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The local stability of unsymmetric laminated structures is significantly affected by bending‐extension coupling and the comparatively low transverse shear stiffnesses, which have to be included in the structural analysis. If such structures have flat surfaces in segments, they can be investigated with the discrete plate analysis. In this analysis, the individual segments are considered as plates with rotational restraints that represent the supporting effect of the surrounding structure. The aim of this work is to improve the analytical stability of laminated plates. Therefore, Lévy‐type solutions for the buckling load of the mentioned laminated plates are considered and refined. This offers exact solutions for unsymmetrical cross‐ply laminates as well as antisymmetric angle‐ply laminates. In order to show the influence of shear deformations, the solutions for classical laminated plate theory (CLPT), first‐order shear deformation theory (FSDT), and third‐order shear deformation theory (TSDT) are worked out and compared to each other. In the context of TSDT, a new formulation for the rotational elastic restraint is presented, which affects the rotation and the warping of the plate cross‐section. This investigation presents the influence of shear deformations on different laminates and classifies the benefits of the different laminated plate theories with respect to the stability behaviour under different boundary conditions. In addition, the influence of bending‐extension coupling on different fibre angles and layer sequences is analysed. [ABSTRACT FROM AUTHOR]

Optimizing the core thickness of a sandwich structure can be a computationally expensive task. In this work, an optimization approach for slender columns is presented. The approach iteratively determines the optimal thickness distribution using the second derivative of the eigenmodes as an input for the shape function. To demonstrate its capabilities, it is applied to simple columns constrained according to Euler's buckling cases. The optimization results are validated with detailed finite element models and compared to those from a nonlinear least squares‐based optimization. [ABSTRACT FROM AUTHOR]

Induction heating has many engineering applications. To accurately describe the induction heating process of thin steel sheets one needs to account for their mechanical deformation. This might strongly affect the magnetic configuration since thin sheets are prone to thermal buckling, leading to large supercritical deformations. We suggest a modelling strategy combining a computationally highly efficient structural mechanical shell description for the thin sheet with a standard continuum model for eddy current and thermal problems through an iterative coupling algorithm. All benchmark problems are solved numerically using the finite element method. [ABSTRACT FROM AUTHOR]

The local stability of thin‐walled fibre‐reinforced plastic composite beams can be reduced to individual laminates using discrete plate theory. These individual plates receive a supporting effect from their surrounding structure, which is modelled with rotational restraints. In the present investigation, this buckling problem is described by a closed‐form solution. The energy‐based method works with the Rayleigh quotient and the principle of the stationary value of the elastic potential energy. For the analysis of unsymmetrically laminated plates, the classical laminated plate theory (CLPT) considers both the plate deflection and the in‐plane displacements. The first‐order shear deformation theory (FSDT) and third‐order shear deformation theory (TSDT) additionally describe the cross‐sectional rotations and thus take transverse shear deformations into account. In addition to the direct consideration of the bending‐extension couplings, these have also been investigated using the reduced bending stiffness (RBS) method. The investigation shows the influence of bending‐extension coupling on the stability of compressively loaded unsymmetrically laminated plates. Moreover, it is found that the transverse shear stiffness reduces the critical load at relatively high plate thicknesses. The closed‐form analytical solution and the RBS method show good agreement with finite element analyses. The presented closed‐form analytical methods provide explicit solutions for the critical compressive load of unsymmetric laminates under different boundary conditions. Due to the explicit solution, this method is significantly more computationally efficient than numerical, semi‐analytical or exact methods. The present methods are characterised by a simple applicability as well as a very high computational efficiency and are very suitable for preliminary design as well as optimisation of laminated structures. [ABSTRACT FROM AUTHOR]

Typical thin‐walled structures are found in applications like aircraft, spacecraft and marine vessels. For this type of structure, stability behaviour is crucial. The better this behaviour is understood, the better the full lightweight potential can be exploited. For composite structures especially, new fast analysis tools for preliminary design are required to address this issue. Therefore, the local postbuckling of omega‐stringer‐stiffened composite panels is the subject of a new computational model. The analysis method is computationally highly efficient because it is based on a closed‐form analytical approach. The explicit solution is derived based on the principle of the minimum of the total elastic potential. Furthermore, the solution assumes that the initial eigenform does not substantially change in the early postbuckling regime. In this way, the plates of the skin and stringer can be included explicitly in the analysis. Compared to finite element analysis and a closed‐form computational model found in the literature, the new analysis tool is assessed. The results indicate excellent agreement for panels, where the bay plate is the most critical element of the panel. The new computational model promises to be a highly efficient tool in the preliminary design framework. [ABSTRACT FROM AUTHOR]

