Simulation of the Pseudoplasticity Effect in a Magnetoactive Elastomer under Compression and Tension

Purpose. Construction of a mathematical model of the behavior of a мagnetoactive elastomer (MAE), which takes into account magnetic and elastic interactions between filler particles and allows describing the effect of pseudoplasticity under compression and tension in an external magnetic field. Development of a software that implements this model. Methods. When solving an elastic problem in the framework of the theory of small deformations, the esys/escript library was used (this is a tool for implementing mathematical models in Python using the finite element method). To describe the MAE, the total energy is written, consisting of elastic and magnetic parts. To minimize it, taking into account the constraints in the form of non-penetration of particles, nonlinear programming algorithms from the libraries JuMP (this is a domain-specific modeling language for mathematical optimization built into the Julia language) and Ipopt - Interior Point Optimizer - is an open source software package for large-scale nonlinear optimization.

Results. A mathematical model of the behavior of a мagnetoactive elastomer is constructed, which takes into account magnetic and elastic interactions between filler particles, which makes it possible to describe the effect of pseudoplasticity (magnetic shape memory effect) during compression and tension in an external magnetic field. A software has been developed that implements this mathematical model. Loading curves in a magnetic field under compression and tension of a MAE sample are obtained.

Conclusion. From the results of the numerical calculation, it can be seen that the yield stress and residual strain in the MAE sample under compression and tension have significant differences. An explanation of the mechanisms responsible for pseudoplasticity when the sign of the load changes is proposed. The results obtained can be used to develop a phenomenological model of the MAE behavior with a structural parameter.

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