bluuebunny/crossref_metadata_2025 huggingface dataset:
A multi‐scale time‐dependent constitutive model of soft collagenous tissue
Authors: Hillgärtner Markus , Linka Kevin , Itskov Mikhail
Published: October 2015

This contribution presents a micro‐mechanically motivated, time‐dependent constitutive model of soft biological tissues. It considers seperate contributions of the matrix material, collagen fibrils, proteoglycans (PGs) as well as their interactions. It is based on the observations [6], that PG bridges facilitate sliding between fibrils.

The initial overlapping lengths of the PG bridges are statistically distributed and decrease due to slippage. A linear‐elastic force response of a PG bridge is assumed. Damage of the PG bridges is reversible and decays over time (cf. Gupta et al. [1]). This behaviour is taken into account by a healing model based on the evolution of the overlapping length.

The damage of the PG bridges decreases the PG density and in turn increases the fibril contact, leading to fibril stretch. The strain energy function of fibrils is based on the response of single tropocollagen molecules and takes both, an entropic and an energetic regime into account. At higher strains, fibrils can additionally undergo damage, which in contrast to the PG damage is irreversible.

The so obtained constitutive model is capable to predict several mechanical phenomena of soft tissues, such as non‐linearity, Mullins effect, hysteresis and permanent set. Finally the model is compared against experimental data available in the literature. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of skin anisotropy directions for identifying stress free reference configuration of the female breast
Authors: Li Xuhui , Jabareen Mahmood , Raith Stefan , Itskov Mikhail
Published: October 2015

Biomechanical simulations of the female breast are important for surgical applications such as implants augmentation, tumorectomy and reconstruction after the tumor removal. One of the main challenges for such breast simulations is to define its reference configuration which can be considered as a stress free state. Indeed, MRI (Magnetic Resonance Imaging) scans of the breast can be obtained only under gravitational load which introduces a considerable stress and strains level for any position of the patient. Moreover, realistic material properties especially anisotropy of skin should be taken into account. This anisotropy can play an important role but has not so far been considered in biomechanical simulations of the breast. In the current contribution, we implement an iterative method to define the reference configuration of the breast model according to MRI data of certain individuals in the prone position by taking into account the anisotropy directions of skin. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The role of microvascular tortuosity in tumor transport phenomena and future perspective for drug delivery
Authors: Penta Raimondo , Ambrosi Davide
Published: October 2015

We tackle the fluid transport problem in vascularized tumors by solving a double Darcy model obtained via multiscale homogenization. The hydraulic conductivities of the capillary and interstitial compartments are computed solving classical problems on the representative periodic cell, which encodes details of the microvasculature. Microvascular tortuosity leads to a dramatic decrease of the capillary hydraulic conductivity, and the corresponding lowering in the pressure drop impairs tumor blood flow and consequently advection of molecules. Further perspectives for anti‐cancer agents delivery are illustrated. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An algorithmic strategy for the simulation of bone healing directly on computed tomography data
Authors: Roland Michael , Tjardes Thorsten , Dahmen Tim , Otchwemah Robin , Slusallek Philipp , Bouillon Bertil , Diebels Stefan
Published: October 2015

An algorithmic strategy for the modelling and simulation of bone healing is presented. The algorithm works directly on the computed tomography data and simulates, after an appropriate volume meshing, a mechainically driven healing concept which is based on competitive and dynamical mechanical parameters. The finite element simulations are done with realistic boundary conditions from patient‐specific OpenSim simulations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechanics of growing tumors: impact of modeling assumptions and boundary conditions on reliability of numerical results
Authors: Sciumè Giuseppe , Schrefler Bernhard A. , Santagiuliana Raffaella , Zavarise Giorgio
Published: October 2015

A recent computational model for tumor growth is presented. The mathematical model, based on thermodynamically constrained averaging theory (TCAT), is shortly summarized in the first part; then the attention is focused on modeling hypothesis and their impact on numerical results. Perspectives for future developments of the presented multiphase model are outlined at the end of the paper. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Evolution of Mechanical Properties in Tissues Undergoing Deformation‐Related Fiber Remodeling Processes
Authors: Topol Heiko , Demirkoparan Hasan
Published: October 2015

