High polymer deformation model construction method based on variable-order fractional derivative

Abstract

The invention discloses a high polymer deformation model construction method based on a variable-order fractional derivative, and the method specifically comprises the following steps: S1, building a discrete fractional derivative constitutive model related to a strain rate according to the mechanical behavior of a high polymer in a compression or tensile deformation process; s2, establishing an inverse function relationship between relaxation time theta and a loading strain rate c in the fractional derivative constitutive model; s3, establishing a relationship between an elastic modulus E and a strain rate c of the fractional derivative constitutive model; s4, describing the order change of the fractional derivative in the fractional derivative constitutive model by adopting a power function; and S5, establishing a strain rate-related high polymer continuous variable fractional derivative constitutive model, fitting experimental data, and determining model parameters. The strain rate-related variable-order fractional derivative constitutive model which is convenient to apply, clear in physical concept and capable of meeting the precision requirement is provided for compression or tensile deformation of a high polymer, so that the defects of a linear variable-order model in description of compression or tensile strain strengthening behaviors of the high polymer are overcome.

Description

technical field [0001] The invention belongs to the technical field of polymer mechanical behavior modeling, in particular to a method for constructing a constitutive model of polymer deformation based on variable order fractional derivative. Background technique [0002] Due to the development of finer and higher levels, polymers have become ubiquitous in various fields such as industrial and agricultural production, cutting-edge technology and even medical products. As an exploration of more potential applications, the mechanical properties of polymers have important implications for engineering applications. In recent decades, researchers have carried out extensive experiments to study the mechanical response of various polymers, such as polyurea, polyethylene terephthalate, polyurethane, polypropylene, and even semi-crystalline polymers. The experimental results show that the stress-strain response exhibits complex nonlinearity and strong strain rate dependence under la...

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Problems solved by technology

However, the existing constitutive models present a complex mathematical form when describing the stress-strain behavior related to the loading strain rate, so it is urgent to propose an effective model that is accurate and has fewer parameters to describe the mechanical behavior of polymers.

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