A constitutive macroscale model for compressible magneto-active polymers based on computational homogenization data: Part II — Magnetic nonlinear regime

This paper presents a comprehensive, microstructure-guided framework for the macroscopic, continuum-based modeling of isotropic, compressible magneto-active polymers (MAPs). Based on the methodology along with the foundations that were laid in the first part of this paper series, we further extend the constitutive framework in this follow-up contribution towards the magnetic nonlinear regime. Key idea of the constitutive approach is an additive split of the material part of the total energy density function into three contributions associated with (i) an elastic ground-stress, (ii) a magnetically induced mechanical stress, and (iii) the magnetization, respectively. We propose suitable constitutive functions in an energy-based setting that allow to accurately capture occurring saturation effects. The constitutive macroscale model fulfills the poly-convexity condition for a large set of {F̄,B̄}, which implies Legendre–Hadamard ellipticity and thus ensures material stability. The accuracy and excellent predictive performance of the proposed phenomenological macroscale model is demonstrated by the direct comparison with the homogenized material response of the underlying microstructure for various load cases. This is supplemented by a detailed comparative study with previously developed macroscale models that points out the advantages and superior performance of the proposed formulation. Further characteristics and modeling capabilities are illustrated by the solution of some application-oriented boundary value problems along with the application of a micro-macro decoupling scheme. The main emphasis of the numerical studies lies on the investigation of the magnetostrictive and magnetorheological effect of compressible MAPs at the macroscale level.