We consider a biological fibrous soft tissue in which fibers are distributed in all directions. The mechanical properties of the fibers evolve due to a continuous remodeling process. The model to describe these fiber properties is based on the strain energy density of the protofibers and a survival kernel which describes the deformation‐related property changes. In particular, this study investigates the development of the fiber orientation density for different choices of the fiber creation rate and fiber dissolution rate models. It has been shown that the fiber orientation density depends on both the history of the deformation and the deformation state of the fibers at the time of their creation. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computation of Residual Stress Distributions and Opening Angles of 3D Patient‐Specific Arterial Walls
Authors: von Hoegen Markus , Schröder Jörg
Published: October 2015

A method to incorporate residual stresses in arteries, based on the assumption of smooth transmural stress measure distributions with slight slopes, is discussed. The artery is first loaded with the internal blood pressure without considering any residual stresses. With help of suitable stress invariants and volume averaged mean values on specific sectors domains, the stress gradient is iteratively decreased in radial direction. In order to assess the accuracy of the method, a three‐dimensional patient‐specific arterial geometry, suffering from atherosclerosis, is considered. These was reconstructed from ultrasound based medical imaging, see [2]. Moreover, the radially sliced arteries can be loaded exclusively with the calculated residual stresses in order to predict the opening angle. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermo‐mechanical modeling of crack propagation in dynamically loaded elastomer specimens using a scaled boundary finite element approach
Authors: Behnke Ronny , Kaliske Michael
Published: October 2015

Recently, a scaled boundary finite element (SBFE) formulation for geometrically and physically nonlinear materials has been developed using the scaled boundary finite element method (SBFEM). The SBFE formulation has been employed to describe plane stress problems of notched and unnotched hyperelastic elastomer specimens. In this contribution, the derived SBFE formulation is extended to nonlinear time‐ and temperature‐dependent material behavior. Subsequently, the SBFE formulation is incorporated into a crack propagation scheme to model crack propagation in cyclically loaded elastomer specimens of the so‐called tear fatigue analyzer (TFA). (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Investigation of an elastoplastic material model coupled to nonlocal damage in an implicit‐gradient framework
Authors: Brepols Tim , Wulfinghoff Stephan , Reese Stefanie
Published: October 2015

In this work, an elastoplastic material model coupled to nonlocal damage is discussed which is based on an implicit gradient‐enhanced approach. Combined nonlinear isotropic and kinematic hardening as well as continuum damage of Lemaitre‐type are considered. The model is a direct nonlocal extension of a corresponding local model which was presented earlier (see e. g. [1], [2], [3]). Conclusions drawn from a numerical benchmark test performed in this study demonstrate that the nonlocal damage model is suitable to provide mesh‐independent solutions in finite element simulations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Model reduction and clustering techniques for crash simulations
Authors: Fehr Jörg , Grunert Dennis
Published: October 2015

Model reduction in car crash simulations is a fairly new research field. In this paper, a possible workflow is presented: Since nonlinear behavior can occur, parts with linear and nonlinear behavior need to be separated with clustering methods such as k‐means or spectral clustering. For the latter, a nonlinear reduction technique such as POD‐DEIM needs to be applied. A longitudinal chassis beam of a 2001 Ford Taurus is used to examine the different clustering methods. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On corner singularities in Reissner‐Mindlin's theory of elastic plates
Authors: Felger Julian , Becker Wilfried
Published: October 2015

In the framework of linear elasticity, singularities occur in domains with non‐smooth boundaries. Particularly in Fracture Mechanics, the local stress field near stress concentrations is of interest. In this work, singularities at re‐entrant corners or sharp notches in Reissner‐Mindlin plates are studied. Therefore, an asymptotic solution of the governing system of partial differential equations is obtained by using a complex potential approach which allows for an efficient calculation of the singularity exponent λ. The effect of the notch opening angle and the boundary conditions on the singularity exponent is discussed. The results show, that it can be distinguished between singularities for symmetric and antisymmetric loading and between singularities of the bending moments and the transverse shear forces. Also, stronger singularities than the classical crack tip singularity with free crack faces are observed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Finite element method for the vibration of cracked beams with varying cross section
Authors: Haskul Mehmet , Kısa Murat
Published: October 2015

