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Method for predicating periodic porous material equivalent young's modulus

A technology of Young's modulus and porous materials, which is applied in the direction of testing the strength of materials by applying a stable bending force, and can solve the problem of predicting the equivalent Young's modulus of materials that cannot reflect changes in cell size

Inactive Publication Date: 2011-03-02
NORTHWESTERN POLYTECHNICAL UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0004] In order to overcome the deficiency that the equivalent Young's modulus of materials predicted by the prior art method cannot reflect the change of cell size, the present invention provides a method for predicting the equivalent Young's modulus of periodic porous materials, a method for equivalent bending strain energy, When predicting the equivalent Young's modulus of periodic porous materials, it can accurately reflect the influence of cell size changes on the mechanical properties of the unit cell

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  • Method for predicating periodic porous material equivalent young's modulus
  • Method for predicating periodic porous material equivalent young's modulus
  • Method for predicating periodic porous material equivalent young's modulus

Examples

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Embodiment 1

[0036] Example 1: Equivalent Young's modulus of a square hole unit cell.

[0037] 1) To establish a porous beam structure with periodic square holes, its parameters include the length of the beam L=60, the period length l=1 of the microstructure along the x direction, the thickness of the beam along the z direction h=2l, and the wall thickness of the square hole unit cell t=0.1; the properties of the solid material are: Young's modulus E=70e9, Poisson's ratio v=0.34, density ρ=2774; set the scaling factor n=1 at this time.

[0038] 2) Perform pure bending loading on the periodic square hole porous beam structure, according to the periodicity and symmetry of the structure along the x direction, the bending strain energy U on a single period l b for:

[0039] U b = M 2 2 ∫ 0 l 1 E ( ...

Embodiment 2

[0058] Example 2: Equivalent Young's modulus of equilateral triangular pore unit cell.

[0059] 1) To establish a porous beam structure with periodic equilateral triangular holes, its parameters include the length L=60 of the beam, the period length l=1 of the microstructure along the x direction, and the thickness of the beam along the z direction h = 3 2 l , The wall thickness of the equilateral triangular hole unit cell is t=0.1; the material properties of the entity are: Young's modulus E=70e9, Poisson's ratio v=0.34, and density ρ=2774; set the scale factor n=1 at this time.

[0060] 2) Perform pure bending loading on the porous beam structure with periodic equilateral triangular holes. According to the periodicity and symmetry of the structure along the x direction, the bending strain energy U on a single period lb for:

[0061] U b = ...

Embodiment 3

[0080] Example 3: Equivalent Young's modulus of regular hexagonal pore unit cells.

[0081] 1) To establish a porous beam structure with periodic regular hexagonal holes, its parameters include the length L=60 of the beam, the period length 3l=3 of the microstructure along the x direction, and the thickness of the beam along the z direction h = 3 l , The wall thickness of the regular hexagonal hole unit cell is t=0.1; the property of the solid material is:

[0082] Young's modulus E=70e9, Poisson's ratio v=0.34, density ρ=2774; set the scaling factor n=1 at this time.

[0083] 2) Perform pure bending loading on the porous beam structure with periodic regular hexagonal holes. According to the periodicity and symmetry of the structure along the x direction, the bending strain energy U on a single period l b for:

[0084] U b = M 2 ...

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Abstract

The invention discloses a method for forecasting an equivalent Young's modulus of a periodic porous material, which comprises the following steps: firstly, establishing an entity model of a periodic porous girder structure; carrying out pure bending loading on the entity model of the periodic porous girder structure; equalizing the periodic porous girder into the homogenized girder; loading the same equivalent bending moment on the homogenized girder; and forecasting the equivalent Young's modulus of the periodic porous material and the equivalent Young's modulus of the periodic porous material single cell. A bending strain energy equivalence method is adopted, to solve the phenomena that the prior art cannot reflect the dimension effect of the equivalent Young's modulus of the periodic porous material along the dimension change of a microstructure when the prior art forecasts the equivalent Young's modulus of the periodic porous material, provide an analytic function relation betweenthe equivalent Young's modulus of the periodic porous material and a dimension scaling factor n, really reflect the dimension effect of the equivalent Young's modulus of the periodic porous material along the change of the dimension scaling factor n of the microstructure.

Description

technical field [0001] The invention relates to a method for predicting the equivalent Young's modulus of a material, in particular to a method for predicting the equivalent Young's modulus of a periodic porous material. Background technique [0002] Document 1 "B Hassani, E Hinton. A review of homogenization and topology optimization II-analytical and numerical solution of homogenization equations. Computers and Structures 69, 1998, 719-738." discloses a method based on small-scale asymptotic expansion to solve the solid layer The homogenization method of the equivalent modulus of the composite material unit cell is given, and the numerical calculation results of the equivalent modulus of the rectangular hole material unit cell are given. This method establishes a strict mathematical description relationship between the material equivalent performance at the macro scale and the microstructure configuration at the material scale, the mechanical properties of the component ma...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G01N3/20
Inventor 张卫红戴高明张进
Owner NORTHWESTERN POLYTECHNICAL UNIV
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