Aerothermodynamical loads cause buckling and plastic deformation of thin‐walled structures under boundary conditions, which restrict the structural movement. We present the numerical computation of a loosely coupled fluid‐structure interaction for thermal buckling. The task of the research is to provide a mechanical model which incorporates the correct material behaviour and is suitable for thermal panel buckling. For this, an elasto‐viscoplastic material model with non‐linear isotropic hardening is used, which also includes nonlinearly temperature dependent material parameters. This material model is implemented into a user material in Abaqus FEA. The structural computation is coupled with the fluid computation within the fluid‐structure interaction code ifls from the TU Braunschweig. For the fluid solver TAU from the DLR is used. [ABSTRACT FROM AUTHOR]

Lattice structures with low density tend to localize under compressive loading. The localizations start in a single cell band due to buckling of the beams and lead to compaction of the cells. To identify an appropriate discretization and to determine the influence of damage in an elasto‐plastic material behavior two simple load cases are analyzed with the finite element (FE) method. Simulations of an axial loaded beam in the post‐buckling regime with and without damage are carried out. In addition, a triangular cell under compression with different discretizations is analyzed. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an approximate approach for the local buckling analysis of prismatic composite laminated beams under uniaxial compression wherein the segments of the beams (i.e. flanges and webs) are assumed to be moderately thick so that advanced plate theories that transcend the restrictions of classical laminated plate theory (CLPT) need to be employed. We present a novel approximate analysis method based on the so‐called discrete plate approach during which the segment of interest is separated from the beam and is subjected to rotational restraints at the cutting edges. The analysis itself employs rather simple shape functions for the local buckling modes in conjunction with a Rayleigh‐type approach using the principle of minimum elastic potential of the buckled segment wherein we use the kinematic assumptions of Reddy's third‐order shear deformation theory (TSDT). The results are compared to comparative computations based on CLPT and first‐order shear deformation theory (FSDT), and a good agreement is found especially between FSDT and TSDT which lends credibility to the present approach, however neither employing the strict limitations of CLPT imposed by Kirchhoff's classical kinematic assumptions, nor requiring shear correction factors as they are generally required in the framework of FSDT and which is still a topic of on‐going research. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Buckling of shear‐deformable laminated plates is investigated in the present study. A closed‐form method to determine the buckling load is developed within the framework of Reddy's Third Order Shear Deformation Theory (TSDT). The considered orthotropic plates are under uniaxial compression and simply supported at all edges with rotational restraints at the unloaded edges. This allows the modelling of a number of structural situations, e.g. local buckling of beams or the skin fields of stiffened composite panels, for which only the rotational stiffness of the surrounding structure is required. The analysis approach is based on the Ritz method and employs simple shape functions with few variables for the deflection and rotations, which finally leads to an explicit approximate solution for the critical buckling load. The comparison to the Lévy‐type solution shows a satisfactory agreement. The new approach is very simple and highly computationally efficient, which provides a great advantage for example in optimisations. [ABSTRACT FROM AUTHOR]

In this work, a concurrent atomistic-continuum multiscale approach is applied in order to analyse the buckling behaviour of carbon nanotubes. In particular, the bridging domain method that is grounded on an overlapping domain partitioning scheme with an energy-based blending of the subdomains is used. The atomistic subdomain is modelled by means of a molecular statics approach and the continuum subdomain is handled using the finite element method. Outcomes of numerical simulations of defective single-walled carbon nanotubes under bending load are presented. More specifically, the impact of variably located Stone-Wales defects on the buckling behaviour of a nanotube is studied using the concurrent multiscale approach. The results of the multiscale model are validated against a full atomistic molecular statics simulation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Laminated fibre-reinforced composites are prone to delamination damage. This interlaminar defect lowers the critical buckling load of a strut and may lead to unstable postbuckling. Thus, the critical load of laminated and delaminated struts are the topic of investigation herein. Small scale experimental investigations were undertaken and comparison is sought with analytical formulations whilst a model for a delaminated strut is introduced. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this work, we apply the Reduced Basis (RB) Method to the field of nonlinear elasticity. In this first stage of research, we analyze a buckling problem for a compressed 2D column: Here, the trivial linear solution is computed for an arbitrary load; the critical load, marking the transition to nonlinearity, is then identified through an eigenvalue problem. The linear problem satisfies the Lax-Milgram conditions, allowing the implementation of both a Successive Constraint Method for an inexpensive lower bound of the coercivity constant and of a rigorous and efficient a posteriori error estimator for the RB approximation. Even though only a non-rigorous estimator is available for the buckling problem, the actual RB approximation of the output is more than satisfactory, and the gain in computational efficiency significant. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