Vibration analysis of cracked beams having linearly varying cross‐sections both in thickness and width was investigated. A computer program using the finite element method has been written to find the dynamical characteristics (natural frequencies and mode shapes) of the cracked beam. The cracked section in the beam has been modeled by a massless spring whose flexibility depens on the local flexibility induced by the crack. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expression. Some examples have been given to explain the proposed method and investigate the effects of the depth and location of cracks on the natural frequencies and mode shapes. The results of current study and those in the literature are compared and good agreements have been found. Consequently it is showed that proposed method is reliable and simple. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fatigue mechanisms of cord–rubber composites
Authors: Jha Niraj Kumar , Nackenhorst Udo
Published: October 2015

This article presents a continuum damage mechanics approach to characterize fatigue mechanisms of cord‐rubber composites. An airspring bellow which consists of layers of rubber and reinforcing cords is considered for this work. The phenomenological material model for rubber is formulated for the purpose of analyzing the rate dependent behavior under cyclic loading. The rate dependency and hysteretic behavior are characterized by using the concept of internal variables [1]. The implementation of the constitutive formulation for rubber material is done in ABAQUS via UMAT.

A fatigue failure mechanisms of cord‐reinforced airspring is for example interfacial debonding. Within the framework of finite element cohesive zone modeling, a user element is developed to study the cord‐rubber interfacial debonding. Furthermore, the developed methodology can be easily extended to understand the long‐term effects of e.g. temperature, frequency, loading rates, amplitudes etc. on the fatigue life of airsprings. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stabilizing the XFEM for static and dynamic crack simulations
Authors: Loehnert Stefan
Published: October 2015

For many crack geometries the standard XFEM may lead to badly conditioned equation systems. Recently a number of remedies to that problem have been published. In this contribution the stabilization technique presented in [1] is extended to dynamic and possibly nonlinear fracture mechanics and additionally combined with the SGFEM / SXFEM [2]. The performance of the different strategies is demonstrated in a linear elastic 3D mode 1 crack problem for which the analytical solution exists. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A three‐dimensional progressive damage model for fiber reinforced composites with an implicit‐explicit integration scheme
Authors: Maass Grischa , Gruttmann Friedrich
Published: October 2015

This contribution proposes a fully three dimensional “continuum damage model” (CDM) to describe the interlaminar and intralaminar failure mechanisms of transversely isotropic elastic‐brittle materials under static loading. The constitutive model is derived from an energy function with independent damage variables for each damage mode. The evolution law is based on energy dissipation within the damage process, taking into account the critical energy release rate to weaken the effect of mesh dependent outcome. The onset of damage can be predicted with Cuntze's failure mode concept [1] as well as with Hashin's failure criteria. In this model linear stress decreasing is assumed. In addition, an implicit‐explicit integration scheme, first proposed by Oliver [3] for isotropic damage models, is adapted to increase the stability and robustness of numerical simulations and to decrease the computational cost of material failure analyses. By comparing the results from implicit‐explicit integration schemes and standard implicit integration schemes, a high level of agreement is found. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Crack propagation at bi‐material interfaces
Authors: Alam Mahabub , Parmigiani John P.
Published: October 2015

There is currently a gap in the understanding of how crack propagation by intergranular versus transgranular fracture varies with changes in material properties and grain size. Much of the prior work in this area has been in terms of LEFM and criterion based on toughness alone. More recent work has shown that a toughness‐and‐strength approach is required. In this study a strength‐and‐energy approach is applied to intergranular‐versus‐transgranular fracture through a cohesive‐zone approach implemented in a finite element model. Results show that intergranular fracture becomes more likely, and has an increasing shear component, as grain toughness increases and grain stiffness and grain size decrease. These results can help guide material development. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Macroscopic damage modeling for silicon nitride
Authors: Ruck Johannes , Othmani Yamen , Lube Tanja , Khader Iyas , Kailer Andreas , Böhlke Thomas
Published: October 2015

