Energy absorption box based on negative Poisson's ratio structure and design method thereof

Abstract

The invention belongs to the technical field of automobile safety, and particularly relates to an energy absorption box based on a negative Poisson's ratio structure and a design method thereof. The energy absorption box comprises a front mounting plate, a negative Poisson's ratio structure and a rear mounting plate. The front and rear ends of the negative Poisson's ratio structure are respectively connected with the front mounting plate and the rear mounting plate; the negative Poisson's ratio structure is integrally arranged between a front bumper and a rear bumper of a vehicle body and a gap between a crossbeam in the vehicle. The negative Poisson's ratio structure is formed by periodically arranging negative Poisson's ratio cell elements. The method has the characteristic that the material layout of the energy absorption box structure can be optimal by taking the specified negative Poisson's ratio value as a constraint condition and taking the overall maximum energy absorption as a target function through a topological optimization design method.

Description

Technical Field

[0001] The present invention belongs to the technical field of automobile safety, and in particular relates to an energy absorption box based on a negative Poisson's ratio structure and a design method thereof. Background Art

[0002] Crash boxes are thin-walled metal structures installed between the front and rear anti-collision beams and the longitudinal rails of a vehicle. Their primary function is to absorb energy during a collision by deforming, reducing the impact on the longitudinal rails and passenger compartment. Their design is based on the principle of "crush energy absorption." When the impact force exceeds a threshold, the crash box preferentially crumples and deforms, converting kinetic energy into heat, thereby reducing energy transfer efficiency.

[0003] Due to structural limitations, conventional thin-walled metal energy absorption boxes (such as those with square cross-sections) experience lateral contraction due to the Poisson effect when axially compressed, resulting in uncontrollable buckling modes (such as alternating symmetrical and asymmetric folding), low energy absorption efficiency, and excessively high initial peak forces, which can easily cause secondary damage to the protected structure. As a new type of multicellular structure, the negative Poisson's ratio structure, due to its unique lateral contraction characteristics, can produce greater volumetric strain during deformation, thereby significantly improving its energy absorption capacity. Existing negative Poisson's ratio structures (such as concave hexagonal honeycombs and chiral structures) mostly rely on parameter optimization or empirical methods to improve deformation modes, making it difficult to achieve a global optimization of the structural energy absorption capacity and can only provide suboptimal solutions that meet basic design requirements.

[0004] Therefore, it is very important to design an energy absorption box based on a negative Poisson's ratio structure and a design method thereof that can increase the passive safety of automobiles. Summary of the Invention

[0005] The present invention aims to overcome the problem in the prior art that existing negative Poisson's ratio structures (such as concave hexagonal honeycombs and chiral structures) mostly rely on parameter optimization or empirical methods to improve deformation modes, making it difficult to achieve global optimization of the structural energy absorption capacity. The present invention provides an energy absorption box based on a negative Poisson's ratio structure and a design method thereof, which can achieve optimal material layout of the energy absorption box structure through a topology optimization design method, with a specified negative Poisson's ratio value as a constraint condition and overall maximum energy absorption as the objective function.

[0006] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions: The present invention provides an energy absorption box based on a negative Poisson's ratio structure, comprising: A front mounting plate, a negative Poisson's ratio structure, and a rear mounting plate; the front and rear ends of the negative Poisson's ratio structure are connected to the front and rear mounting plates, respectively; the negative Poisson's ratio structure is positioned entirely between the front and rear bumpers and the interior beam of the vehicle; the negative Poisson's ratio structure is composed of stacked negative Poisson's ratio cells connected end to end; the negative Poisson's ratio cells are composed of a triangular region at the top and a circular region at the bottom connected by an inclined connecting edge, forming a continuous and smooth geometric shape. Stacking the negative Poisson's ratio cells end to end, i.e., connecting the upper and lower cell walls, to form a unit structure, fully utilizes the negative Poisson's ratio characteristics, enabling coordinated lateral contraction and deformation during impact, effectively extending the energy absorption path and significantly improving energy absorption efficiency.

