CN116702631B - Electron beam additive manufacturing constitutive relation calculation method based on artificial neural network - Google Patents

Electron beam additive manufacturing constitutive relation calculation method based on artificial neural network Download PDF

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CN116702631B
CN116702631B CN202310988095.1A CN202310988095A CN116702631B CN 116702631 B CN116702631 B CN 116702631B CN 202310988095 A CN202310988095 A CN 202310988095A CN 116702631 B CN116702631 B CN 116702631B
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equivalent
plastic strain
equivalent plastic
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CN116702631A (en
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张宏
张意达
彭堃恩
张博
杨洋
胡正纬
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Sichuan University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/10—Additive manufacturing, e.g. 3D printing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P10/00—Technologies related to metal processing
    • Y02P10/25—Process efficiency

Abstract

The invention discloses a method for calculating constitutive relation of electron beam additive manufacturing based on an artificial neural network, which comprises the steps of obtaining a stress-strain curve of an electron beam additive manufacturing material; according to the stress-strain curve of the electron beam additive manufacturing material, calculating equivalent plastic strain and equivalent stress of test stress by adopting a data iteration method; establishing a mapping relation between equivalent stress and yield stress of equivalent plastic strain and test solution stress and equivalent plastic strain increment based on an artificial neural network; and calculating a constitutive model of the electron beam additive manufacturing material according to the established mapping relation. The invention not only can improve the accuracy of the material constitutive model and provide a data driving means for manufacturing the material constitutive model by electron beam additive, but also can complete the establishment of the material constitutive model through experimental data, and does not need to utilize a large amount of knowledge reserves and carry out formula deduction to obtain the material constitutive model.

