CN-121980679-A - Near-field dynamics-based material multistage linear plastic hardening model construction and implementation method

CN121980679ACN 121980679 ACN121980679 ACN 121980679ACN-121980679-A

Abstract

The invention belongs to the technical field of engineering mechanics and materials, and discloses a method for constructing and implementing a material multi-section linear plastic hardening model based on near field dynamics, which is used for effectively solving nonlinear hardening behaviors of a material. The method comprises the steps of constructing a near-field dynamics initial numerical discrete model, setting boundary conditions required to be applied to the initial numerical discrete model, calculating current configuration parameters of an N-th time step, constructing a multi-section linear plastic hardening model parameter matrix, constructing a yield judgment criterion, judging a yield state on the basis of the multi-section linear plastic hardening model parameter matrix and the yield judgment criterion, calculating equivalent plastic strain increment according to the yield state, and updating a near-field dynamics force density vector and a plastic related quantity according to the equivalent plastic strain increment. On the premise of ensuring the precision, the calculation efficiency of the near-field dynamics elastoplasticity problem is obviously improved, and the calculation obstacle is cleared for applying the high-precision fracture mechanics analysis to a large-scale engineering structure.

Inventors

LIU YIYANG
LIU JINGXI
YI XIANG

Assignees

华中科技大学

Dates

Publication Date: 20260505
Application Date: 20260106

Claims (9)

1. A method for constructing and implementing a material multistage linear plastic hardening model based on near field dynamics is characterized by comprising the following steps: s1, model construction and initialization, namely constructing a near field dynamics initial numerical discrete model based on a material entity structure to be analyzed, dispersing the structure into a plurality of material points, and defining a near field domain for each material point; s2, applying boundary conditions, namely setting corresponding boundary conditions on the initial numerical discrete model according to external load and constraint conditions; S3, calculating time stepping and deformation, namely calculating the position and speed of all object points and the current configuration parameters of each near-field key in the current (n+1) th time step according to the boundary condition and the state of the last time step under an explicit time integration frame, wherein the configuration parameters comprise the elongation rate, the volume expansion quantity and the accumulated equivalent plastic strain of the near-field key; S4, constructing a multistage linear hardening model, namely constructing a multistage linear plastic hardening model parameter matrix based on material properties and nonlinear hardening rate, wherein the construction process comprises the steps of obtaining a real stress-plastic strain curve of a material, dispersing the curve into a plurality of continuous linear line segments from a yield point, determining the tangential modulus of each line segment and the intercept on a plastic strain axis, and forming a parameter lookup table; S5, explicitly judging the yield state, namely constructing a yield judgment criterion based on the current force vector state deflection and accumulated equivalent plastic strain, and judging that each material point is in an elastic loading and unloading state, a plastic unloading state or a plastic loading state currently according to the current configuration parameters obtained in the step S3; S6, plastic response branch processing, namely, performing branch calculation according to the judgment result of the step S5: s6.1, if the elastic loading and unloading state or the plastic unloading state is adopted, enabling the equivalent plastic strain increment of the current time step to be zero, and calculating a force density vector based on a pure elastic constitutive relation; s6.2, if the plastic loading state is adopted, calculating an equivalent plastic strain increment of the current time step based on the current configuration parameter, the yield judgment criterion and the multi-section linear plastic hardening model parameter matrix; S7, updating force states and solving system response, namely updating force density vectors and plastic related quantities of all near-field keys according to the equivalent plastic strain increment determined in the step S6; And S8, iteratively converging and outputting results, namely repeating the steps S3 to S7, advancing the time step until a preset converging condition or a simulation termination condition is met, and outputting simulation results comprising plastic deformation, stress-strain response and crack propagation paths of the material.
2. The method for constructing and implementing a near field dynamics-based material multistage linear plastic hardening model according to claim 1, wherein the method comprises the following steps: Near field bond elongation in step S3 The calculation formula of (2) is as follows: Wherein Y is the particle coordinate of the current configuration, and X is the particle coordinate of the reference configuration; the calculation formula of the volume expansion amount θ is as follows: Where ω is the weight function, x represents the two norms of the reference configuration coordinate, V j represents the mass point volume, j represents the mass point of the same family, and N represents the mass point number of the same family.
3. The method for constructing and implementing a multistage linear plastic hardening model of a material based on near field dynamics as set forth in claim 1, wherein the expression of the multistage linear plastic hardening model in step S4 is as follows: Wherein, the Representing the elastic phase of the model, E is the elastic modulus, In order to be elastically strained, the elastic strain, The plastic phase of the model is represented, Indicating the intersection of the nth line segment with the plastic stress axis, Represents the tangential modulus of the nth line segment, the superscript p represents plasticity, Indicating plastic strain.
4. The method for constructing and implementing the near-field dynamics-based material multistage linear plastic hardening model according to claim 1, wherein the method comprises the following steps of: the yield criterion in step S5 is defined by the following expression: Wherein, the Representing all the sets in which a plastic condition may occur, The yield function is represented by a function of yield, Representing an associated function associated with the plastic component t d , Representing a material function related to the accumulated plastic strain, Representing the Euclidean space associated with the plastic component t d .
5. The method for constructing and implementing the near-field dynamics-based material multistage linear plastic hardening model according to claim 1, wherein the method comprises the following steps of: Force density vector in step S6.1 The calculation formula of (2) is as follows: Wherein, the For the near-field kinetic coefficients, As a function of the weight, Is the judgment value of the elastic deflection of the elongation of the N+1th time step.
6. The method for constructing and implementing the near-field dynamics-based material multistage linear plastic hardening model according to claim 1, wherein the method comprises the following steps of: in step S6.2, the calculation formula of the equivalent plastic strain increment is as follows: Wherein, the In order to be an equivalent plastic strain increment, As the judgment value of the force density vector, For the yield value of the nth plastic segment, For the tangential modulus of the nth plastic segment, The yield value for the i +1 plastic segment, For the yield value of the ith plastic segment, For the tangential modulus of the ith plastic segment, For the tangential modulus of the ith plastic segment, In order to be an equivalent plastic strain, For the tangential modulus of the current plastic segment, 、 Is a near field kinetic coefficient.
7. The method for constructing and implementing the near-field dynamics-based material multistage linear plastic hardening model according to claim 1, wherein the method comprises the following steps of: the specific steps of updating the force density vector in step S7 include: S7.1, updating accumulated equivalent plastic strain; s7.2, updating a plastic deflection part of the elongation of the near-field key according to the associated flow rule; S7.3, calculating a force vector state deflection part and a plasticity related quantity of the (n+1) th time step, wherein the specific calculation formula is as follows: Wherein, the As the equivalent plastic stress of the current time step, In order to be an equivalent plastic strain increment, As the judgment value of the force density vector, Is the increment of elongation plastic deflection of the n+1 step, 、 Is a near field kinetic coefficient.
8. A material plasticity simulation system based on near field dynamics, which is used for realizing the method according to any one of claims 1-7, and is characterized by comprising a model initialization module for constructing a discrete model and applying boundary conditions, a material constitutive module for providing a multi-segment linear plastic hardening model parameter matrix, an explicit solver module for completing time stepping, yield judgment, plastic increment calculation and force state update, and a data output module for outputting and visualizing simulation results.
9. An engineering structure fracture and fatigue evaluation device, which is characterized by comprising the material plastic simulation system based on near field dynamics according to claim 8 and is used for carrying out elastoplastic fracture simulation on ships and aerospace structures so as to predict crack initiation and propagation behaviors and fatigue life.

