CN115312133B - Cross-scale method and device based on constitutive equation automatic construction and parameter extraction - Google Patents
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Abstract
The invention discloses a trans-scale method and a device for automatic construction and parameter extraction based on constitutive equations. Firstly, strain conditions of nano film materials with different thicknesses under different charges are calculated by using a first linear principle and a parallel cross-scale method of continuous medium coupling, and change rule data of the strain in an electrode surface along with charge density and film thickness are obtained; fitting to obtain the surface intrinsic stress and the surface Young modulus of the nano film material, and giving a mathematical relation between the surface intrinsic strain and the surface charge density; the subsequent writing of the numerical simulation of the electrochemical actuation response of the nano-porous material under different surface charge densities by using ABAQUS and PYTHON in secondary development. The invention promotes the macroscopic simulation of the continuous electrochemical actuation phenomenon of the nano porous film material through the cross-scale calculation, and provides a basis for the optimization of the electrochemical actuation performance.
Description
Technical Field
The invention relates to the technical field of actuation, in particular to a trans-scale method and a device based on constitutive equation automatic construction and parameter extraction.
Background
An actuator material is a smart material that can convert chemical energy or physical energy into mechanical energy, and various actuators that can be driven by electric energy, thermal energy, optical energy, or humidity have been developed. The electrochemical actuator can deform or move under the electrochemical stimulation, and has the outstanding advantages of strong controllability, low deformation voltage, good deformability and the like compared with actuators triggered by other external stimuli (such as voltage, heat, light, solvent and the like). Related research has found that electrochemical actuation can be produced in nanoporous materials in electrolyte solutions, which provides sufficient material strength and stiffness for practical application of nanoporous material electrochemical actuators, making it of great interest in artificial muscles and artificial intelligence technology. But compared to experimental observations, there has been little research into micro-computational simulation and macro-theoretical modeling calculations of electrochemical actuation phenomena. The electrochemical actuation characteristics result from changes in the surface charge of the material or surface adsorption of atomic ions, and interaction with the electrolyte solution at the solid-liquid interface. To date, there is still a lack of explicit constitutive functional relationships in the relationship of the ratio between the surface stress strain and the electrochemical parameter under specific conditions. The research on the relationship between the deformation of the material and the mechanical properties and structural parameters of the material under any given external electrode potential can push the macroscopic simulation of the continuous electrochemical actuation phenomenon of the nano porous material, and provide a basis for the optimization of the electrochemical actuation performance.
Therefore, based on the large-scale calculation of experimental phenomena and electron atomic scales, the mechanism of electrochemical actuation phenomena is analyzed, a macroscopic theoretical model and a material structure model are established, the calculation simulation of material performance is carried out, important reference can be provided for the optimization of materials and structures thereof, the screening of the materials and the structures is accelerated, and the experimental cost is reduced.
The Tong-Yi Zhang provides a surface intrinsic stress model, definitely describes the action of mechanics in the relaxation analysis of nano film materials, systematically researches the Young modulus and Greenesen parameters of nano films of Au, ni, cu and the like under tension, compression and bending, also theoretically deduces analytical formulas such as elastic constants related to temperature and size, and the like, and is verified through a first nature principle and molecular dynamics simulation.
Disclosure of Invention
The invention aims to provide a trans-scale method based on constitutive equation automatic construction and parameter extraction, so as to overcome the defects in the prior art.
In order to achieve the purpose, the invention provides the following technical scheme:
the application discloses a trans-scale method based on constitutive equation automatic construction and parameter extraction, which specifically comprises the following steps:
s1, respectively calculating the biaxial Young modulus of bulk gold and the surface biaxial Young modulus and initial stress of thin-film gold;
s2, calculating the surface atomic layer strain of the gold electrodes with different thicknesses under different charges according to the biaxial Young modulus, the surface biaxial Young modulus and the initial stress to obtain a relational expression between the charge density and the surface atomic layer strain;
s3, solving the relation between the whole bulk gold and the charge density according to the relation between the charge density and the surface atomic layer strain;
s4, constructing a nanoporous gold intrinsic stress model through the relationship between the whole bulk gold and the charge density; setting parameters of a nano porous gold intrinsic stress model; generating an example, and submitting the example to calculation;
and S5, after calculation, extracting the actuating strain.