Modeling the damage of brittle materials is of great importance considering a variety of structural components. Prominent examples are high strength engineering ceramics. The present work is concerned with silicon nitride, a material with increasing relevance in industrial applications. In the sense of a hierarchical model structure, effective properties of micromechanical simulations were applied to macroscopic, phenomenological damage models for monotonous and cyclic loading. In the following, both models are introduced and the application of the cyclic damage model to a four point bending test is discussed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A regularization approach for damage models based on a displacement gradient
Authors: Schwarz Stephan , Junker Philipp , Hackl Klaus
Published: October 2015

Common material models that take into account softening effects due to damage encounter the problem of ill‐posed boundary value problems if no regularization is applied. This condition leads to a non‐unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this problem is to apply regularization techniques that take into account the non‐local behavior of the damage [1]. For this purpose a field function is used to couple the local damage parameter to a non‐local level, in which differences between the local and non‐local parameter as well as the gradient of the non‐local parameter can be penalized.

In contrast, we present a novel approach to regularization in which no field function is needed [2]. Hereto, the regularization is carried out by means of the divergence of the displacements and no additional quantity is necessary since the displacements are already defined on a non‐local level. The idea is that with an increasing value of the damage the element's volume will increase as well. This is a result of the softening due to the occurring damage. The increasing volume can be measured by the divergence of the displacements which can be penalized by an additional energy part. The lack of any field function and the regularization by the use of the divergence of the displacements entails several numerical advantages: the computational effort is considerably reduced and the convergence behavior is improved as well. Naturally, the numerical results are mesh independent due to the regularization. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechanical properties of cold sprayed Titanium and Nickel based coatings
Authors: Silvello A. , Cavaliere P.
Published: October 2015

Cold spray is an innovative coating technology. Very fine particles are accelerated, then sprayed on a substrate in condition very far from material melting. The unique mechanical properties experienced by the sprayed material are due to the severe plastic deformation acting during particle impact. In the present paper, the microstructural and mechanical behavior of Ti‐ and Ni‐based nanocomposites coatings produced via cold spray are presented. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Effects of a circular defect size and position on the damage progression in hybrid laminates under compressive loading
Authors: Tala‐Ighil Nacer , Mokhtari Ahcene , Brick Chaouche Amine
Published: October 2015

The effects of a circular defect size and position on the post‐damage response of the FMLs laminates under compressive loading has been studied. Compression tests are performed on composite plates comprising a hole having different diameters (8 mm, 12 mm and 16 mm) and located at different positions (25%, 50% and 75%) in the loading direction. A numerical analysis using the finite element method FEM has permits the identification of the initiation zones and the description of the damage evolution in these laminates. The results of the numerical simulation are in good agreement with the experimental results. The FEM has well predicted the critical damage zones. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Phase‐Field Modeling of Fracture in Anisotropic Media
Authors: Teichtmeister Stephan , Miehe Christian
Published: October 2015

In the recent years phase‐field modeling of fracture has become a promising tool to describe complex crack patterns in all kinds of solid materials. Many of the models assume an isotropic material behavior, which of course is not a meaningful assumption for e.g. biological tissues such as arterial walls. Since the phase‐field approach introduces an additional (smeared) phase describing the evolution of the crack, this method is well suited to be extended to anisotropic materials without thinking about an adaption of the discretization technique. Anisotropy can be incorporated in several ways, like by an extension of the surface energy, i.e. by making the energy release rate orientation dependent, as considered in [1]. Our ansatz is based on a pure geometrical approach, namely on an anisotropic formulation of the crack surface itself. Here, we will focus on transversely isotropic and cubically anisotropic solids, where the latter one makes the incorporation of the second gradient of the crack phase field necessary. At the end one numerical example is shown, which conceptually shows the influence of the anisotropy on the crack path. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical methods for crack loading analyses in quasicrystals
Authors: Wang Zhibin , Ricoeur Andreas
Published: October 2015