[0007] Preferably, the negative Poisson's ratio cell has an axially symmetrical arrow-shaped outline as a whole; the left and right sides of the triangular area extend and narrow symmetrically, and finally converge at the top point, which constitutes the highest point of the entire structure, while the arc-shaped area at the bottom transitions to both sides in a gentle curve, forming the base part of the structure.

[0008] Preferably, the triangular area has a specific height, and its two sides start from the two ends of the bottom arc, extend outward and upward with a uniform slope, and meet at the top to form a sharp angle. The angle of the sharp angle is precisely designed to ensure that deformation in a specific direction can be generated when the material is subjected to stress, thereby triggering a negative Poisson's ratio effect. The length of the side and the inclination angle cooperate with each other, so that during the stress process, the lateral and longitudinal deformations of the structure show an unconventional coupling relationship.

[0009] Preferably, the arc-shaped area at the bottom includes an arc and a vertical straight line segment. The arc has a specific radius. The arc-shaped design not only provides a stable support foundation for the structure, but also forms a local stress concentration and dispersion mechanism when subjected to force, and cooperates with the deformation of the triangular area to achieve overall negative Poisson's ratio performance. The arc has a smooth and continuous curvature, and there is no sudden change at the connection with the vertical straight line segment and the side of the triangle, ensuring the smoothness of the force transmission path.

[0010] The length of the vertical straight line segment is equal to the depth of the circular arc depression, which not only ensures the structural integrity of the upper and lower parts, but also plays a role in transmitting and distributing force in the force analysis, so that the force can be evenly transmitted from the top to the bottom and effectively dispersed in the semicircular area at the bottom, avoiding excessive local stress and causing structural damage. At the same time, the existence of the vertical straight line segment also provides a clear symmetry axis for the entire cell structure, so that the force and deformation on the left and right sides can maintain symmetry, further enhancing the stability and predictability of the negative Poisson's ratio effect.

[0011] Preferably, the negative Poisson's ratio cell structure can be prepared using a variety of materials such as metals, polymers, and ceramics. By adjusting the mechanical properties of the material such as the elastic modulus and yield strength, as well as the geometric parameters of the cell (such as the angle and side length of the triangle, the radius of the arc, etc.), different degrees of negative Poisson's ratio effect can be achieved. The size and material of the cell can be optimized according to the actual stress conditions and performance requirements to achieve the best use effect.

[0012] The present invention also provides a design method for an energy absorption box based on a negative Poisson's ratio structure, comprising the following steps: S1, define the initial design domain and discretize it: The crash box is divided into multiple triangular regions, each of which serves as an optimization region, i.e., the design domain. The design domain is discretized into multiple triangular finite element meshes. The design variable is specified as the relative density of the mesh element material. A multi-constraint optimization model is constructed with the overall maximum energy absorption as the objective function. Constraints include volume fraction constraints and equivalent negative Poisson's ratio constraints. Periodic boundary conditions and displacement load constraints are applied. S2, finite element solution: Import design variables and calculate the stiffness matrix for each variable , integrate the stiffness matrices of all variables to form the global stiffness matrix K , solve the equilibrium equation KU(x)=F , get the global displacement field , F is the accompanying load vector; S3, sensitivity filtering: Calculate the original sensitivity of the objective function and volume fraction constraint to the design variables, and calculate the weighted average of the original sensitivity within the search range to generate the filtered sensitivity; S4, moving asymptote solution: The original optimization problem is constructed into a dual sub-problem, and the moving asymptotic boundary is defined. The Lagrange multiplier update strategy with negative Poisson's ratio constraint is introduced to solve the design variables. S5, output optimization results: Convergence is determined. If convergence is satisfied, the final material layout of the area to be optimized is output. Otherwise, the design variables are updated and the process returns to step S2 until convergence is satisfied.