Preferably, the step S1 specifically includes the steps of:
s11, calculating the energy density of the bulk gold under different strains under the vacuum condition;
s12, obtaining the biaxial Young modulus of the bulk gold through the relation between the energy density and the strain;
s13, calculating the super-cell length of the thin-film gold electrodes with different thicknesses under the charge of 0, and combining the biaxial Young modulus of the bulk gold to obtain the surface biaxial Young modulus and the initial stress.
Preferably, step S2 specifically includes the following steps:
s21, respectively calculating the surface atomic layer strain of 7-15 layers of thin-film gold electrodes under the electric charges of-0.3;
and S22, finding a relational expression between the charge density and the surface atomic layer strain by a symbolic regression method.
Preferably, in step S4, a nanoporous gold intrinsic stress model is constructed by using finite element software.
Preferably, the parameters of the nanoporous gold intrinsic stress model set in step S4 include material properties, application of material surface stress, interaction between components, and boundary conditions.
Preferably, the bulk material is selected from one of Au, C, ni or Cu.
The invention also discloses a trans-scale device based on the constitutive equation automatic construction and parameter extraction, which comprises a memory and one or more processors, wherein executable codes are stored in the memory, and when the one or more processors execute the executable codes, the trans-scale device is used for realizing the trans-scale method based on the constitutive equation automatic construction and parameter extraction.
The invention also discloses a computer readable storage medium, which stores a program, when the program is executed by a processor, the method realizes the above cross-scale method based on the constitutive equation automatic construction and parameter extraction.
The invention has the beneficial effects that:
1. the energy density of the bulk gold under different strains is calculated, and the biaxial Young modulus of the bulk gold is obtained by fitting a relational expression of the energy density and the strains so as to obtain a relational equation between the charge density and the electrode strains. On the basis, the strain of the gold film with different charges and different thicknesses is calculated. And fitting the magnitude of the surface atomic layer strain under different charges according to a data combination formula to obtain a series of surface atomic layer strains related to charge density.
2. The method is based on a symbolic regression method, and combines the dimension analysis, symmetry analysis, homogenization and other methods of the traditional mechanical modeling to find a relational expression between the charge density and the surface atomic layer strain. And constructing a constitutive equation with both accuracy and simplicity. The relation can accurately control the strain magnitude of the electrode by controlling the charge density of the electrode, and can be applied to a thin film Au electrochemical actuator.
3. The method provided by the invention is used for carrying out calculation simulation on the electric actuating response finite element method based on the intrinsic stress model, further promotes the application of the finite element method in the direction of the electrochemical actuator, completely realizes an automatic process through a script program, can effectively improve the pretreatment efficiency and promote the simulation research process, and provides a faster calculation method for rapidly simulating, calculating and researching the electrochemical actuating performance of the material.
4. The method develops a mechanical multi-field coupling model which takes the electrode surface stress strain in a simple charged solid-liquid interface as a core variable and comprises the size effect of the nano-scale material and the influence of electrode potential, and realizes the macroscopic simulation of the electrochemical actuation phenomenon of the nano-porous material. The macroscopic strain of the material obtained through finite element software Abaqus simulation calculation has guiding significance for experiments, and on the basis, the structure of the material can be optimized to a certain extent by combining machine learning, so that the highest strain/voltage ratio is obtained, and the electrochemical actuation performance of the material is improved.
The features and advantages of the present invention will be described in detail by embodiments in conjunction with the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a method from first principles computation to macro-scale simulation.
Fig. 2 is an energy density-strain diagram of bulk gold calculated by DFT, using Au (111) as an example.
FIG. 3 is a strain diagram of Au (111) electrodes with different numbers of layers under different charges
Fig. 4 is a graph of relationship between atomic layer charge density and strain on the surface of Au (111) obtained by a symbolic regression method using Au (111) as an example.