Since the first discovery of quasicrystals in a man made Al‐Mn alloy about thirty years ago, people made great effort to investigate this kind of outstanding material. The materials scientists are constantly trying to produce stable quasicrystalline particles or even a complete single quasicrystalline specimen. On the other hand, the fracture behaviour of quasicrystals is started to be investigated because the coupling effect between phonon and phason fields can rebuild the conventional fracture criteria. This work develops a numerical tool for simulating in‐plane problems of 1D QC and extends the fracture quantities i.e. stress intensity factors (SIF) and strain energy release rate to phason fields. Finally, numerical results are given to reveal what difference the phason field can bring into conventional fracture quantities. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Crack initiation in elliptically notched plates
Authors: Weißgraeber Philipp , Felger Julian , Becker Wilfried
Published: October 2015

In this work, crack initiation in elliptically notched plates under uniaxial tension is studied by means of a Finite Fracture Mechanics analysis. The stress concentration factor changes with the aspect ratio of the half axes: from unity for slender ellipses in loading direction to infinity for crack‐like ellipses normal to the loading. The closed‐form solutions of the stress field and an approximate formulae of the stress intensity factor of mode I cracks allows for an efficient Finite Fracture Mechanics analysis of plates with elliptical notches with arbitrary aspect ratios. The results show that the transition from vanishing stress concentration to infinite (crack‐like) stress concentration is rendered continuously by the present approach. A transition from strength of materials to Linear Elastic Fracture Mechanics is obtained that shows distinct size effects. A comparison to experimental results on size effects of notched plates shows good agreement. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Anisotropic Damage Theories based on 2nd Order Damage Tensors
Authors: Wulfinghoff Stephan , Reese Stefanie
Published: October 2015

Isotropic and anisotropic damage theories are shortly reviewed concerning different aspects like thermodynamical consistency, effective undamaged configurations, crack‐closure effects and the interpretation of the damage variable. A recently proposed damage growth criterion for second order damage tensors is discussed in integral as well as incremental form. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of the discontinuous Galerkin finite element method in small deformation regimes
Authors: Bayat Hamid Reza , Wulfinghoff Stephan , Reese Stefanie
Published: October 2015

In this paper, a finite element formulation is defined in the framework of the discontinuous Galerkin method. Discontinuous Galerkin (dG) methods are classically used in fluid mechanics, however recently their application in solid mechanics has become more vivid among scientists. Of special interest is their application in elliptic problems with constraints such as incompressibility which leads to volumetric locking phenomenon and also in some structural models of shells, plates and beams with compatibility constraints, which brings about shear locking [1]. While classical standard Galerkin methods must be continuous, dG methods can be applied for discontinuities across element boundaries, where a jump of a value (displacement) can be observed. In the present work, a dG method is applied to a linear elastic bar, where a weak discontinuity is allowed in the bar. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Determination of a Constitutive Friction Law Using an Elastic‐Plastic Half‐Space Model
Authors: Beyer Florian , Willner Kai
Published: October 2015

Friction influences metal forming processes both in economic and technical terms. A precise understanding of friction is inevitable as friction restricts the potential of the product design. Friction depends on the occurring contact loads which is especially true for sheet‐bulk metal forming (SBMF) as the incorporated contact loads appear in a very broad range. Numerical simulations, which are verified experimentally, are carried out to analyse contact interactions which typically appear in SBMF. On the one hand the multi‐scale character of rough surfaces requires a very fine resolution of the contact area, on the other hand a large contact area is necessary to be representative. A half‐space model is chosen for the contact analysis, because it only depends on the two‐dimensional surface boundary which consumes less computing capacity than the finite element method (FEM) with its three‐dimensional volume approach for the same surface resolution and area. The outcome is a constitutive friction law (CFL) consisting of two equations. The law is implemented into the framework of FEM to see the impact in a typical SBMF‐process which aims to form metal sheet into cups with integrated gearing teeth. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Corotational flat triangular elements for the nonlinear analysis of thin shell structures
Authors: Caselli Federica , Bisegna Paolo
Published: October 2015