[0013] Preferably, in step S1, the constraint condition is: The design variables satisfy , , the volume fraction constraint is , the equivalent Poisson's ratio constraint is , Represents the equivalent Poisson's ratio of the structure after topology optimization; The objective function C(X) is: , is the global displacement field; Adjoint load vector F Indicates the output displacement degrees of freedom The load component at the DOF is 1, and the load components at other DOFs are 0, that is, ; In the formula, Indicates the optimization process The displacement value of each constraint point; It is e The relative density of each unit material ranges from 0 to 1; represents the optimized volume constraint; f represents the specified volume fraction of the initial region; represents the initial region volume; It is the lower limit of the unit relative density, used to prevent the unit relative density from When it is taken as zero, the resulting unit displacement tends to infinity; is the specified negative Poisson's ratio constraint value.

[0014] Preferably, in step S2, the design variable refers to a column vector composed of density values of discrete grid elements.

[0015] Preferably, step S3 includes the following steps: S31, calculate the derivatives of the objective function and volume constraint score with respect to the design variables, and obtain the original sensitivity and , in the search radius The sensitivity of the objective function and the constraints is calculated by weighted average, and the calculation formula is as follows: ; ; in, is the partial derivative of the filtered objective function with respect to the design variables, is the partial derivative of the filtered constraint equation with respect to the design variables; x j Indicates the unit e Center, radius Neighborhood cells within is the weight of each unit’s sensitivity, It is a unit e With unit j The Euclidean distance between the center points. The closer the weight is to the center, the greater the influence. Time is 0.

[0016] Preferably, step S4 includes the following steps: S41, perform a second-order inverse Taylor expansion on the original objective function and constraint equations, and use the current design variables and gradient information to construct an approximate subproblem with local strict convexity. The approximate subproblem is as follows: The objective function is a subproblem , the constraint equation subproblem is , m is the number of constraints, n is the number of design variables, y i and z are all constructed pseudo-design variables. 、 and All are artificial parameters. and are the physical upper and lower limits of the design variables, Indicates no material. Represents physical material; S42, optimize the approximate subproblem to obtain new design variables, ; S43, adjust the position of the moving asymptote according to the new design variables.

[0017] As a preference, in step S5, the convergence refers to the requirement that the relative fluctuation amplitude of the objective function , is the tolerance for convergence judgment, is the k+1th objective function, is the k-th objective function.

[0018] Compared with the prior art, the present invention has the following beneficial effects: (1) The negative Poisson's ratio energy absorption box design method disclosed in the present invention uses a topology optimization design method, takes a specified negative Poisson's ratio value as a constraint condition, and takes the overall maximum energy absorption as the objective function to optimize the material layout of the energy absorption box structure. Compared with the traditional energy absorption box structure, the obtained negative Poisson's ratio energy absorption box has an energy absorption rate increase of more than 30%, an initial peak load reduction of more than 50%, and an overall energy absorption increase of more than 200%; (2) The unique structural design and negative Poisson's ratio characteristics of the present invention enable the energy absorption box to effectively reduce the damage to the occupants when it is impacted. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of a design method for an energy absorption box based on a negative Poisson's ratio structure in the present invention; Figure 2 A schematic diagram of the structure of an energy absorption box based on a negative Poisson's ratio structure in the present invention; Figure 3 Schematic diagram of a structure of a negative Poisson's ratio cell in the present invention; Figure 4 A schematic diagram of the displacement-impact force curve of two energy absorbing boxes at an impact speed of 3 m / s; Figure 5 A schematic diagram of a displacement-impact force curve of two energy absorbing boxes at an impact speed of 20 m / s; Figure 6 Schematic diagram of energy absorption curves of two energy absorption boxes at an impact speed of 3 m / s; Figure 7 This is an energy absorption curve of two energy absorption boxes at an impact speed of 20m / s.

[0020] In the figure: front mounting plate 1, negative Poisson's ratio structure 2, rear mounting plate 3, side edge 101, inclined connecting edge 102, arc edge 103, vertical straight line segment 104. DETAILED DESCRIPTION

[0021] To more clearly illustrate the embodiments of the present invention, specific embodiments of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings and other embodiments can be obtained based on these drawings without inventive efforts.