FIG. 5 is a strain cloud under electrochemical actuation response calculated after modeling in Abaqus2020 finite element software, using Au (111) as an example;
FIG. 6 is a graph of calculated strain clouds under electrochemical actuation response modeled in Abaqus2020 finite element software, using C (111) as an example;
FIG. 7 is a schematic diagram of surface area to volume ratio (SVR) and actuation strain extracted under the induction of a charge density of 0.03 | e |/A2 for a finite element simulation of the electro-dynamic response proposed in this embodiment for a nano-gold (111) intrinsic stress model of different shapes;
FIG. 8 is a schematic structural diagram of a trans-scale apparatus for automated construction and parameter extraction based on constitutive equations according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood, however, that the detailed description herein of specific embodiments is intended to illustrate the invention and not to limit the scope of the invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
Referring to fig. 1, a cross-scale method based on constitutive equation automatic construction and parameter extraction includes the following steps:
(1) And respectively calculating the biaxial Young modulus of the bulk material, the biaxial Young modulus of the surface of the thin film gold and the initial stress by adopting an intrinsic stress model based on JDFTx software.
The film material is a film extracted from a bulk material, and when the nano material film is extracted from an infinite bulk, the intrinsic stress and the higher surface energy are generated on the surface of the nano material film due to the breakage of chemical bonds on the surface. On this basis, the energy density of the bulk material under different strains under vacuum conditions was calculated, and the biaxial young's modulus of the bulk material was obtained from the relationship between the energy density and the strain. And then calculating the supercell length of the Au (111) surface thin film electrode under different thicknesses and different charges, fitting an intrinsic stress model under 0 charge to obtain a formula 1, and calculating the biaxial Young modulus and the intrinsic stress of the surface. In the calculation process, the electrode part adopts DFT calculation, and the electrolyte solution adopts a continuous medium model.
(2) Respectively calculating the strain of 7-15 layers of thin film material electrodes under-0.3 electric charges, obtaining the magnitude of surface atomic layer strain through a formula 1 of an intrinsic stress model, then finding a relational expression between surface layer strain and loaded charge density by a symbolic regression method, wherein the definition of the loaded charge surface density is that the electric charge added to the whole system is divided by the surface area of the electrode, and finally bringing the regression formula back to the formula 1 to obtain the relational expression between the electrode strain and the surface charge density of the whole material.
Preferably, in the step (2), the magnitude of the surface atomic layer strain is obtained by using a relation between the electrode global strain and the charge density described in the intrinsic stress model:
in the formula:
the strain of the entire electrode due to the surface excess charge,
is a bulk material with biaxial Young's modulus,
surface biaxial Young's modulus, h is the thickness of the entire film,
is the initial intrinsic stress generated by the thin film when the thin film is separated from the three-dimensional structure,
is the strain associated with the surface atomic layer and the charge density.
2. A finite element method of simulating the actuation response of a material electrode in an electrolyte, comprising the steps of:
(1) Establishing an intrinsic stress model of the material electrode, writing a corresponding modeling finite element program code, calling a finite element software Abaqus by using the finite element program code, generating a nanoporous material intrinsic stress model formed by a user-defined digital sequence, and realizing parametric modeling.
(2) Finite element pretreatment is carried out, corresponding finite element pretreatment program codes are written, the constitutive relation of the material is defined by writing subprogram umat, and the obtained constitutive equation is utilized to expand the required material properties. In order to simulate the actuation phenomenon of the material in the electrolyte, program codes are written to realize the application of the surface stress of the material based on an intrinsic stress model, the interaction between components and the setting of boundary conditions.
(3) In order to analyze the results quickly and intuitively, a script program needs to be written to perform post-processing on the model. And calculating the maximum displacement distance and strain by extracting node information of the model. The method for simulating the actuation phenomenon of the material in the electrolyte can calculate the macroscopic strain generated by the materials with different configurations under the induction of different surface charges.