This contribution shows the effectiveness and versatility of the corotational formulation in the development of shell finite elements for geometric and material nonlinear analysis of thin structures. In particular, flat triangular elements especially suited to shell structures made of shape memory alloys (SMA) or soft biological tissues are dealt with. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Non‐linear Stochastic Finite Element
Authors: Caylak Ismail , Dridger Alex , Mahnken Rolf
Published: October 2015

This paper investigates the uncertainty of physically non‐linear problems by modeling the elastic random material parameters as stochastic fields. For its stochastic discretization a polynomial chaos (PC) is used to expand the coefficients into deterministic and stochastic parts. Then, from experimental data for an adhesive material the distribution of the random variables, i.e. Young's modulus E(θ), the static yield point Y0 and the nonlinear hardening parameters q and b, are known. In the numerical example the distribution of the stresses obtained by the PC based SFEM and Monte Carlo simulation is compared. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On a Mathematical Problem of Cusped Double‐Layered Plates
Authors: Chinchaladze Natalia
Published: October 2015

The present paper is devoted to the system of degenerate partial differential equations arise from the investigation of elastic two layered prismatic shells. Harmonic vibration of cusped double‐layered plates is consider. The weak setting of the BVPs in the case of the zero approximation of hierarchical models is considered. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An efficient and robust Reissner–Mindlin shell formulation for isogeometric analysis
Authors: Dornisch Wolfgang , Müller Ralf , Klinkel Sven
Published: October 2015

The novel idea of isogeometric analysis is to use the basis functions of the geometry description of the design model also for the analysis. Thus, the geometry is represented exactly on element level. A closer integration of design and analysis is fostered by the usage of one common geometry model for design and analysis. A prevalent choice for the geometry description in isogeometric shell analysis are Non‐Uniform Rational B‐spline (NURBS) surfaces, which are commonly used in industrial design software to model thin structures. In order to directly compute structures defined by NURBS surfaces, an efficient isogeometric shell formulation is required. In this contribution an isogeometric Reissner–Mindlin shell formulation derived from the continuum theory is presented. The shell body is described by a shell reference surface, which is defined by NURBS surfaces, and a director vector. The director vector in the current configuration is computed by an orthogonal rotation using Rodrigues' tensor in every integration point. The axial vector of the rotation is interpolated. A multiplicative update formulation for the rotations accounts for finite rotations. A benchmark example shows the superior accuracy of the presented shell formulation for nonlinear computations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechanical Analysis of Metallic SLM‐Lattices on Small Scales: Finite Element Simulations versus Experiments
Authors: Didam S. , Eidel B. , Ohrndorf A. , Christ H.‐J.
Published: October 2015

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)
On the Mechanics of Ultralight Hollow Microlattices
Authors: Eidel B.
Published: October 2015

The objective of the present work is a thorough understanding of the mechanics of microlattices by finite element analysis. A thin‐shell model for a unit‐cell along with an isotropic material law of elasto‐plasticity captures for compression experiments (i) significant deformation characteristics in terms of stress‐strain curves, (ii) the interplay of inelasticity with shell geometrical features and (iii) the scaling behavior of stiffness and strength for various densities. The octet cell in comparison to the bcc cell shows an increase in elastic stiffness and strength by 1‐2 orders of magnitude, thus making a step towards ultralight and ultratight properties of structural materials. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of non‐stationary vibration signals based on the modified Kronecker sequences
Authors: Girip Iulian , Munteanu Ligia
Published: October 2015

The paper establishes a representation model for non‐stationary random vibration signals based on the modified Kronecker sequences. The modified Kronecker sequence constructed via generalizing golden ratio is one of the special types of low discrepancy sequences which have better dimensional projections [1]. The actual modeling and simulation of non‐stationary random data is more suitable for seismological signals and not for the vehicle vibrations [2, 3]. Under these circumstances, this paper presents a new algorithm for finding the modified Kronecker sequences in order to generate non‐stationary vehicle vibration signals which mostly withhold the amplitude‐frequency‐time distribution of the sample signal. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A model reduction approach for hyperelastic materials based on Proper Orthogonal Decomposition
Authors: Hürkamp André , Kaliske Michael
Published: October 2015

