N is the crosslinking density; and k is the Boltzmann constant. The volume of a single small molecule; It is a dimensionless parameter; denoted as the diffusion coefficient of small molecules.

5. The method for controlling the structure of DLP-printed hydrogels based on a theoretical model as described in claim 4, characterized in that, To quantitatively predict the swelling behavior of each hydrogel cured layer under corresponding cumulative immersion time, firstly... and Equivalent to and used as the parameter to be solved, while The elongation ratio is kept constant at 1, and the hydrogel is used to balance the swelling under constrained conditions in the plane direction where swelling needs to be controlled. As boundary conditions, and with the initial condition set to 1, the nonlinear diffusion partial differential equation is numerically solved to obtain... ; Then, for each hydrogel solidification layer, based on the solution obtained... And the cumulative immersion time corresponding to this hydrogel curing layer. In the direction of the layer plane where swelling needs to be controlled Moment Spatial distribution By integrating, the structural dimensions of this hydrogel solidified layer after swelling along the plane of the layer are obtained.

6. The method for controlling the structure of DLP-printed hydrogels based on a theoretical model as described in claim 1, characterized in that, Steps S2 and S3 require multiple iterations. After obtaining the compensated digital model each time, the quantitative prediction needs to be re-executed to obtain the predicted shape of the hydrogel print after swelling, and then the reverse deformation compensation design is re-executed. When the deviation between the predicted shape of the hydrogel print after swelling and the target shape is within the tolerance range, the iteration terminates and the final digital model is used for actual DLP printing to obtain a hydrogel print that conforms to the target shape.

7. The method for controlling the structure of DLP-printed hydrogels based on a theoretical model as described in claim 1, characterized in that, In the DLP printing process, the light source is below the moving platform, and the printing proceeds layer by layer from bottom to top. The moving platform moves upward layer by layer, leaving space for the next layer to cure below the already printed hydrogel curing layer.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it can realize the DLP printing hydrogel structure control method based on the theoretical model as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the DLP printing hydrogel structure control method based on a theoretical model as described in any one of claims 1 to 7.

10. A computer electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to, when executing the computer program, implement the DLP printing hydrogel structure control method based on the theoretical model as described in any one of claims 1 to 7.

Images