According to the invention, firstly, the strain conditions of the nanometer material film electrodes with different thicknesses under different charges are calculated by using a first principle and a parallel cross-scale method of continuous medium coupling, and the change rule data of the in-plane strain of the electrode along with the charge density and the film thickness are obtained. Then, a surface intrinsic stress model is used, the surface intrinsic stress and the surface Young modulus of the material are obtained through fitting, and a mathematical relation between the surface intrinsic strain and the surface charge density is given through a machine learning symbolic regression method. Then, the invention realizes the numerical simulation of the electrochemical actuation response of the nano material thin film electrode under different surface charge densities by writing an intrinsic stress model which is based on an ABAQUS user subprogram and can apply stress to the surface and bringing in a constitutive relation of the electrode potential and the surface intrinsic strain.
The method firstly builds a mechanical-electrochemical coupled digital normal form constitutive equation by means of a machine learning method and a development method. The constitutive equation is constructed so that continuous medium scale mechanics multi-field coupling calculation and simulation of a complex system can be carried out. And then, the electrochemical actuation phenomenon of the material is effectively simulated and predicted, and the simulation process needs less computing resources and computing time, and has higher efficiency and lower cost. The idea framework and the flow of the invention have generality, can be used for reference by research of other material systems, and have certain guiding significance.
The first embodiment is as follows:
firstly, DFT is adopted to calculate the energy density of bulk gold under different strains under vacuum conditionAnd obtaining the biaxial Young modulus of the bulk gold according to the relation between the energy density and the strain. As shown in FIG. 2, a series of block gold energy densities are obtained by applying biaxial strains of-0.02 to the block, and the biaxial Young's modulus of the block gold can be obtained by fitting equation 2
In the formula: c is a constant.
When the electrode is not electrified, the electrode surface excess charge is 0, namely the strain caused by the charge
Initial stress at the moment when the surface has only a thin film extracted from the bulk
. Namely, the original formula is changed into:
in the formula:
the strain of the entire electrode due to the surface excess charge,
is a bulk gold biaxial Young's modulus,
surface biaxial Young's modulus, h is the thickness of the entire film,
when the film is bonded from a three-dimensional bodyInitial intrinsic stress is generated in the thin film when the structure is separated.
By calculating the different thickness of gold thin film electrodes under 0 charge, substituting into the biaxial Young's modulus of bulk gold
Initial stress can be obtained
Surface biaxial Young's modulus
。
After determining the energy density of Au (111) and fitting the magnitude of biaxial Young's modulus, the strain of the surface atomic layer due to charge was determined
The strain of the gold thin film with different charges and different thicknesses is calculated, and the result is shown in fig. 3. Surface atomic layer strain under different charges is then fitted
Can be used to obtain a series of strains of the surface atomic layer related to the charge density.
Finally, by a symbolic regression method, finding a relation between the charge density q and the surface atomic layer strain as follows:
finally, the obtained formula is substituted into the relation between the whole electrode strain and the charge density to obtain the relation between the strain and the charge of different layers, and the result is shown in fig. 4, and the relation between the charge density and the whole Au electrode is obtained:
therefore, for a thin film Au electrode, the strain magnitude of the electrode can be directly calculated through the thickness of the electrode and the density of the applied charges.
The present embodiment is directed to the finite element simulation calculation of the development of the actuation reaction of the Au (111) material in the electrolyte, and the development of the finite element simulation for the reaction mechanism is further promoted by the secondary development of the Abaqus and Python.
And (4) carrying out finite element method simulation of electrochemical actuation of the Au electrode in the electrolyte according to the obtained equation of the strain of the Au electrode changing along with the charge. The method comprises the following steps:
(1) The method is characterized in that a Fortran script, namely a for file, is written, constitutive relation is provided for an intrinsic stress model of the Au electrode strain according to an equation of the Au electrode strain changing along with charge, and the constitutive relation is defined by a Jacobian (Jacobian) matrix written in a program file, namely the change rate of a stress increment to a strain increment.
(2) The python script, i.e., the py file, is written, mainly containing the following simulation parameters:
and (2-1) carrying out parameterization generation on the intrinsic stress model of the nanoporous gold (111) by setting relevant parameters of the model size, utilizing a parameter control path method, and adopting a translation rotation and mirror image method.