This paper considers the buckling of transverse shear‐deformable orthotropic laminated plates under uniaxial compression, which is modeled with the third‐order shear deformation theory (TSDT). The consideration of transverse shear deformation is relevant for plates with small transverse shear stiffness or small length to thickness ratio. The supporting effect of the surrounding structure is represented by laterally attached rotational restraints. The present analysis approach uses a simple energy‐based formulation in the form of a Rayleigh‐quotient for which specific shape functions for the out‐of‐plane buckling deformations as well as for the rotational degrees of freedom are employed. A comparison of the results with the Lévy‐type solution shows that the analysis approach works with satisfying accuracy, thus making it suitable for engineering analysis of plates with arbitrary thickness especially when computational time and effort are essential factors. [ABSTRACT FROM AUTHOR]

The present work deals with the local buckling of thin‐walled composite‐beams with I, Z, C, L and T‐cross‐sections under axial load. In this study the analysis of the buckling load of the complete composite‐beam is performed using the Ritz‐method. The individual webs and flanges of the beam are assembled by suitable continuity conditions in one system. In order to achieve that, new displacement shape functions for web and flange that fulfill all boundary conditions have been developed. The present closed‐form analytical method enables the explicit representation of the buckling load for the entire composite‐beam under axial load. The comparison between the present approach and finite element simulations shows a satisfactory conformity. The present method is highly efficient in terms of computational effort and its practical suitability. [ABSTRACT FROM AUTHOR]

Structural stability is an important issue to ensure the safety of thin walled structures. Shell structures are considered in context of linear and non-linear buckling. The design sensitivity analysis with respect to modifications in shape is motivated. Analytically derived gradient information is employed for shape optimisation purposes using solid shells. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

This paper presents a semi‐analytical method for the mixed‐mode buckling problem of composite beams, i.e. the interaction between the local buckling modes of the segments of shear deformable symmetrically laminated composite I‐beams. The buckling analysis employs Reddy's third‐order shear deformation theory and the Ritz‐method in conjunction with adequate series expansions for the buckling degrees of freedom wherein the webs and flanges are considered separately and are later on unified by employing Lagrangian multipliers. The results are compared with the buckling loads as obtained by finite element computations, and a very satisfying agreement is found. [ABSTRACT FROM AUTHOR]

A numerical approach simulating the effects of coupled local-global mode interaction on the postbuckling of axially compressed sandwich beam columns is presented. The formulation is based on the weak form of the balance of linear momentum whilst large strains are considered. An open source software is used to solve the formulation and results are presented showing good phenomenological agreement with analytically derived solutions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

