Modelling the residually stressed magneto-electrically coupled soft elastic materials

Bifurcation analysis of residually stressed neo-Hookean and Ogden electroelastic tubes

“…Shmuel & deBotton [17] investigate the propagation of waves in a finitely deformed tube subject to a radial electric field for different tube geometries for fixed axial stretch and zero axial load. In recent years, the importance of including the residual stress field in the analysis of residually stressed materials has been recognized and is reflected by the increase of recent publications on this topic [18][19][20][21][22][23][24][25][26]. Ciarletta et al [27] use the theory of incremental deformation superimposed on a finitely deformed circular cylindrical configuration to study the stability of an incompressible hyperelastic tube with the resulting equations solved for both radial and circumferential residual stresses.…”

Anisotropic stress softening of electromagnetic Mullins materials

“…In Section 5, the invariants l i , a i and b i are spectral variables [1] that depend on U , f , and g. The invariants a i are considered as material parameters, which have a constant value in an elastic free energy function. The use of spectral invariants requires that a free energy must have a unique value when two or more of the principal stretches have the same value and it must satisfy some symmetry conditions [22].…”

“…Multifunctional materials, such as electromagnetic materials, are innovative and smart as they can adapt their physical and mechanical properties as a result of external stimuli; brief introductions on these materials can be found, e.g., in Shariff et al [1] and hence, to avoid repetition, we skip detailed introduction on this topic.…”

“…The presence of electromagnetic fields in elastic solids has been the essence of numerous publications (see, for example, references [1][2][3][4] and the references therein). There is a considerable interest in the mechanical behaviour of electromagnetic materials in recent years and attempts to comprehend the mechanical influence of electromagnetic fields on solid materials can be found in the literature [1][2][3][4]; however, in most of the works, the materials have been assumed to be hyperelastic bodies, but in reality, most materials are not purely elastic and quite often they exhibit an anisotropic stress-softening phenomenon widely known as the Mullins effect [5]. If the stress is softened significantly, modelling the materials as a purely elastic deformation can be erroneous.…”

“…Spectral invariants and damage function, which mechanically characterize the proposed infinite family of strain energy functions and are fundamental in our modelling, are presented in Section 5. Based on the work of references [1,[11][12][13], we propose an infinite-family-strain-energy prototype in Section 6. We then use this prototype to give results, in Section 7, for boundary value problems that could be useful in laboratory experiments.…”