[0022] Step 1: Define the initial design domain and discretize it. Take an equilateral triangle as the design domain with a base of 20 mm and a height of 30 mm. Discretize the design domain into a triangular unit grid with a grid density of 60×60. The material properties are defined as 6061 aluminum alloy with an elastic modulus of E 0 =70GPa, Poisson's ratio is 0.33, external load is 10KN, the midpoint of the bottom edge is fixed, negative Poisson's ratio constraint v 0 -0.8, filter radius is 1.2, volume ratio constraint V 0 is 0.3; Step 2: Finite element solution. Divide the design domain into 60×60 design variables and calculate the local stiffness matrix for each element. , , integrate all element stiffness matrices to form a global stiffness matrix K , ,in , is the relative density of the e-th unit material, initially is 1; p is the penalty factor, take 0.3; solve the linear equations KU=F , obtain the node displacement; Step 3: Sensitivity filtering. By controlling the derivative of the objective function with respect to the design variable, the sensitivity of the design variables corresponding to adjacent units will not change too much. The sensitivity of the objective function is: ; The sensitivity of the constraint is .

[0023] In search radius The sensitivity of the objective function and the constraints is calculated by weighted average, and the calculation formula is as follows: ; ; in, is the partial derivative of the filtered objective function with respect to the design variables, is the partial derivative of the filtered constraint equation with respect to the design variables; x j Indicates the unit e Center, radius Neighborhood cells within is the weight of each unit’s sensitivity, It is a unit e With unit j The Euclidean distance between the center points. The closer the weight is to the center, the greater the influence. Time is 0.

[0024] Step 4: Solve by moving asymptotic method. Convert the original optimization problem into a series of sub-problems. k The objective function of the subproblem of step 1 is , the constraints are ,in =1, =1000, =0,th k The solution of the sub-problem is calculated by the dual method and used as the initial solution of the k+1th iteration, and finally the approximate solution of the original problem is achieved by using the solution of the sub-problem.

[0025] Step 5: Output the optimization results. Set the convergence criterion. If the relative change of the objective function , output the final material layout of the optimized area, otherwise update the design variables and return to step 2 until the convergence conditions are met.

[0026] In addition, if Figure 2As shown, the present invention also provides a crash box based on a negative Poisson's ratio structure. This unit structure is formed by stacking negative Poisson's ratio cells end to end, i.e., by connecting the upper and lower cell walls. This unit structure is then arrayed along the axial direction of the crash box to form a negative Poisson's ratio structure 2. The front and rear ends of the periodically arranged negative Poisson's ratio structures are connected to a front mounting plate 1 and a rear mounting plate 3, respectively, to form the negative Poisson's ratio crash box. The overall dimensions are 80 mm × 60 mm × 90 mm, with a wall thickness of 1.2 mm.

[0027] like Figure 3 As shown, the height of the triangular area of the negative Poisson's ratio cell structure is 30 mm, the length of the side 101 is 15 mm, the angle with the symmetry axis is 34°, the angle between the inclined connecting edge 102 and the symmetry axis is 8°, the arc radius is 36 mm, and the length of the vertical straight line segment 104 is the same as the depth of the concave arc edge 103.

[0028] The negative Poisson's ratio cell has an axisymmetric arrow-shaped outline as a whole. The negative Poisson's ratio cell is composed of a sharp triangular area at the top and an arc-shaped area at the bottom connected by an inclined connecting edge, forming a continuous and smooth geometric shape. The left and right sides of the triangular area extend and narrow symmetrically, and finally converge at the sharp point at the top, which constitutes the highest point of the entire structure, while the arc-shaped area at the bottom transitions to both sides in a gentle curve, forming the base of the structure.

[0029] The triangular area has a specific height, and its two sides start from the two ends of the bottom arc and extend outward and upward at a uniform slope, converging at the top to form a sharp angle. The angle of this sharp angle is precisely designed to ensure that it can produce deformation in a specific direction when the material is subjected to stress, thereby triggering a negative Poisson's ratio effect. The length of the side and the inclination angle are coordinated with each other, so that during the stress process, the lateral and longitudinal deformations of the structure show an unconventional coupling relationship.