Description

Electron beam additive manufacturing constitutive relation calculation method based on artificial neural network
Technical Field
The invention relates to the technical field of electron beam additive manufacturing, in particular to an artificial neural network-based constitutive relation calculation method for electron beam additive manufacturing.
Background
Electron beam additive manufacturing is an additive manufacturing technology in which high-energy electron beams are used as heat sources to enable materials to undergo melting and solidification processes, so that layer-by-layer stacking of the materials is achieved. The materials used for electron beam additive manufacturing are mainly metal powders. Johnson-Cook plastic models are mainly used in engineering practice to describe the viscoplasticity of metals. The specific parameters of the Johnson-Cook plastic model need to be identified through experiments, and then the parameters are applied to the specific finite element calculation process.
The Johnson-Cook plastic model requires identifying constitutive model parameters from experimental data, which is difficult. Furthermore, the Johnson-Cook plastic model has difficulty accurately characterizing the constitutive model of the material used in the additive manufacturing process. Therefore, it is necessary to develop a material constitutive model with wider applicability and simpler operation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an electron beam additive manufacturing constitutive relation calculation method based on an artificial neural network.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
an electron beam additive manufacturing constitutive relation calculating method based on an artificial neural network comprises the following steps:
s1, obtaining a stress-strain curve of an electron beam additive manufacturing material;
s2, calculating equivalent plastic strain and equivalent stress of test stress by adopting a data iteration method according to a stress-strain curve of the electron beam additive manufacturing material;
s3, establishing a mapping relation between equivalent stress and yield stress of equivalent plastic strain and test solution stress and equivalent plastic strain increment based on an artificial neural network;
s4, calculating a constitutive model of the electron beam additive manufacturing material according to the mapping relation established in the step S3.
Further, the step S2 specifically includes the following steps:
s21, initializing initial equivalent plastic strain, initial yield stress, initial equivalent plastic strain increment and equivalent stress of test solution stress;
s22, calculating the yield stress of the first iteration step and the equivalent stress of the test solution stress according to the initial equivalent plastic strain, the initial yield stress and the set equivalent plastic strain increment of the first iteration step;
s23, calculating the equivalent stress of the yield stress and the test solution stress of the current iteration step according to the equivalent plastic strain, the yield stress and the equivalent plastic strain increment of the previous iteration step and the set equivalent plastic strain increment of the current iteration step.
Further, the calculation formula of the yield stress of the first iteration step in step S22 is:
；
wherein ,for the yield stress of the first iteration step, +.>For initial yield stress>For the set equivalent plastic strain increment of the first iteration step +.>Is the initial equivalent plastic strain.
Further, in step S22, the calculation formula of the equivalent stress of the test solution stress in the first iteration step is:
；
wherein ,equivalent stress of the test solution stress for the first iteration step, +.>As the yield stress of the first iteration step,Gfor shear modulus>Is the equivalent plastic strain increment of the first iteration step.
Further, in step S23, the calculation formula of the equivalent plastic strain in the previous iteration step is:
；
wherein ,for the last iteration stepnEquivalent plastic strain of-1, < >>Last iteration step of settingnEquivalent plastic strain increment of-1, +.>For the last two iteration stepsn-equivalent plastic strain of 2.
Further, the calculation formula of the yield stress of the current iteration step in step S23 is:
；
wherein ,for the current iteration stepnYield stress of>For the last iteration stepnThe yield stress of the (E) -1,for the current iteration step of the settingnIs>For the last iteration stepn-1 equivalent plastic strain.
Further, in step S23, the calculation formula of the equivalent stress of the test solution stress in the current iteration step is:
；
wherein ,for the current iteration stepnEquivalent stress of test solution stress of +.>For the current iteration stepnIs used to produce the product,Gfor shear modulus>For the current iteration step of the settingnIs a significant increase in equivalent plastic strain.
Further, the step S3 specifically includes the following steps:
s31, constructing an input vector by using the equivalent plastic strain obtained in the step S2 and the equivalent stress of the test stress;
s32, constructing a prediction vector according to the yield stress and the equivalent plastic strain increment obtained in the step S2;
s33, training the artificial neural network by taking the input vector and the predicted vector as training data, and establishing a mapping relation between the equivalent stress of the equivalent plastic strain and the test solution stress and the yield stress and the equivalent plastic strain increment.
Further, the step S4 specifically includes the following steps:
s41, calculating test stress and equivalent stress of the test stress according to the yield stress, the equivalent plastic strain and the equivalent plastic strain increment obtained in the step S2;
s42, judging whether the yield condition is met currently; if yes, go to step S44; otherwise, go to step S43;
s43, updating the stress according to the equivalent stress of the test stress obtained in the step S41, and performing a step S47;
s44, calculating a plastic flow direction according to the test stress and the equivalent stress of the test stress obtained in the step S41;
s45, obtaining corresponding yield stress and equivalent plastic strain increment based on the mapping relation established in the step S3 according to the equivalent plastic strain and the equivalent stress of the test solution stress obtained in the step S41;
s46, updating stress according to the equivalent stress of the test stress obtained in the step S41 and the equivalent plastic strain increment obtained in the step S45;