For the symmetrically supported Euler buckling column with both ends hinged the classical stability theory yields simple trigonometric functions as buckling modes, i.e. w( x) = A sin αx. The eigenvalues α are just multiples of π. In comparison, the analysis of the asymmetrically supported Euler buckling column with one end clamped and the other end hinged is more complicated: The buckling modes are a combination of trigonometric functions in form of w( x) = A (sin αx − αx cos ( αL)). The eigenvalues follow from a transcendental equation. Applying a geometrically exact theory to the aforementioned Euler buckling problems, a similar relation in the complexity of the analyses will naturally arise. Using, e.g., the elastica model the buckling behavior of the symmetrically supported column is represented by elliptic integrals. However, the determination of the buckling behavior of the asymmetrically supported column turns out to be much more complex and elaborate. This article presents a direct comparison of the symmetrically and asymmetrically supported buckling columns regarding their analyses by means of classical stability theory and by the geometrically exact theory of the elastica. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Simply supported rectangular elasto-plastic plates which are uniformly compressed buckle either before or beyond the elastic limit. Consequently, the post critical behaviour, the position of first membrane yield and folding mode differ significantly whether buckling happens before or beyond the elastic limit. A distinct folding-line perpendicular to the loading direction develops only for plates which buckle beyond the elastic limit. This article analysis the post-buckling behaviour and the folding mode of uniformly compressed plates and points out the correlation to the folding mode of axially crushed profiles. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Wrinkling phenomena emerging from mechanical instabilities in inhomogeneously compressed soft bilayered systems can evoke a wide variety of surface morphologies. Applications range from undesired instabilities in engineering structures such as sandwich panels, via fabricating surfaces with controlled buckling patterns of unique properties, to wrinkling phenomena in living matter such as lungs, mucosas, and brain convolutions. While moderate compression evokes periodic sinusoidal wrinkles, higher compression induces secondary instabilities - the surface bifurcates into increasingly complex morphologies. Periodic wrinkling has already been extensively studied, but the rich pattern formation in the highly nonlinear post-buckling regime remains poorly understood. Here, we establish a computational model of differential growth to explore the evolving buckling pattern of a growing layer bonded to a non-growing substrate. Our model provides a mechanistic understanding of growth-induced primary and secondary instabilities. We show that amongst all possible secondary bifurcations, the mode of period-doubling is energetically favorable. We experimentally validate our numerical results by examining buckling of a compressed polymer film on a soft foundation. Our computational studies have broad applications in the microfabrication of distinct surface patterns as well as in the morphogenesis of living systems, where growth is progressive and the formation of structural instabilities is critical to biological function. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A glass fiber reinforced elastomer (FRE) sheet is used to design a simple clamping mechanism for prospective engineering applications. The mechanism is based on the phenomena of snap‐through buckling of a segment of a shallow cylindrical shell. It is simply supported at the straight edges and actuated by edge moments. The main objective of such a mechanism is the resulting clamping force, being related to the response of the material under bending. Bending includes compressive stresses, and since the fibers are embedded in a very soft matrix, it is important to understand their contribution to the compressive stiffness of the FRE sheet. For this purpose, numerical simulations by means of the Finite Element Method are performed and a simulation strategy for predicting the clamping force of the mechanism is presented. The clamping forces predicted for FRE composites with and without the contribution of fibers to the compressive stiffness are compared to that of the pure elastomer. The results illustrate the potential of FRE based structures in mechanism‐like applications. If an adequate clamping force is desired, the pure elastomer is not suitable for being used in this kind of clamping mechanism and the fiber reinforcement is necessary. If the fibers contribute to the compressive stiffness, a significantly higher clamping force is predicted. Furthermore, the FRE based structure shows a complex snap‐through deformation pattern, which has to be taken into account in the design of the mechanism and which requires non‐trivial simulation strategies. [ABSTRACT FROM AUTHOR]

The stability behavior is critical for thin‐walled composite structures. This type of structures is for example employed in aircraft, spacecraft and marine vessels, where weight is an important factor in the design. For stiffened panels of, e.g. a fuselage structure, shear is a relevant load case. A new approximate computational model for the local buckling behavior of omega‐stringer‐stiffened panels under shear loading is presented that is based on energy methods. To assess the quality of the derived solution, the results of suitable parameter studies are discussed. In comparison to numerical methods, the new model reduces the computational effort necessary for the preliminary design of omega‐stringer‐stiffened composite panels. Thus, it contributes to increase the performance of structures and consequently reduces the weight of the mentioned applications. [ABSTRACT FROM AUTHOR]

The imperfection sensitivity of stiffened cylinders is analysed on the basis of a critical perturbation associated with a minimum of strain energy. To identify worst perturbations including displacements and stresses, the perturbation energy concept is used, which is developed for mixed finite elements. Disadvantages in modelling branched structures due to stress discontinuities are avoided by transferring the concept to a mixed‐hybrid formulation. Beside an evaluation of common design recommendations, the identification of non‐initial perturbations lead to an insight into the quite complex buckling behaviour of stiffened shells. [ABSTRACT FROM AUTHOR]

Motivated by the experimental investigations on cold rolled sheet metal presented in [1], this contribution focuses on a specific modelling approach to capture the evolution of (plastic) material symmetry groups that is induced by finite plastic deformation processes. The ensuing developments are based on the general theoretical framework by Lu and Papadopoulos with regard to evolving material symmetries proposed in [2, 3]. In particular, we elaborate a specific form of the evolution equation for the structural tensor that characterises the respective material symmetry group and show that the simulation results are in good accordance with the experimental findings. [ABSTRACT FROM AUTHOR]