[0030] The arc-shaped area at the bottom consists of an arc and a vertical straight line segment. The arc has a specific radius. The arc-shaped design not only provides a stable support foundation for the structure, but also forms a local stress concentration and dispersion mechanism when subjected to force, coordinating the deformation of the triangular area to achieve overall negative Poisson's ratio performance. The arc has a smooth and continuous curvature, and there are no sudden changes at the connection with the vertical straight line segment and the side of the triangle, ensuring the smoothness of the force transmission path.

[0031] The length of the vertical straight line segment is equal to the depth of the circular arc depression, which not only ensures the structural integrity of the upper and lower parts, but also plays a role in transmitting and distributing force in the force analysis, so that the force can be evenly transmitted from the top to the bottom and effectively dispersed in the semicircular area at the bottom, avoiding excessive local stress and causing structural damage. At the same time, the existence of the vertical straight line segment also provides a clear symmetry axis for the entire cell structure, so that the force and deformation on the left and right sides can maintain symmetry, further enhancing the stability and predictability of the negative Poisson's ratio effect.

[0032] The 6061 aluminum material properties are given to the energy absorption box of the embodiment, and its density is , elastic modulus is 70GPa, Poisson's ratio is 0.33, and yield strength is 300MPa. Calculated by finite element method, the calculation results are as follows Figures 4 to 7 As shown in the figure, under the impact speed of 3m / s and 20m / s, the initial peak load (PCF) of the negative Poisson's ratio energy absorption box is 37896N and 189435N, the average impact load (MCF) is 56883N and 57486N, and the total absorbed energy is 5870N and 7963N, respectively. Compared with the traditional square energy absorption box, the average impact load of the Poisson's ratio energy absorption box under the conditions of 3m / s and 20m / s is increased by 185.8% and 114.6%, the initial peak load is reduced by 89.7% and 50.8%, and the total energy absorption is increased by 293.6% and 302.9%, respectively.

[0033] The above description is only a detailed description of the preferred embodiments and principles of the present invention. For ordinary technicians in this field, based on the ideas provided by the present invention, there may be changes in the specific implementation methods, and these changes should also be considered as the scope of protection of the present invention.

Claims

1. The energy absorption box based on the negative Poisson's ratio structure is characterized by: include: a front mounting plate, a negative Poisson's ratio structure, and a rear mounting plate; The front and rear ends of the negative Poisson's ratio structure are connected to the front mounting plate and the rear mounting plate respectively; The negative Poisson's ratio structure is arranged as a whole between the front and rear bumpers of the vehicle body and the gap between the vehicle beam; the negative Poisson's ratio structure is composed of negative Poisson's ratio cells stacked end to end; the negative Poisson's ratio cell is composed of a triangular area at the top and an arc-shaped area at the bottom connected by an inclined connecting edge.

2. The energy absorption box based on the negative Poisson's ratio structure according to claim 1 is characterized in that: The negative Poisson's ratio cell has an axially symmetrical arrow-shaped outline as a whole; the left and right sides of the triangular area extend and narrow symmetrically, and finally converge at the top point, which constitutes the highest point of the entire structure, while the arc-shaped area at the bottom transitions to both sides in a gentle curve, forming the base of the structure.

3. The energy absorption box based on the negative Poisson's ratio structure according to claim 2 is characterized in that: The two sides of the triangular area start from the two ends of the bottom arc, extend outward and upward with a uniform slope, and meet at the top to form a sharp angle.

4. The energy absorption box based on the negative Poisson's ratio structure according to claim 3 is characterized in that: The arc-shaped area includes an arc and a vertical straight line segment; the length of the vertical straight line segment is the depth of the arc depression.

