A computational framework for incompressible electromechanics based on convex multi-variable strain energies for geometrically exact shell theory

TLDR: In this paper, a new computational framework for the analysis of incompressible Electro Active Polymer (EAP) shells subjected to large strains and large electric fields is presented, based on a rotationless description of the kinematics of the shell, enhanced with extra degrees of freedom corresponding to the thickness stretch and the hydrostatic pressure.

About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2017-04-15 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Shell (structure) & Hydrostatic pressure.

Figures

Figure 5: Summary of FEM discretisation spaces for examples 6.1.1 and 6.1.2 used in (a), the MŴF formulation [4] and (b), in the proposed shell formulation. Notice that the superscripts C and D have been used to indicate the continuous or discontinuous character of a field, respectively.

Figure 15: Hyperboloid piezoelectric polymer. Geometry and boundary conditions. t = 12m, D = 9.95m, H = 0.05m and q, a surface load per unit undeformed area.

Figure 6: Bending actuator configuration 1. Contour plot of σ11 (a) for the shell formulation and (b) the MŴF, respectively. Incompressible model in (52). Total number of dofs for shell and continuum formulation ({x, ϕ, p}) of 14498 dofs (refer to Figure 4) and {3 × (8019), 8019, 800} (32876 dofs) (not including the discontinuous fields, refer to Figure 5a), respectively.

Figure 1: Deformation mapping of a continuum (EAP) and associated kinematics variables: F , H , J .

Figure 16: Hyperboloid piezoelectric polymer. Contour plot of the electric potential ϕ for the proposed shell formulation. Results obtained for a value of the surface load per unit undeformed area of q = λ×(16×106)Pa, with (a) λ = 0.0065; (b) λ = 0.0221; (c) λ = 0.0716; (d) λ = 0.25; (e) λ = 0.664; (f) λ = 1. Constitutive model in (58). Finite Element discretisation of 64 × 27 elements. CBC approach for ϕ and γ with ns = 1 (47). Number of dofs for {x0,v, ϕ, γ, p, λ} of {3× 7095, 3× 1820, 3× 7095, 1× 1728, 1× 1728, 1820}.

Figure 11: Helicoidal actuator. Geometry description and electrical boundary conditions.

Frequently asked questions

Q1. What have the authors contributed in "A computational framework for incompressible electromechanics based on convex multi-variable strain energies for geometrically exact shell theory" ?

In this paper, a new computational framework for the analysis of incompressible Electro Active Polymer ( EAP ) shells subjected to large strains and large electric fields is presented. Two novelties are incorporated in this work. First, the variational and constitutive frameworks developed by the authors in recent publications [ 1–4 ] in the context of three-dimensional electromechanics are particularised/degenerated to the case of geometrically exact shell theory. The proposed formulation follows a rotationless description of the kinematics of the shell, enhanced with extra degrees of freedom corresponding to the thickness stretch and the hydrostatic pressure, critical for the consideration of incompressibility. More specifically, convex multi-variable ( three-dimensional ) constitutive models, complying with the ellipticity condition and hence, satisfying material stability for the entire range of deformations and electric fields, Corresponding author: r. ortigosa @ swansea. Different approaches are investigated for the interpolation of these extra fields and that of the electric potential across the thickness of the shell. 

Q2. What are the future works mentioned in the paper "A computational framework for incompressible electromechanics based on convex multi-variable strain energies for geometrically exact shell theory" ?

Moreover, the kinematics of the shell allows for the possibility of compression and stretch across the thickness of the shell [ 17 ], crucial for the consideration of incompressible behaviour. Two approaches have been considered for the interpolation of the electric potential across the thickness of the shell.