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Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct and converse piezoelectric effects, for instance, is used for both actuation and sensing in diverse engineering applications. The response of ferroelectric materials depends on their state of remanent polarization and the presence of an external electric field. To extend the operational range of sensors and actuators, an accurate understanding of the evolution of the material's state of polarization is imperative, which requires both physical and geometric nonlinearities to be taken into account. Moreover, polymeric smart materials like PVDF allow significantly larger deformation as compared to conventional piezoelectric ceramics. The electromechanical coupling in piezoelectric materials manifests in ferroelectric and ferroelastic hystereses, which are related to both reversible and irreversible processes. Focusing on the latter, we transfer phenomenological models for domain switching in ferroelectric materials to the geometrically nonlinear regime. For this purpose, we follow related concepts of geometrically nonlinear elastoplasticity, where the concept of a multiplicative decomposition of the deformation gradient plays a key role. Accordingly, an additional deformation path that describes the evolution of the poled state from the unpoled referential configuration is introduced. The constitutive response of the material to mechanical and electrical loads is discussed, and dissipative internal forces that drive the evolution of the remanent polarization are derived within a thermodynamical framework and the principle of maximum dissipation. [ABSTRACT FROM AUTHOR]

The buckling and postbuckling of a shear-deformable cantilever is studied using Reissner's geometrically exact relations for the planar deformation of beams. The cantilever is subjected to a compressive follower force whose line of action passes through a spatially fixed point. To study the buckling behavior, a consistent linearization of equilibrium and kinematic relations is introduced. The influence of shear deformation and extensibility on the critical loads is studied. The buckling behavior turns out to crucially depend on the ratio between the shear stiffness and the extensional stiffness of the structure. Closed-form solutions in terms of elliptic integrals for buckled configurations of the cantilever are derived in the present paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a complete direct approach to nonlinear modeling of thin plates, which are made of incompressible dielectric elastomers. In particular, the dielectric elastomers are assumed to exhibit a neo-Hookean elastic behavior, and the effect of electrostatic forces is incorporated by the purely electrical contribution to the augmented Helmholtz free energy. Our approach does not involve any extraction-type procedure from the three-dimensional energy to derive the plate augmented free energy, but directly postulates the form of this energy for the structural plate problem treated in this paper. Results computed within the framework of this novel approach are compared to results available in the literature as well as to our own three-dimensional finite element solutions. A very good agreement is found. [ABSTRACT FROM AUTHOR]

Subject of the present work is the enhancement of the buckling load of beam-type structures under a compressive force by means of active feedback control. The focus of this paper lies on experimental aspects that show the feasibility of the proposed approach. For this purpose, a cantilever beam loaded by a compressive force is considered. The compressive force is applied with the help of a cable which is fixed at the tip of the free end and passes through the foundation of the cantilever. A laser displacement sensor is used to measure the structural displacements at the beam's tip. For actuation, piezoelectric transducers are attached on each side of the cantilever beam. Two kinds of constant gain feedback control approaches are investigated on the experimental setup. The buckling load could be increased by a factor of 2.05. The experimental results agree very well with the performed numerical simulations. As a theoretical basis, a consistent theoretical formulation is presented using the Bernoulli-Euler beam theory. The formulation of the system includes also a general feedback controller with discrete displacement measurements and distributed piezoelectric patches. The influence of the controller on the buckling load, control amount by means of applied voltage and limits of the investigated active buckling control approaches are emphasized. [ABSTRACT FROM AUTHOR]

The buckling and postbuckling of beams is revisited taking into account both the influence of axial compressibility and shear deformation. A theory based on Reissner's geometrically exact relations for the plane deformation of beams is adopted, in which the stress resultants depend linearly on the generalized strain measures. The equilibrium equation is derived in a general form that holds for the statically determinate and indeterminate combinations of boundary conditions representing the four fundamental buckling cases. The eigenvalue problem is recovered by consistent linearization of the governing equations, the critical loads at which the trivial solution bifurcates are determined, and the influence of shear on the buckling behavior is investigated. By a series of transformations, the equilibrium equation is rearranged such that it allows a representation of the solution in terms of elliptic integrals. Additionally, closed-form relations are provided for the displacement of the axis, from which buckled shapes are eventually obtained. Even for slender beams, for which shear deformation can usually be neglected, both the buckling and the postbuckling behavior turn out to be affected by shear not only quantitatively, but also qualitatively. [ABSTRACT FROM AUTHOR]

In problems of beams that may move relative to one of their spatially fixed supports, the length of the reference configuration of the beam that is currently located in between the supports depends on the deformation and therefore on the intensity of the external loads. In the present paper, the large deformation of a slender beam under a concentrated force is considered, for which one end is clamped while the other may slide through another clamping device in horizontal direction. The geometric symmetry properties allow the complete structure to be partitioned into four similar parts, each of which represents a cantilever beam under a tip force. In the analysis, a beam theory based on Reissner's geometrically exact relations for the plane deformation of beams is utilized, from which the equation of a cantilever beam with an extensible axis is obtained by adopting a linear dependence of the stress resultants on the generalized strain measures. For this non-linear equation, a closed-form solution in terms of elliptic integrals is presented, from which the equilibrium shape of the entire structure is constructed afterward. The mid-span deflection and the additional length, by which the reference configuration exceeds the distance between the supports, are discussed and compared with the relations of the inextensible elastica, which exhibits bending deformation only. Moreover, a critical load is found for which no equilibrium configuration exists. [ABSTRACT FROM AUTHOR]