(2-2) subjecting the built mold to solid processing into a shell to obtain a shell member. By General-User Material, material constants, such as modulus of elasticity and poisson's ratio, are defined and assigned to the corresponding component.
(2-3) adding an analysis Step-1, setting the time length to be 1, setting the maximum increment Step number to be 100, setting the minimum increment Step to be 1e-5, and opening the geometric nonlinearity.
(2-4) after the solid part and the shell part are assembled, setting the two parts to interact, wherein the property is binding.
(2-5) setting a hinge (U1 = U2= U3= 0) boundary condition on the body center of the model, namely (0, 0) point, and setting the midpoint in the outermost layer in each direction of the solid component as a point set.
(2-6) tetrahedrally meshing the solid part using C3D10 cells in Abaqus/Standard using a free meshing technique, with a mesh size of 2.5.
(2-7) performing linear, reduction integral and quadrilateral shell unit (S4R) meshing on the shell component by adopting an advanced algorithm in an Abaqus/Standard by using a free meshing technology, wherein the size of the mesh is 2.5.
(2-8) calling the Umat subprogram written in the step (1) and submitting a task
(3) And compiling a post-processing script, and extracting and calculating required information and results through post-processing. And performing coordinate operation by extracting a point set in the model, and finally outputting the coordinate operation in a txt file form, wherein the actuating effect of the structure is represented by the result of the post-processing.
(4) And (3) importing the flows in the steps (2) and (3) into a script program, and running the script program by using Abaqus finite element software to obtain a calculation result.
The simulation results are shown in fig. 5. As can be seen from the figure, the surface stress applied by the outer shell unit is distributed more uniformly on the surface of the solid unit and generates reasonable strain, which is in accordance with the actuation reaction phenomenon of Au (111) in the electrolyte.
Example two:
FIG. 6 is a finite element method simulation of electrochemical actuation of the C electrode in electrolyte, the simulation method and the specific steps are the same as those in the first embodiment; it can be seen from the figure that the surface stress applied by the outer shell unit is distributed more uniformly on the surface of the solid unit and generates reasonable strain, which is consistent with the actuation reaction phenomenon of C (111) in the electrolyte.
Fig. 7 presents the surface area to volume ratio (SVR) extracted under induction with a charge density magnitude of 0.03 | e |/a 2 versus actuation strain for models of different shapes for the finite element simulation of the electro-dynamic response proposed in this embodiment. It can thus be seen that the maximum actuation strain among the simulated structures is 1.03%, corresponding to a structure having a surface-to-volume ratio (SVR) of 0.80506.
The embodiment of the cross-scale method based on the constitutive equation automatic construction and parameter extraction can be applied to any equipment with data processing capability, such as computers and other equipment or devices. The apparatus embodiments may be implemented by software, or by hardware, or by a combination of hardware and software. The software implementation is taken as an example, and as a logical device, the device is formed by reading corresponding computer program instructions in the nonvolatile memory into the memory for running through the processor of any device with data processing capability. In terms of hardware, as shown in fig. 8, a hardware structure diagram of any device with data processing capability in which a cross-scale method based on constitutive equation automatic construction and parameter extraction is located according to the present invention is shown in fig. 8, except for the processor, the memory, the network interface, and the nonvolatile memory shown in fig. 8, any device with data processing capability in which an apparatus in the embodiment is located may also include other hardware according to an actual function of the any device with data processing capability, which is not described again. The implementation process of the functions and actions of each unit in the above device is specifically described in the implementation process of the corresponding step in the above method, and is not described herein again.
For the device embodiment, since it basically corresponds to the method embodiment, reference may be made to the partial description of the method embodiment for relevant points. The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present invention. One of ordinary skill in the art can understand and implement it without inventive effort.
The embodiment of the present invention further provides a computer readable storage medium, on which a program is stored, and when the program is executed by a processor, the method implements a cross-scale method based on constitutive equation automatic construction and parameter extraction in the above embodiments.