In this contribution, we present a model reduction approach for hyperelastic materials based on Proper Orthogonal Decomposition. A separation of the solution into time and space dependent functions is performed, which allows to compute reduced solutions within real time. The functionality of the method is demonstrated by a tensile test and is further applied to a stochastic analysis and a multi‐parametric analysis involving non‐linear material behaviour and large deformations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Energy‐momentum conserving discretization of mixed shell elements for large deformation problems
Authors: Janz Alexander , Betsch Peter
Published: October 2015

In the present paper we consider structure‐preserving integration methods in the context of mixed finite elements. The used low‐order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy‐momentum (EM) consistent time‐stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu‐Washizu‐type variational formulation we develop a second‐order accurate structure‐preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A high‐order enrichment strategy for the finite cell method
Authors: Joulaian Meysam , Zander Nils , Bog Tino , Kollmannsberger Stefan , Rank Ernst , Düster Alexander
Published: October 2015

Thanks to the application of the immersed boundary approach in the finite cell method, the mesh can be defined independently from the geometry. Although this leads to a significant simplification of the mesh generation, it might cause difficulties in the solution. One of the possible difficulties will occur if the exact solution of the underlying problem exhibits a kink inside an element, for instance at material interfaces. In such a case, the solution turns out less smooth – and the convergence rate is deteriorated if no further measures are taken into account. In this paper, we explore a remedy by considering the partition of unity method. The proposed approach allows to define enrichment functions with the help of a high‐order implicit representation of the material interface. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A surface oriented solid formulation based on a hybrid Galerkin‐collocation method
Authors: Klinkel Sven , Chen Lin , Dornisch Wolfgang
Published: October 2015

The contribution is concerned with a numerical method to analyze the mechanical behavior of 3D solids. The method employs directly the geometry defined by the boundary representation modeling technique, which is frequently used in CAD to define solids. It combines the benefits of the isogeometric analysis methodology with the scaled boundary finite element method. In the present approach, only the boundary surfaces of the solid are discretized. No tensor‐product structure of three‐dimensional objects is exploited to parametrize the physical domain. The weak form is applied only on the boundary surfaces. The governing partial differential equations of elasticity are transformed to an ordinary differential equation (ODE) of Euler type. The isogeometric Galerkin approach is employed to approximate the displacement response at the boundary surfaces. It exploits the two‐dimensional NURBS objects to parametrize the boundary surfaces. To solve the Euler type ODE, the NURBS based collocation approach is applied. The accuracy of the method is validated against the analytical solutions. The presented method is able to analyze solids, which are bounded by an arbitrary number of surfaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A projection approach to optimal control of elastic beam dynamics
Authors: Kostin Georgy
Published: October 2015

Controlled lateral motions of an elastic beam – extended body with a cuboid shape – are studied. A generalized statement of the initial‐boundary value problem is given in the frame of 3D linear elasticity based on the integral formulation of constitutive relations. A numerical approach relying on the Fourier method and semi‐discretization technique is proposed to design the optimal boundary control that moves the beam to a given final state and minimizes a quadratic cost function. Some results of numerical simulation and quality analysis are presented and discussed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A stress‐velocity least‐squares mixed finite element formulation for incompressible elastodynamics
Authors: Nisters Carina , Schwarz Alexander , Steeger Karl , Schröder Jörg
Published: October 2015

In the framework of solving elastodynamic problems using a least‐squares mixed finite element method (LSFEM) the implementation of a stress‐velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first‐order div – grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L2‐norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two‐dimensional problem. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mixed Tetrahedral Elements for the Analysis of Structures with Material and Geometric Nonlinearities
Authors: Nodargi Nicola A. , Bisegna Paolo
Published: October 2015