Description

Near-field dynamics-based material multistage linear plastic hardening model construction and implementation method Technical Field The invention belongs to the technical field of engineering mechanics and materials, and particularly relates to a method for constructing and implementing a material multistage linear plastic hardening model based on near field dynamics. Background The structural fracture of a ship is one of the main causes of a sunken ship accident. Through accurate fracture mechanics analysis and fatigue life assessment, the strength and life of the structure under various load conditions can be predicted, so that catastrophic accidents are avoided. The ship is accompanied by plastic strengthening and crack propagation during the fracture, eventually causing the overall fracture. It is therefore important to simulate the plastic strengthening and crack propagation processes of metals by numerical means. Simulating the crack initiation and propagation process of a crack by numerical methods has been a very challenging scientific topic. In continuous media mechanics, constitutive relationships of materials are typically described by differential equations. However, when crack tips or cracks occur, the control equation expressed in differential form loses physical meaning at these locations. This presents a number of difficulties in conventional continuous media mechanics in addressing the problems associated with discontinuous fields. In recent years, an emerging mesh-free method based on a non-local idea, i.e. a near field dynamics (PD) method, has been widely used to simulate crack growth problems. In this method, the substance is discretized into substance points, each substance point interacts with the substance points in its vicinity, and the problem of simulating the discontinuous region is effectively solved by controlling the equation in an integral form. For the traditional nonlinear plastic strengthening method, a Newton iteration method and other corresponding numerical methods are needed to solve the near-field dynamics equivalent plastic strain increment, however, the process needs a complicated numerical iteration process, so that the PD calculation efficiency can be greatly reduced, and the real-ship scale fracture and fatigue calculation can be influenced. The iteration process has huge calculation cost, and severely restricts the application of the near-field dynamics method in large-scale engineering problems such as real ship scale and the like. Aiming at the problems, in order to realize rapid plastic calculation of PD under the real ship scale, the invention provides a method for constructing and implementing a material multistage linear plastic hardening model based on near field dynamics, which is used for effectively solving the nonlinear hardening behavior of a material, and the discrete nonlinear hardening curve is used for a plurality of linear sections, so that iterative calculation is avoided, and the calculation efficiency is remarkably improved. Disclosure of Invention Aiming at the defects or improvement demands of the prior art, the invention provides a method for constructing and implementing a material multi-section linear plastic hardening model based on near field dynamics, which aims to quickly solve the nonlinear hardening behavior of a material, thereby solving the technical problem that the calculation efficiency is low due to complex iteration when the equivalent plastic strain increment is calculated by the existing plastic hardening model. According to one aspect of the invention, there is provided a method for constructing and implementing a near field dynamics based material multi-segment linear plastic hardening model, comprising the steps of: s1, model construction and initialization, namely constructing a near field dynamics initial numerical discrete model based on a material entity structure to be analyzed, dispersing the structure into a plurality of material points, and defining a near field domain for each material point; s2, applying boundary conditions, namely setting corresponding boundary conditions on the initial numerical discrete model according to external load and constraint conditions; S3, calculating time stepping and deformation, namely calculating the position and speed of all object points and the current configuration parameters of each near-field key in the current (n+1) th time step according to the boundary condition and the state of the last time step under an explicit time integration frame, wherein the configuration parameters comprise the elongation rate, the volume expansion quantity and the accumulated equivalent plastic strain of the near-field key; S4, constructing a multistage linear hardening model, namely constructing a multistage linear plastic hardening model parameter matrix based on material properties and nonlinear hardening rate, wherein the construction process comprises the steps of obtaining a real stre