A Generalised Time-Dependent Mathematical Formulation for Magnetoelectrically Coupled Soft Solids at Finite Strains

To date, the mechanical models of magnetoelectric couplings at finite strains have mainly been limited to time-independent constitutive equations. This paper enhances the literature by developing a time-dependent electromagnetic constitutive equation to characterise the mechanical behaviour of soft solids at finite strains and take into account the full form of the Maxwell equations. Our formulation introduces a symmetrical total stress and uses recently developed spectral invariants in the amended energy function; as a result, the proposed constitutive equation is relatively simple and is amenable to a finite-element formulation.

Automated summary

This paper improves the existing literature by developing a time-dependent electromagnetic constitutive equation to describe the mechanical behavior of soft solids at finite strains, considering the full form of the Maxwell equations. The proposed model introduces a symmetrical total stress and utilizes recently developed spectral invariants in the amended energy function, making it relatively simple and suitable for finite element analysis.