A multiplicative approach for nonlinear electro-elasticity

• Published in: Computer methods in applied mechanics and engineering 2012-10, Vol.245-246, p.243-255
• Main Authors: Skatulla, S., Sansour, C., Arockiarajan, A.
• Format: Article
• Language: English
• Subjects: Applied classical electromagnetism; Applied sciences; Deformation; Elastic deformation; Elastomers; Electric fields; Electro-active polymers (EAP); Electro-mechanical coupling; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Industrial polymers. Preparations; Joining; Mathematical analysis; Mathematical models; Mathematics; Meshfree method; Methods of scientific computing (including symbolic computation, algebraic computation); Non-linear electrostatics; Nonlinearity; Numerical analysis. Scientific computation; Physics; Polymer industry, paints, wood; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Technology of polymers; Tensors
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2012.07.002

► Electromechanics approach based on multiplicative split of deformation gradient. ► Separate constitutive law for electrically induced part of deformation gradient. ► Exponential representation of electrically induced part of deformation gradient. ► Direct applicability of already available elastic free energy functions. ► Numerical formulation of the theoretical framework based on a meshfree method. The recent interest in dielectric elastomers has given rise to a pressing need for predictive non-linear electromechanical coupling models. Since elastomers behave elastically and can sustain large deformations, the constitutive laws are naturally based on the formulation of adequate free energy functions. Due to the coupling, such functions include terms which combine the strain tensor and the electric field. In contrast to existing frameworks, this paper proposes to establish the electromechanical coupling by the multiplicative split of the deformation gradient into a part related to the elastic behavior of the material and further one which describes the deformation induced by the electric field. Already available and well tested functions of elastic free energy functions can be immediately deployed without any modifications provided the argument of the function is the strain tensor alone which in turn is defined by the elastic part of the deformation gradient only. An appropriate constitutive relation is formulated for the electrically induced part of the deformation gradient. The paper discusses in depth such a formulation. The approach is elegant, straightforward and above all, provides clear physical insight. The paper presents also a numerical formulation of the theoretical framework based on a meshfree method. Various numerical examples of highly non-linear coupled deformations demonstrate the potential and strength of the theory.