Dielectric materials such as electro-active polymers (EAPs) belong to the class of functional materials which are used in advanced industrial environments as sensors or actuators and in other innovative fields of research. Driven by Coulomb-type electrostatic forces EAPs are theoretically able to withstand deformations of several hundred percents. However, large actuation fields and different types of instabilities prohibit the ascend of these materials. One distinguishes between global structural instabilities such as buckling and wrinkling of EAP devices, and local material instabilities such as limit- and bifurcation-points in the constitutive response. We outline variational-based stability criteria in finite electro-elastostatics and design algorithms for accompanying stability checks in typical finite element computations. These accompanying stability checks are embedded into a computational homogenization framework to predict the macroscopic overall response and onset of local material instability of particle filled composite materials. Application and validation of the suggested method is demonstrated by representative model problems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Recent applications require the extension of stability theory to axially loaded viscoelastic bars. For elastic bars it is known that a pulsating load leads to a Mathieu equation. Meaning, there are some instable regions before the static buckling load and some stable regions beyond, depending on the excitation (amplitude, frequency, offset). To fill this gap we follow along the lines of Weidenhammer and adopt the classical Euler‐Bernoulli beam kinematics for coupled longitudinal and bending vibrations. Modeling viscoelasticity by the Standard Linear Solid model introduces an internal variable. Hence, there are auxiliary transversal and longitudinal displacements corresponding to the internal variable in addition to the physical transversal and longitudinal displacements of the bar centerline. The modeling further assumes only longitudinal vibrations in the stable regime, thus there are no bending vibrations and the description simplifies to a system of linear partial differential equations. Further, a one‐sided coupling is assumed for the stability analysis, i.e. the longitudinal vibrations are prescribed and induce bending vibrations. Still, the time‐variant coefficients of the transversal dynamics make it difficult to find an analytical solution. Consequently, an approximation is obtained by Ritz method from Hamilton's principle. Applying the eigenforms of elastic buckling as trial functions finally leads to a system of rheolinear ordinary differential equations. Its stability chart with respect to static and harmonic load components is calculated numerically by Floquet theory. [ABSTRACT FROM AUTHOR]

Postbuckling responses of delaminated composite struts are semi-analytically modelled. The model used allows to describe the postbuckling behaviour beyond the state where delamination growth is initiated. In the current work, a multi-layered composite strut of differently stacked transversally isotropic unidirectional layers is investigated. A pre-existing delamination is assigned in between two layers. By using only four generalized coordinates postbuckling responses incorporating delamination growth are determined. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The influence of the pore structure characteristics on the macroscopic mechanical properties of open‐porous cellular materials has been computationally investigated in this contribution. While the effects of the pore‐size distribution on the macroscopic mechanical response of open‐porous cellular materials have been studied previously, the investigations regarding the effects of the pore structure characteristics are relatively scarce. The pore walls of open porous cellular materials are often modelled as beams and the pore wall structure is assumed to have a constant cross section. Although this assumption is valid for a large class of materials, insights into the influence of this assumption on the calculations of the properties of those materials that exhibit a rather pearl‐necklace‐like pore wall morphology are described in this paper. On comparing the simulation results for a corrugated pore‐wall with that having a constant cross‐section, it is observed that the maximal stresses in the pore wall may differ significantly. [ABSTRACT FROM AUTHOR]

In the present work, we investigate the onset of structural instabilities occuring in soft hydrophilic elastomers undergoing geometrically constrained swelling, which is characterized by large elastic deformations coupled with transient fluid diffusion. We model this phenomenon using a minimization‐based variational formulation having the deformation map and the fluid flux as the independent variables [1,3]. The space‐time‐discrete form of the variational problem is implemented using a conforming Raviart–Thomas‐type finite element formulation, which yields a symmetric and positive definite global tangent matrix for a stable deformation state. The onset of instability is captured as the point where the tangent matrix loses its positive definiteness [4,5]. To validate the proposed theoretical framework, we consider the surface wrinkling phenomenon observed in constrained hydrogel bilayers subjected to fluid diffusion. Variations in the critical buckling load and the corresponding mode number with respect to the geometry and material parameters of the bilayer are studied. These studies could, for instance, serve as potential design guidelines for applications of such materials in microsensors or in the fabrication of soft microgears for actuators, where the buckling modes are exploited to produce a desired mechanical output [8]. [ABSTRACT FROM AUTHOR]

