A method for obtaining macroscopic three-dimensional equivalent properties of materials

Abstract

The invention belongs to the technical field of material mechanics, and discloses a method for obtaining material macroscopic three-dimensional equivalent attribute. The method for obtaining material macroscopic three-dimensional equivalent attribute comprises the following steps of (1) establishing a double-scale coordinate system used for describing the material and the microstructure, and constructing a material macroscopic equivalent attribute model based on a progressive extension theory; (2) constructing a periodic boundary model of a three dimensional microstructure; (3) establishing a periodic constraint relation of the three dimensional microstructure through finite element analysis; (4) establishing a linear elasticity equilibrium equation of the three dimensional microstructure based on the periodic constraint relation, and obtaining a displacement field of the microstructure according to the linear elasticity equilibrium equation; and (5) solving unit strain energy based on finite element analysis and the displacement field of the microstructure, and obtaining the material macroscopic three-dimensional equivalent attribute. According to the invention, unit interactive energy is introduced in finite element analysis, a equivalence relation between the total strain energy of the microstructure under the unit test strain and the material attribute is established, and the material attribute is efficiently obtained.

Description

technical field

[0001] The invention belongs to the technical field of material mechanics, and more specifically relates to a method for obtaining macroscopic three-dimensional equivalent properties of materials. Background technique

[0002] The research on the prediction of equivalent performance of materials has a long history. Initially, it only involved the performance of each component of the material and its volume ratio, such as the most basic voiget-Reuss upper and lower limits of equivalent performance of materials, and the more accurate two-dimensional Hill-Hashin upper and lower bounds for isotropic materials and Hashin-shtrikman upper and lower bounds for three-dimensional isotropic materials. Later, it developed into a more complicated prediction of the upper and lower limits of the equivalent performance of anisotropic materials. For example, Torquato introduced a point correction function, which made the upper and lower limits of the equivalent performance pr...

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