5. A design method for an energy absorption box based on a negative Poisson's ratio structure, based on the energy absorption box based on a negative Poisson's ratio structure according to any one of claims 1 to 4, characterized in that: The design method of the energy absorption box based on the negative Poisson's ratio structure includes the following steps: S1, define the initial design domain and discretize it: The collision box is divided into multiple triangular regions, each of which is a region to be optimized, namely the design domain, and the design domain is discretized into multiple triangular finite element meshes; Specify the design variable as the relative density of the mesh element material; A multi-constraint optimization model was constructed with the overall maximum energy absorption as the objective function. Constraints included volume fraction constraints and equivalent negative Poisson's ratio constraints. Periodic boundary conditions and displacement load constraints were also applied. S2, finite element solution: Import design variables and calculate the stiffness matrix for each variable , integrate the stiffness matrices of all variables to form the global stiffness matrix K , solve the equilibrium equation KU(x)=F , get the global displacement field , F is the accompanying load vector; S3, sensitivity filtering: Calculate the original sensitivity of the objective function and volume fraction constraint to the design variables, and calculate the weighted average of the original sensitivity within the search range to generate the filtered sensitivity; S4, moving asymptote solution: The original optimization problem is constructed into a dual sub-problem, and the moving asymptotic boundary is defined. The Lagrange multiplier update strategy with negative Poisson's ratio constraint is introduced to solve the design variables. S5, output optimization results: Convergence is determined. If convergence is satisfied, the final material layout of the area to be optimized is output. Otherwise, the design variables are updated and the process returns to step S2 until convergence is satisfied.

6. The design method of the energy absorption box based on the negative Poisson's ratio structure according to claim 5 is characterized in that: In step S1, the constraints are: The design variables satisfy , , the volume fraction constraint is , the equivalent Poisson's ratio constraint is , Represents the equivalent Poisson's ratio of the structure after topology optimization; The objective function C(X) is: , is the global displacement field; Adjoint load vector F Indicates the output displacement degrees of freedom The load component at the DOF is 1, and the load components at other DOFs are 0, that is, ; In the formula, Indicates the optimization process The displacement value of each constraint point; It is e The relative density of each unit material ranges from 0 to 1; represents the optimized volume constraint; f represents the specified volume fraction of the initial region; represents the initial region volume; It is the lower limit of the unit relative density, used to prevent the unit relative density from When it is taken as zero, the resulting unit displacement tends to infinity; is the specified negative Poisson's ratio constraint value.

7. The design method of an energy absorption box based on a negative Poisson's ratio structure according to claim 5 is characterized in that: In step S2, the design variables refer to column vectors composed of density values of discrete grid elements.

8. The design method of an energy absorption box based on a negative Poisson's ratio structure according to claim 5 is characterized in that: Step S3 includes the following steps: S31, calculate the derivatives of the objective function and volume constraint score with respect to the design variables, and obtain the original sensitivity and , in the search radius The sensitivity of the objective function and the constraints is calculated by weighted average, and the calculation formula is as follows: ； ； in, is the partial derivative of the filtered objective function with respect to the design variables, is the partial derivative of the filtered constraint equation with respect to the design variables; x j Indicates the unit e Center, radius Neighborhood cells within is the weight of each unit’s sensitivity, It is a unit e With unit j The Euclidean distance between the center points. The closer the weight is to the center, the greater the influence. Time is 0.

9. The design method of an energy absorption box based on a negative Poisson's ratio structure according to claim 5 is characterized in that: Step S4 includes the following steps: S41, perform a second-order inverse Taylor expansion on the original objective function and constraint equations, and use the current design variables and gradient information to construct an approximate subproblem with local strict convexity. The approximate subproblem is as follows: The objective function is a subproblem , the constraint equation subproblem is , m is the number of constraints, n is the number of design variables, y i and z are all constructed pseudo-design variables. 、 and All are artificial parameters. and are the physical upper and lower limits of the design variables, Indicates no material. Represents physical material; S42, optimize the approximate subproblem to obtain new design variables, ; S43, adjust the position of the moving asymptote according to the new design variables.

10. The design method of an energy absorption box based on a negative Poisson's ratio structure according to claim 5, characterized in that: In step S5, the convergence refers to the relative fluctuation amplitude of the objective function. , is the tolerance for convergence judgment, is the k+1th objective function, is the k-th objective function.

Images