The reduced bending stiffness method is used in the framework of computational models for stringer stiffened panels. Here, the stringer foot is often stacked on top of the skin of the panel and leads to a stacked laminate with extensional bending stiffness coupling. The validity of the reduced bending stiffness method for the mentioned laminate type is investigated and assessed, as only unsymmetrical laminates without eccentricity have been considered in existing literature. In exemplary studies, the influence of the coupling effects is shown, which allows drawing conclusions on the error that is introduced in, e. g. closed‐form analytical approximate solutions for the buckling of stringer stiffened panels. [ABSTRACT FROM AUTHOR]

We present our work on a new variational approach for thermodynamic topology optimization of hyperelastic structures: building upon our previous works, we follow a thermodynamic approach for deriving a field equation that describes the evolution of the density. The problem of topology optimization is consequently solved without the need of expensive optimization routines. Furthermore, our new formulation can also be applied to hyperelastic structures which show a remarkable difference to structures optimized for small deformations. Important aspects like tension/compression asymmetry and buckling are inherently included in the topology optimization approach due to the large deformation formulation. [ABSTRACT FROM AUTHOR]

This contribution deals with the mathematical description and algorithmization of expert knowledge so that this expert knowledge can be used within automatic optimization procedures with a focus on the topology optimization of crashworthiness structures. Up to now, a purely mathematical topology optimization of crashworthiness structures is not possible. The reasons for that are the nonlinearities coming from the large displacements and rotations, contact phenomena and complex material behaviour (e.g. plasticity, failure and strain rate dependency). One approach to overcome these problems by using heuristics based on expert knowledge and an application example are shown in this contribution. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The contribution is concerned with a finite element formulation that deals with thin structures made from dielectric elastomer material. For that a special solid shell formulation, which uses eight nodes per element and four degrees of freedom (three displacements and one for the electric potential) per node, is presented. It is based on a Hu-Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. In recent years structures made from dielectric elastomers have been investigated by many researchers. This interest is caused by the ability of such devices to efficiently transform electric energy into mechanical work at inexpensive cost of production. The efficiency increases with a higher area to thickness ratio, thus the need to accurately simulate thin structures is well-founded. On the other hand a 3d description of the constitutive behavior is necessary to capture all nonlinear effects arising from the material. Thus a 3d constitutive law with respect to the electro-mechanical coupling incorporated in a finite element solid shell formulation is presented. Some examples demonstrate how it deals with finite strains and large deformations of thin structures by applying electrical loading conditions. The analyzed devices respond with elongation, bending, or buckling, depending on the mode of activation. The electrically induced buckling can be utilized to obtain large deformations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A numerical approach simulating the effects of interlaminar defects on the buckling stability of layered composite struts is presented. The formulation is based on the weak form of the balance of linear momentum whilst large strains are considered. First results are presented whilst comparisons are drawn to analytically derived results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Soft matter electro-elastic, magneto-elastic and magneto-electro-elastic composites exhibit coupled material behavior at large strains. Examples are electro-active polymers and magneto-rheological elastomers, which respond by a deformation to applied electric or magnetic fields, and are used in advanced industrial environments as sensors and actuators. Polymer-based magneto-electro-elastic composites are a new class of tailor-made materials with promising future applications. Here, a magneto-electric coupling effect is achieved as a homogenized macro-response of the composite with electro-active and magneto-active constituents. These soft composite materials show different types of instability phenomena, which even might be exploited for future enhancement of their performance. This covers micro-structural instabilities, such as buckling of micro-fibers or particles, as well as material instabilities in the form of limit-points in the local constitutive response. Here, the homogenization-based scale bridging links long wavelength micro-structural instabilities to material instabilities at the macro-scale. This work outlines a comprehensive framework of an energy-based homogenization in electro-magneto-mechanics, which allows a tracking of postcritical solution paths such as those related to pull-in instabilities. Representative simulations demonstrate a tracking of inhomogenous composites, showing the development of postcritical zones in the microstructure and a possible instable homogenized material response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Smart or functional materials are in focus in broad fields of recent research. In particular, electroactive polymers (EAPs) with their large actuator strains are used for innovative design in robotics. These materials become practical as soon as the material is robust, reliable and long lived. However, EAPs suffer from different types of instabilities, such as unstable thinning of actuators, local buckling induced by coexistent states and electrical breakdown. One distinguishes between structural instability, i.e. instabilities in the global structural response like buckling or wrinkling and local or material instability, e.g. the formation of microstructures and phase decompositions. These effects are well known and analyzed for purely mechanical phenomena, but not fully developed in the context of electro-mechanically coupled problems. To this end, we develop new variational-based stability criteria in finite electro-elastostatics, by postulating an electro-mechanical quasi-convexity condition for weakly convex energy and weakly convex-concave energy-enthalpy formulations. Starting from distinct variational principles, we develop criteria for local and global stability and construct stability checks, which accompany equilibrium paths for the detection of critical points in finite element models. Numerical examples validate the developed concepts for boundary value problems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