s47, updating the equivalent plastic strain according to the equivalent plastic strain obtained in the step S41 and the equivalent plastic strain increment obtained in the step S45;
s48, updating the jacobian matrix.
The invention has the following beneficial effects:
the invention aims at the characteristics of the electron beam additive manufacturing process and the requirement of numerical simulation calculation to innovatively invent an artificial neural network constitutive model aiming at the process, so that the artificial neural network constitutive model can be used for constructing a reasonable additive manufacturing material constitutive model and can be applied to the calculation of the electron beam additive manufacturing process, and the constitutive model of the material is extracted from a stress-strain curve obtained by an experiment by a data driving method. The method not only can improve the accuracy of the material constitutive model and provide a data driving means for manufacturing the material constitutive model by electron beam additive, but also can complete the establishment of the material constitutive model through experimental data, and does not need to utilize a large amount of knowledge reserves and conduct formula deduction to obtain the material constitutive model.
Drawings
Fig. 1 is a schematic flow chart of a method for calculating constitutive relation of electron beam additive manufacturing based on an artificial neural network in the invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, an embodiment of the present invention provides a method for calculating constitutive relation of electron beam additive manufacturing based on an artificial neural network, which includes steps S1 to S4 as follows:
s1, obtaining a stress-strain curve of an electron beam additive manufacturing material;
in an alternative embodiment of the present invention, the stress-strain curve of the electron beam additive manufacturing material is obtained from experimental data by performing a simulation test of the electron beam additive manufacturing material.
S2, calculating equivalent plastic strain and equivalent stress of test stress by adopting a data iteration method according to a stress-strain curve of the electron beam additive manufacturing material;
in an alternative embodiment of the present invention, a data iteration method is adopted in the present embodiment, and the data points of the stress-strain curve of the electron beam additive manufacturing material obtained in the step S1 are interpolated, so as to obtain equivalent plastic strain and equivalent stress of the test stress, which are used as training data for subsequently constructing the artificial neural network constitutive model.
The step S2 specifically comprises the following steps:
s21, initializing initial equivalent plastic strain, initial yield stress, initial equivalent plastic strain increment and equivalent stress of test solution stress;
specifically, the present embodiment first requires initializing parameters, including initializing an initial equivalent plastic strainInitial yield stress->Initial equivalent plastic Strain increment->Equivalent stress of test solution stress>。
S22, calculating the yield stress of the first iteration step and the equivalent stress of the test solution stress according to the initial equivalent plastic strain, the initial yield stress and the set equivalent plastic strain increment of the first iteration step;
specifically, the present embodiment performs a first-step iterative calculation, and first randomly sets an equivalent plastic strain increment for each iterative step according to the magnitude required for the calculation.
Equivalent plastic strain increment according to the first iteration stepInitial equivalent plastic Strain->And initial yield stress>Calculating yield stress of the first iteration step>The calculation formula is as follows:
。
yield stress according to the calculated first iteration stepAnd the set equivalent plastic strain increment of the first iteration step +.>Calculating equivalent stress of the trial stress of the first iteration step +.>The calculation formula is as follows:
；
wherein ,Gis the shear modulus.
S23, calculating the equivalent stress of the yield stress and the test solution stress of the current iteration step according to the equivalent plastic strain, the yield stress and the equivalent plastic strain increment of the previous iteration step and the set equivalent plastic strain increment of the current iteration step.
Specifically, similarly to step S22, the present embodiment performs the second-step iterative calculation, first according to the set equivalent plastic strain increment of the first iterative stepAnd initial equivalent plastic strain->Calculating the equivalent plastic strain of the first iteration step +.>The calculation formula is as follows:
。
equivalent plastic strain according to the calculated first iteration stepEquivalent plastic strain increment of the second iteration step>And yield stress of the first iteration step +.>Calculating yield stress of the second iteration step>The calculation formula is as follows:
。
yield according to the calculated second iteration stepStressAnd the set equivalent plastic strain increment of the second iteration step +.>Calculating equivalent stress of the trial stress of the second iteration step +.>The calculation formula is as follows:
；
similar to the second iterative calculation, the present embodiment performs the firstnStep of iterative calculation, firstly according to the set firstnEquivalent plastic strain increment of-1 iteration stepAnd (d)n-2 equivalent plastic strain of iterative steps +.>Calculate the firstn-1 equivalent plastic strain of iterative steps +.>The calculation formula is as follows:
。
according to the calculated firstn-1 equivalent plastic strain of iterative stepSet firstnEquivalent plastic strain increment of iteration step +.>And (d)n-1 yield stress of iteration step->Calculate the firstnBy iterative stepsYield stress->The calculation formula is as follows:
。
according to the calculated firstnYield stress of iteration stepAnd set up the firstnEquivalent plastic strain increment of iteration stepCalculate the firstnEquivalent stress of the trial stress of the iteration step +.>The calculation formula is as follows:
。
the required training data is finally obtained by continuously repeating the above process.
S3, establishing a mapping relation between equivalent stress and yield stress of equivalent plastic strain and test solution stress and equivalent plastic strain increment based on an artificial neural network;
in an alternative embodiment of the present invention, step S3 of this embodiment specifically includes the following steps:
