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The present article, provides a novel mixed finite element formulation for elastoplasticity which is suitable for the discretization of thin‐walled structures using highly anisotropic volume elements. We present a thermodynamically consistent framework for the modeling of elastoplastic stress response, where dissipative effects are considered through a dissipation function instead of explicit flow rules. Along these lines, a mixed incremental principle, in which stresses are included as independent unknowns, is derived. We propose to employ tangential‐displacement normal‐normal‐stress (TDNNS) elements for a Galerkin discretization of the underlying variational problem. These elements were originally developed for linear elasticity, where it could be shown that they do not suffer from shear locking if the element's aspect ratio deteriorates. Excellent computational performance and accuracy of the proposed method are demonstrated in several benchmark problems. [ABSTRACT FROM AUTHOR]

This paper presents a novel system‐level model order reduction scheme for flexible multibody simulation, namely the system‐level affine projection (SLAP). Contrary to existing system‐level model order reduction approaches for multibody systems simulation, this methodology allows to obtain a constant reduced order basis which can be obtained in a noninvasive fashion with respect to the original flexible multibody model. It is shown that this scheme enables an automatic joint constraint elimination which can be obtained at low computational cost through exploitation of the component level modes typically employed in flexible multibody simulation. The equations of motion are derived such that the computational cost of the resulting SLAP model is independent of the original model size. This approach results in a set of ordinary differential equations with a constant mass matrix and nonlinear internal forces. This structure makes the resulting model suitable for a range of estimation, control, and design applications. The proposed approach is validated numerically on a flexible four‐bar mechanism and shows good accuracy for a very low‐order SLAP model. [ABSTRACT FROM AUTHOR]

We are concerned with the mathematical modeling of the polarization process in ferroelectric media. We assume that this dissipative process is governed by two constitutive functions, which are the free energy function and the dissipation function. The dissipation function, which is closely connected to the dissipated energy, is usually non‐differentiable. Thus, a minimization condition for the overall energy includes the subdifferential of the dissipation function. This condition can also be formulated by way of a variational inequality in the unknown fields strain, dielectric displacement, remanent polarization and remanent strain. We analyze the mathematical well‐posedness of this problem. We provide an existence and uniqueness result for the time‐discrete update equation. Under stronger assumptions, we can prove existence of a solution to the time‐dependent variational inequality. To solve the discretized variational inequality, we use mixed finite elements, where mechanical displacement and dielectric displacement are unknowns, as well as polarization (and, if included in the model, remanent strain). It is then possible to satisfy Gauss' law of zero free charges exactly. We propose to regularize the dissipation function and solve for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve. [ABSTRACT FROM AUTHOR]

As compared to conventional mechanisms, compliant mechanisms exploit flexible deformation rather than rigid‐body motion of its components. The key advantage of jointless or monolithic structures lies in the absence of relative motion between the links. Besides the reduction in parts required to perform a task, compliant mechanisms typically show little friction, if any, and do not require lubrication to minimize wear. On the downside, design and synthesis of compliant mechanisms become much more involved than in rigid‐body linkages. In particular, optimization of compliant mechanisms relying on (sub‐)structures subjected to large flexible deformation is a challenging task, in which diverse aspects need to be considered. First and foremost, kinematic analysis of compliant mechanisms usually requires geometric non‐linearities to be accounted for. Further, limitations in actuation forces and torques impose constraints on the design. Depending on the application, the performance of compliant mechanisms may crucially depend on the natural frequencies and their change over the range of operation. In view of the diverse aspects, one typically has to deal with multi‐objective optimization problems in comparatively high‐dimensional parameter spaces. [ABSTRACT FROM AUTHOR]

The present paper deals with vibrations of axially moving beams. Large displacements and finite deformations with respect to a co-moving reference configuration are studied. For that sake, an extension of Reissner's non-linear beam theory is used, which allows working with constitutive relations stated at the stress-strain level of continuum mechanics. We restrict to plane deformations and to the Bernoulli-Euler assumption for slender beams. In extension to formulations in the literature, we study a situation, in which a reference configuration with an unknown length is to be considered. Exemplary numerical results are presented for the case of a statically pre-deformed beam with an initially unknown reference configuration, which is set into an accelerated axial motion, where the length of the reference configuration however is kept fixed during the onset of vibrations. [ABSTRACT FROM AUTHOR]

Bringing into focus the design aspect of thin film electro‐active polymer actuators justifies the deployment of a structural mechanics framework. We propose a physically consistent constitutive model for such actuators, which is valid for plates and shells as material surfaces within a complete direct formulation. To this end, we use the principle of virtual work to deduce the general form of the constitutive law from an augmented Helmholtz free energy, as a function of the structural Green‐Lagrange type strain measures and of the material electric field, without the need of a‐priori assumptions concerning the state of strain and stress. Mechanical deformations of thin film devices– e.g. made of polyurethane– under the action of an external electric field, are caused by two different sources. On the one hand, the applied electric field causes a dielectric polarization of the polymer matrix, yielding to corresponding attractive electrostatic forces between the electroded surfaces resulting into a squeezing of the film. On the other hand, crystalline graft units with a certain natural, but arbitrarily directed polarization, embedded in between the polymer chains, have to align in the direction of the applied electric field such that a rotation of the whole crystal unit takes place. This rotation results in an additional macroscopic thickness squeeze– known as the electrostrictive effect. We treat both electromechanical coupling phenomena separately, where it turns out, that the electrostatic forces can be accounted for by an electrical contribution to the augmented free energy, whereas, the electrostrictive effect is taken into account in the elastic part of the augmented free energy by virtue of a hybrid multiplicative and additive decomposition of the plate/shell deformation measures. Benefiting from the structural mechanics formulation, we gain a lower– two‐dimensional– formulation, which provides a clear physical insight into the nature of the deformation process initiated by the external electric field. E.g. for the linearised problem, a comparison to the literature on thermoelastic plates and shells uncovers the action of the electric field as a combined source of self‐stresses. In order to solve particular problems, the constitutive relation of the geometrically and physically nonlinear formulation is implemented into our in‐house finite element code. The computed results, which were tested against results from the literature as well as against test problems of our previous work (where numerical integration of the three dimensional plate/shell augmented free energy through the thickness was employed), show a very good agreement. [ABSTRACT FROM AUTHOR]