More recently, a concept of energy-based categorization of buckling was proposed. It represents a symbiosis of mechanics of solids and spherical geometry. The fundamental mathematical background of this concept is the so-called consistently linearized eigenproblem. The numerical solution of this eigenproblem by means of the finite element method is a key issue of the mentioned concept. This solution is obtained with the help of the commercial finite element software MSC.MARC. An iterative process, involving the programming lanuages PYTHON and FORTRAN 77 and the software MATLAB, is devised, making use of the available element library, of different types of solvers, and of further modeling tools. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Abstract: This work is dedicated to multi‐scale stability analysis, especially macroscopic and microscopic stability analysis of periodic electroactive polymer (EAP) composites with embedded fibers. Computational homogenization is considered to determine the response of materials at macro‐scale depending on the selected representative volume element (RVE) at micro‐scale [4, 5]. The quasi‐incompressibility condition is considered by implementing a four‐field variational formulation on the RVE, see [7]. Based on the works [1–3, 6, 8] the macroscopic instabilities are determined by the loss of strong ellipticity of homogenized moduli. On the other hand, the bifurcation type microscopic instabilities are treated exploiting the Bloch‐Floquet wave analysis in context of finite element discretization, which allows to detect the changed critical size of periodicity of the microstructure and critical macroscopic loading points. Finally, representative numerical examples are given which demonstrate the onset of instability surfaces, the stable macroscopic loading ranges, and further a periodic buckling mode at a microscopic instability point is presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The trend to extend the working ranges of flexure hinges implies large deformations during operation. To conduct a failure analysis the total deformation is decomposed into desired deformation and deviations. In particular, a flexure hinge of leaf-spring type is examined. It is modeled by the theory of elastica. The resulting boundary value problem is solved numerically for the static case by Ritz's method. It is discretized into trial functions and their free coefficients are determined from the minimum of potential energy by optimization methods. The crucial point is that the elastic energy stored in the beam is formulated intrinsically, while the potential of external conservative loads is formulated in a space-fixed coordinate system. The well-known special case of buckling of a straight cantilever beam is used for verification. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In structural mechanics, when the design contains two different materials with opposite mechanical behaviours and costs, the optimum design cannot exactly found. In that case, numerical optimization algorithms are a good source. Reinforced concrete design shows that behaviour since concrete is a cheap material comparing to steel while the tensile strength of concrete is very low to use. The cross sections are effective on the stresses and balance of tensile and compressive forces. This situation shows the importance of the dimension optimization of reinforced concrete members. Also, the number and size of the reinforcements need an optimization. The place of the reinforcements is effective on the place of tensile forces in the calculation of axial force and flexural moment capacity. In this paper, reinforced concrete columns are optimized for the cost minimization by employing a bio-inspired metaheuristic algorithm called bat algorithm. The idealization of the echolocation behaviour of bats is the inspiration of the bat algorithm. Differently from the algorithms, the bat algorithm uses global and local optimization with a changeable probability. The optimization process considers the security measures and slenderness of the according to the design regulation called ACI 318. The slenderness is taken into consideration by using a magnified design flexural moment, which is factored by a value defined according to the buckling load and axial load of columns. The proposed approach is applied for different numerical cases and the results are compared with the approach using harmony search algorithm. The present approach is effective for the optimization problem. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The present contribution deals with the mechanics of metallic microlattices from selective laser melting (SLM). Finite element analyses with elasto-plastic material parameters identified in experiments investigate the structural load bearing behavior of different unit cell topologies. Typical failure modes like local buckling as well as global localization in shear bands are analyzed in simulations and experiments for compression tests. Ashby diagrams for the scaling behavior of stiffness and strength at various densities are determined for both bending- and stretch-dominated lattice types. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