s31, constructing an input vector by using the equivalent plastic strain obtained in the step S2 and the equivalent stress of the test stress;
s32, constructing a prediction vector according to the yield stress and the equivalent plastic strain increment obtained in the step S2;
s33, training the artificial neural network by taking the input vector and the predicted vector as training data, and establishing a mapping relation between the equivalent stress of the equivalent plastic strain and the test solution stress and the yield stress and the equivalent plastic strain increment, wherein the mapping relation is expressed as:
。
since the functional relationship of the yield stress equivalent plastic strain is complex, the functional relationship is required to be obtained through parameter identification based on experimental data in a conventional algorithm. Therefore, the embodiment establishes the mapping relation between the equivalent stress of the equivalent plastic strain and the test solution stress and the increment of the yield stress and the equivalent plastic strain by means of the data driving characteristic of the neural network, thereby obtaining the constitutive model of the artificial neural network by encoding. The embodiment utilizes the artificial neural network to input equivalent plastic strainEquivalent stress to test solution stress->Yield stress +.>And equivalent plastic strain increase->。
After training the constitutive model of the artificial neural network, the embodiment can also verify and calculate the constitutive model of the artificial neural network, check the calculation result, and finally obtain the constitutive model of the artificial neural network applicable to the current experimental materials. If the checking result is poor, the constitutive model of the artificial neural network can be continuously trained through a simulation or experimental means, and finally a proper result is obtained.
S4, calculating a constitutive model of the electron beam additive manufacturing material according to the mapping relation established in the step S3.
In an alternative embodiment of the present invention, step S4 of the present embodiment specifically includes the following steps:
s41, calculating test stress and equivalent stress of the test stress according to the yield stress, the equivalent plastic strain and the equivalent plastic strain increment obtained in the step S2;
specifically, the present embodiment obtains the flexion according to step S2Stress of clothingEquivalent plastic strain->And equivalent plastic strain increase->Calculating the test relief stress +.>And equivalent stress of test stress +.>。
S42, judging whether the yield condition is met currently; if yes, go to step S44; otherwise, go to step S43;
specifically, the present embodiment determines whether or not the elastic assumption is satisfied by the yield condition. If the stress is met, the electron beam additive manufacturing material reaches the yield condition, the elasticity is assumed to be wrong, the equivalent plastic strain increment is calculated through the constitutive model of the artificial neural network, and the stress updating is completed. If the yield condition is not met, the electron beam additive manufacturing material is not yielding, the elasticity assumption is correct, and the stress is updated according to the elasticity.
S43, updating the stress according to the equivalent stress of the test stress obtained in the step S41, and performing a step S47;
specifically, in this embodiment, when the electron beam additive manufacturing material is not yielding, the equivalent plastic strain increment is setYield stress->The stress is relieved according to the test obtained in step S41>Equivalent stress update stress->The update formula is:
。
s44, calculating a plastic flow direction according to the test stress and the equivalent stress of the test stress obtained in the step S41;
specifically, the present embodiment obtains the test stress according to step S41And test equivalent stress of stressCalculating the plastic flow directionnThe calculation formula is as follows:
。
s45, obtaining corresponding yield stress and equivalent plastic strain increment based on the mapping relation established in the step S3 according to the equivalent plastic strain and the equivalent stress of the test solution stress obtained in the step S41;
specifically, the present embodiment utilizes an artificial neural network to input equivalent plastic strainEquivalent stress to test solution stress->Yield stress +.>And equivalent plastic strain increase->。
S46, updating stress according to the equivalent stress of the test stress obtained in the step S41 and the equivalent plastic strain increment obtained in the step S45;
specifically, the present embodiment obtains the equivalent stress of the test solution stress according to step S41And equivalent plastic strain increment obtained in step S45 +.>Update stress->The update formula is:
。
s47, updating the equivalent plastic strain according to the equivalent plastic strain obtained in the step S41 and the equivalent plastic strain increment obtained in the step S45;
specifically, the present embodiment obtains equivalent plastic strain according to step S41And equivalent plastic strain increment obtained in step S45 +.>Update equivalent plastic strain->The update formula is:
。
s48, updating the jacobian matrix.
Specifically, the present embodiment updates the jacobian matrix according to the stress and equivalent plastic strain updated in steps S41 to S47.
The invention aims at the characteristics of the electron beam additive manufacturing process and the requirement of numerical simulation calculation to innovatively invent an artificial neural network constitutive model aiming at the process, so that the artificial neural network constitutive model can be used for constructing a reasonable additive manufacturing material constitutive model and can be applied to the calculation of the electron beam additive manufacturing process, and the constitutive model of the material is extracted from a stress-strain curve obtained by an experiment by a data driving method. The method can not only improve the accuracy of the material constitutive model, but also provide a data driving means for manufacturing the material constitutive model by electron beam additive, and can complete the establishment of the material constitutive model through experimental data, and the constitutive model of the material is obtained by carrying out formula deduction without utilizing a large amount of knowledge reserves.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.