The computer readable storage medium may be an internal storage unit, such as a hard disk or a memory, of any data processing device described in any previous embodiment. The computer readable storage medium may also be any external storage device of a device with data processing capabilities, such as a plug-in hard disk, a Smart Media Card (SMC), an SD Card, a Flash memory Card (Flash Card), etc. provided on the device. Further, the computer readable storage medium may include both an internal storage unit and an external storage device of any data processing capable device. The computer-readable storage medium is used for storing the computer program and other programs and data required by the arbitrary data processing capable device, and may also be used for temporarily storing data that has been output or is to be output.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents or improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A trans-scale method based on constitutive equation automatic construction and parameter extraction is characterized by comprising the following steps:
s1, respectively calculating the biaxial Young modulus of a bulk material and the surface biaxial Young modulus and initial stress of a thin film material;
s2, calculating the surface atomic layer strain of the thin film material electrodes with different thicknesses under different charges according to the biaxial Young modulus, the surface biaxial Young modulus and the initial stress to obtain a relational expression between the charge density and the surface atomic layer strain;
s3, obtaining the relation between the whole block material and the charge density according to the relation between the charge density and the surface atomic layer strain;
the steps S2 and S3 specifically include the following operations:
respectively calculating the strain of 7-15 layers of thin film material electrodes under-0.3 charge, and using the strain between the whole strain of the electrodes and the charge density described in an intrinsic stress modelObtaining the magnitude of the surface atomic layer strain by using the relational expression, then finding the relational expression between the surface layer strain and the loaded charge density by using a symbolic regression method, wherein the definition of the loaded charge surface density is that the charges added to the whole system are divided by the surface area of the electrode, and finally bringing the relational expression between the surface layer strain and the loaded charge density back to the relational expression between the whole electrode strain and the charge density described in the intrinsic stress model to obtain the relational expression between the whole material electrode strain and the surface charge density; the relationship between electrode bulk strain and charge density described in the intrinsic stress model:
(ii) a In the formula:
the strain of the entire electrode due to the surface excess charge,
is a block material with a biaxial Young modulus,
surface biaxial Young's modulus, h is the thickness of the entire film,
is the initial intrinsic stress generated by the thin film when the thin film is separated from the three-dimensional structure,
is the strain related to the surface atomic layer and the charge density;
s4, constructing a nano porous material intrinsic stress model through the relation between the whole block material and the charge density; setting parameters of the intrinsic stress model of the nano porous material; generating an example, and submitting the example to calculation;
and S5, after calculation, extracting the actuating strain.
2. The cross-scale method for automatic construction and parameter extraction based on constitutive equations as claimed in claim 1, wherein the step S1 specifically comprises the following steps:
s11, calculating the energy density of the block material under different strains under the vacuum condition;
s12, obtaining the biaxial Young modulus of the block material according to the relation between the energy density and the strain;
s13, calculating the supercell length of the thin film material electrodes with different thicknesses under the charge of 0, and combining the biaxial Young modulus of the bulk material to obtain the surface biaxial Young modulus and the initial stress.
3. The trans-scale method based on constitutive equation automatic construction and parameter extraction as claimed in claim 1, wherein in step S4, finite element software is adopted to construct the intrinsic stress model of the nano-porous material.
4. The trans-scale method for automatically constructing and extracting parameters based on the constitutive equation as claimed in claim 1, wherein the parameters of the intrinsic stress model of the nano-porous material set in the step S4 comprise material properties, application of material surface stress, interaction between components and boundary conditions.
5. The trans-scale method for automatic construction and parameter extraction based on constitutive equations as claimed in claim 1, wherein the bulk material is selected from one of Au, C, ni or Cu.
6. A trans-scale device based on constitutive equation automatic construction and parameter extraction is characterized in that: comprising a memory having stored therein executable code and one or more processors that, when executing the executable code, perform a cross-scale method for automated construction and parameter extraction based on constitutive equations as claimed in any one of claims 1 to 5.
7. A computer-readable storage medium characterized by: stored thereon a program which, when executed by a processor, implements a cross-scale method for automated construction and parameter extraction based on constitutive equations as claimed in any one of claims 1 to 5.
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