Construction and solving method of elastic and viscous plastic material fractal constitutive model

Abstract

The invention discloses a construction and solving method of an elastic and viscous plastic material fractal constitutive model, basic mechanical element modules are combined and connected to form a primitive module, the primitive module is utilized to iterate the basic mechanical element modules on the basis of the primitive module to obtain a fractal element constitutive model, and in the iteration process, the parameter of each basic mechanical element module in the first iteration newly-added part is a preset multiple of the parameter of each basic mechanical element module in the element module; and starting from the second iteration, the parameter of each basic mechanical element module in the newly added part of the next iteration is a preset multiple of the parameter of each basic mechanical element module in the newly added part of the previous iteration. The model constructed by the invention not only can well describe the elastic, viscoplastic and plastic mechanical properties of the material, but also can well describe the very complicated actual physical structure of the material in the microscopic aspect; in addition, the complexity of the fractal constitutive model can be expressed, the number of parameters can not be increased, and solving of the constructed fractal constitutive model can be well achieved.

Description

technical field [0001] The invention relates to the technical field of material mechanics, in particular to a method for constructing and solving a fractal constitutive model of an elastic-viscoplastic material. Background technique [0002] Materials in nature have complex physical and mechanical properties, including various forms of elasticity, viscosity, plasticity and combinations thereof. The component model uses several basic mechanical components to describe the elasticity, viscosity and plasticity of materials simply and intuitively, and is an important means to study the mechanical properties of materials. [0003] The mathematical essence of the component model is a differential equation, and its order is related to the complexity of the model. Every time a basic mechanical component is added to the model, the order of the differential equation will increase by one order. When the model is more complex, it will lead to difficulties in solving the equation. Even a...

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Problems solved by technology

[0003] The mathematical essence of the component model is a differential equation, and its order is related to the complexity of the model. Every time a basic mechanical component is added to the model, the order of the differential equation will increase by one order. When the model is more complex, it will lead to difficulties in solving the equation. can't even get an analytical solution

[0004] At present, commonly used component models such as Maxwell and Burgers have a small number of components. Although they are easy to solve, the model is not expressive enough to describe the elasto-viscoplastic mechanical properties of materials well, and adding components will lead to differential equations Unable to solve

On the other hand, the actual physical structure of the material at the mesoscopic level is very complex, and the component model simplifies the physical structure of the material into a series-parallel combination of several basic mechanical elements, which does not match the actual structure

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