Claims (2)

1. An electron beam additive manufacturing constitutive relation calculating method based on an artificial neural network is characterized by comprising the following steps of:
s1, obtaining a stress-strain curve of an electron beam additive manufacturing material;
s2, calculating equivalent plastic strain and equivalent stress of test stress by adopting a data iteration method according to a stress-strain curve of the electron beam additive manufacturing material; the method specifically comprises the following steps:
s21, initializing initial equivalent plastic strain, initial yield stress, initial equivalent plastic strain increment and equivalent stress of test solution stress;
s22, calculating the yield stress of the first iteration step and the equivalent stress of the test solution stress according to the initial equivalent plastic strain, the initial yield stress and the set equivalent plastic strain increment of the first iteration step;
the calculation formula of the yield stress of the first iteration step is as follows:
；
wherein ,for the yield stress of the first iteration step, +.>For initial yield stress>For the set equivalent plastic strain increment of the first iteration step +.>Is the initial equivalent plastic strain;
the calculation formula of the equivalent stress of the test solution stress in the first iteration step is as follows:
；
wherein ,equivalent stress of the test solution stress for the first iteration step, +.>As the yield stress of the first iteration step,Gfor shear modulus>Equivalent plastic strain increment for the first iteration step;
s23, calculating the equivalent stress of the yield stress and the test solution stress of the current iteration step according to the equivalent plastic strain, the yield stress and the equivalent plastic strain increment of the previous iteration step and the set equivalent plastic strain increment of the current iteration step;
wherein the calculation formula of the equivalent plastic strain in the previous iteration step is as follows:
；
wherein ,for the last iteration stepnEquivalent plastic strain of-1, < >>Last iteration step of settingnEquivalent plastic strain increment of-1, +.>For the last two iteration stepsn-equivalent plastic strain of 2;
the calculation formula of the yield stress of the current iteration step is as follows:
；
wherein ,for the current iteration stepnYield stress of>For the last iteration stepn-yield stress of 1->For the current iteration step of the settingnIs>For the last iteration stepn-equivalent plastic strain of 1;
the calculation formula of the equivalent stress of the test solution stress in the previous iteration step is as follows:
；
wherein ,for the current iteration stepnEquivalent stress of test solution stress of +.>For the current iteration stepnIs used to produce the product,Gfor shear modulus>For the current iteration step of the settingnEquivalent plastic strain increment of (2);
s3, establishing a mapping relation between equivalent stress and yield stress of equivalent plastic strain and test solution stress and equivalent plastic strain increment based on an artificial neural network; the method specifically comprises the following steps:
s31, constructing an input vector by using the equivalent plastic strain obtained in the step S2 and the equivalent stress of the test stress;
s32, constructing a prediction vector according to the yield stress and the equivalent plastic strain increment obtained in the step S2;
s33, training the artificial neural network by taking the input vector and the predicted vector as training data, and establishing a mapping relation between the equivalent stress of the equivalent plastic strain and the test solution stress and the yield stress and the equivalent plastic strain increment;
s4, calculating a constitutive model of the electron beam additive manufacturing material according to the mapping relation established in the step S3.
2. The method for calculating the constitutive relation of electron beam additive manufacturing based on the artificial neural network according to claim 1, wherein the step S4 specifically comprises the following steps:
s41, calculating test stress and equivalent stress of the test stress according to the yield stress, the equivalent plastic strain and the equivalent plastic strain increment obtained in the step S2;
s42, judging whether the yield condition is met currently; if yes, go to step S44; otherwise, go to step S43;
s43, updating the stress according to the equivalent stress of the test stress obtained in the step S41, and performing a step S47;
s44, calculating a plastic flow direction according to the test stress and the equivalent stress of the test stress obtained in the step S41;
s45, obtaining corresponding yield stress and equivalent plastic strain increment based on the mapping relation established in the step S3 according to the equivalent plastic strain and the equivalent stress of the test solution stress obtained in the step S41;
s46, updating stress according to the equivalent stress of the test stress obtained in the step S41 and the equivalent plastic strain increment obtained in the step S45;
s47, updating the equivalent plastic strain according to the equivalent plastic strain obtained in the step S41 and the equivalent plastic strain increment obtained in the step S45;
s48, updating the jacobian matrix.
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基于正交试验-BP神经网络的GH4169膜片微束TIG焊接工艺优化;余果;尹玉环;高嘉爽;郭立杰;;焊接学报(第11期);全文 *
电弧增材制造综述：技术流派与展望;马驰;刘永红;纪仁杰;李常龙;;电加工与模具(第04期);全文 *

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