A Convex Multi-Variable based computational framework for multilayered electro-active polymers

Finite electro-elasticity with physics-augmented neural networks

“…5, c.f. [56]. The two phases a and b occupy volume fractions c a = h a 0 / h a 0 + h b 0 and c b = 1 − c a , respectively, where h a 0 and h b 0 denote the thicknesses of the phases in the initial configuration B 0 (with small h a 0 , h b 0 to comply with homogenization theory).…”

“…5, c.f. [56]. Now, the macroscopic deformation gradient F and electric displacement field d 0 are defined as the weighted sum of those in each phase, namely…”

“…In [56] it was shown that Eq. (C.9) can be written as Marín et al [56] showed that D 2 e ⋆ [δα, δβ; δα, δβ] is positive provided that both e a and e b are elliptic, c.f. see Eq.…”

A polyconvex transversely-isotropic invariant-based formulation for electro-mechanics: stability, minimisers and computational implementation

“…The two-field variational formulation Π Ψ (φ, ϕ) in equation (2.27) has been considered using the aforementioned Finite Element discretisation. A volumetric force acting along the positive 0X A similar study was conducted in [61,62], where a squared membrane, made of a rankone laminated DE, was subjected to electrical stimuli in order to observe the development of instabilities as it deforms. In this work, we consider the transversely isotropic constitutive model given in equation (5.15).…”

In-silico design of electrode meso-architecture for shape morphing dielectric elastomers

“…To the best of the authors' knowledge, analogous physical bounds for the case nonlinear electromechanics are not known and hence, we will use p = 3 in what follows. Above representation (33) can be further manipulated to yield…”