FEM forming simulations are often performed using an explicit solver, which usually requires time‐scaled and often mass‐scaled simulation approaches. Explicit simulation with the commercial software LS‐DYNA also provides very good results for the forming simulation of the innovative process of ""Die‐Less‐Hydroforming" when time‐scaling and relatively very strong mass‐scaling are used. Nevertheless, this paper presents an implicit forming simulation for "Die‐Less‐Hydroforming" using LS‐DYNA, which can be used on the one hand (in addition to costly experimental investigations) as comparison and verification of the explicit simulation. On the other hand, the simulation of the forming process, which in reality is quasi‐static, corresponds more precisely with regard to the mapping of its process time, since neither time‐scaling nor mass‐scaling are required when using the implicit solver in comparison to the calculation with the explicit solver. [ABSTRACT FROM AUTHOR]

The material properties of green wood in the shaft of vital trees differ significantly from the generally known material properties of technically processed, dried wood. Furthermore, completely different residual stresses and fracture mechanisms are present in the natural full cross‐section [1]. The properties also depend on the tree species. Our work focuses on green wood from european beech (Fagus sylvatica). A large number of experiments on small test specimens of green wood are known from [2]. We present both, experiments on small and large‐scaled specimens. Latter are bending test on trunks with full cross‐section. Combining results and considering micro‐mechanical properties of cellular wood components [3], a computational model is fitted to our experimental results. This aspect influences the fracture resistance of a tree and should be representable in a computational model. This is particularly important in order to better assess the risk of building on vital trees. [ABSTRACT FROM AUTHOR]

Recently proposed constitutive models that describe the mechanical behavior of open‐porous cellular materials take into account the random pore sizes of the materials but not the randomness in the pore shapes [1]. In the present contribution, a computational model to reconstruct the highly irregular structure of porous materials is developed using sphere packing and Laguerre‐Voronoi tessellation [2]. The mechanical structure‐property relationship is then investigated by means of finite element methods. Under compression, porous materials demonstrate linear‐elastic behaviour followed by an irreversible deformation resulting in a plateau region followed by densification [3]. In this contribution, such mechanical responses of porous materials under cyclic loading are investigated using elasto‐plastic material models. Furthermore, effects of tensile loading on the model are also discussed. [ABSTRACT FROM AUTHOR]

In order to describe elastic waves propagation in metamaterials, i.e. solids with heterogeneities or microstructure, it is necessary to consider non‐local or higher‐order models. The relaxed micromorphic model (RMM) proposed here can describe these effects as a continuous material with enriched kinematics. We present a new unit cell giving rise to a metamaterial for acoustic application. The microstructure is engineered to show a band‐gap in the low acoustic regime (600‐2000 Hz) for which waves cannot propagate through the material. We concentrate on the size effects to make full advantage of the particularly beneficial structure that the model provides. The RMM material parameters are fitted using a new algorithm relying on cutoffs and asymptotes (obtained via a Bloch‐Floquet analysis). In particular, by enhancing the kinetic energy of the model with a new inertia term, we enable decreasing curves (modes with negative group velocity). [ABSTRACT FROM AUTHOR]

Thanks to the advancement of additive manufacturing technologies, mechanical metamaterials have attracted a great deal of attention in recent years. With the employment of such technologies, materials with exceptional or tailored mechanical properties can be easily manufactured mainly by 3D printing of different microstructures rather than by changing the material composition. These lattice materials can provide remarkable material properties in spite of being significantly lighter than typical bulk materials. Due to the large number of degrees of freedom for engineering structures, single‐scale numerical simulation of such cellular materials is computationally demanding. Therefore, two‐scale computational homogenization approaches, such as FE2 and FE‐FFT, can perform a key role in the cost‐effective numerical modeling of metamaterials. Two‐scale computational homogenization methods rely on solving a boundary value problem (BVP) for each of the macroscopic and microscopic scales in a nested procedure. Although representative homogenization techniques have been widely used to study materials with heterogeneous microstructures, there still exist some challenges in their employment for lattice materials. This study addresses main challenges in two‐scale‐based computational homogenization methods for numerical modeling of mechanical metamaterials. High dependence of convergence rate and accuracy on phase contrast for fast Fourier transform (FFT) solvers and comparable macro and micro characteristic lengths in metamaterials (i.e. the applicability of the principle of scale separation) are some examples of such challenges. [ABSTRACT FROM AUTHOR]