A new mixed tetrahedral element, particularly suited for the analysis of structures exhibiting nonlinear material and geometric behavior, is here presented. Its derivation is based on a Hu–Washizu type formulation, including also rotation and skew‐symmetric stress fields as independent variables, instrumental to equip the element with nodal rotational degrees of freedom. A Gauss‐point‐discontinuous interpolation is selected for the total strain field, in order to account for its possibly highly nonlinear spatial distribution due to inelastic strains. Accordingly, the resulting tetrahedron can properly describe inelastic effects occurring over a space scale smaller than the element size. An original and efficient iterative procedure is proposed to perform the element state determination. Geometric nonlinearities are treated by means of the corotational approach. A numerical simulation is presented to analyze the element performances. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
XFEM for Deformation Theory of Plasticity
Authors: Omerović Samir , Fries Thomas‐Peter
Published: October 2015

In this work, an approach is presented to improve global accuracy properties for physically non‐linear problems in the frame of elastoplasticity. The work is motivated by the fact that convergence characteristics of a finite element solution are dominated by the regularity of the exact solution. For a material undergoing inelastic deformations, however, very few analytical solutions for the field variables are known, especially for the displacement field. Considering a simple, one‐dimensional example, it is shown that the convergence rates are far from optimal. The reason is explained by establishing ties to a familiar, but more demonstrative problem. In the next section two remedies for the problem, based on the Extended Finite Element Method (XFEM) are presented and discussed, in the last section a 2D‐problem is considered. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Discussion of the Particle Finite Element Method in the Context of Strength of Materials
Authors: Sabel Matthias , York Duran José L. , Sator Christian , Müller Ralf
Published: October 2015

In the context of the particle finite element method (PFEM) a body is considered as a set of particles that are meshed with standard finite elements before every load step. This enables the method to cope with large topological changes where the standard FEM often fails. To mesh the set of particles, its boundary needs to be detected which is accomplished with the α‐shape method, and although this method is often used within the PFEM, the crucial parameter α is not well understood. This article provides a physical interpretation of α and shows its meaning in the context of strength of materials. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Weighted overconstrained least‐squares mixed finite elements for hyperelasticity
Authors: Schwarz Alexander , Steeger Karl , Schröder Jörg
Published: October 2015

The present contribution aims to improve the least‐squares finite element method (LSFEM) with respect to the approximation quality in hyperelasticity. We consider a geometrically nonlinear elastic setup and here especially bending dominated problems. Compared with other variational approaches as for example the Galerkin method, the main drawback of least‐squares formulations is the unsatisfying approximation quality in terms of accuracy and robustness of especially lower‐order elements, see e.g. SCHWARZ ET AL. [1]. In order to circumvent these problems, we introduce an overconstrained first‐order stress‐displacement system with suited weights. For the interpolation of the unknowns standard polynomials for the displacements and vector‐valued Raviart‐Thomas functions for the approximation of the stresses are used. Finally, a numerical example is presented in order to show the improvement of performance and accuracy. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Comparison of a mixed least‐squares formulation using different approximation spaces
Authors: Steeger Karl , Schröder Jörg , Schwarz Alexander
Published: October 2015

The main goal of the present work is the comparison of the performance of a least‐squares mixed finite element formulation where the solution variables (displacements and stresses) are interpolated using different approximation spaces. Basis for the formulation is a weak form resulting from the minimization of a least‐squares functional, compare e.g. [1]. As suitable functions for
$H^1(\cal{B})$
standard interpolation polynomials of Lagrangian type are chosen. For the conforming discretization of the Sobolev space
$H({\rm div}, \cal{B})$
vector‐valued Raviart‐Thomas interpolation functions, see also [2], are used. The resulting elements are named as PmPk and RTmPk. Here m (stresses) and k (displacements) denote the approximation order of the particular interpolation function. For the comparison we consider a two‐dimensional cantilever beam under plain strain conditions and small strain assumptions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Interlaminar stress recovery for arbitrarily curved shells
Authors: Winkler Robert , Haller Herbert , Plakomytis Dimitrios , Gerstmayr Johannes
Published: October 2015

An established postprocessing procedure for the determination of interlaminar shear and normal stresses based on the results of a conventional shell finite element analysis is generalized for arbitrarily curved laminated shells. The method relies on the three‐dimensional equilibrium conditions and an extended lamination theory. Underlying approximations are discussed and exemplary results are presented. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability and bifurcation behaviour of a Laval‐Rotor considering fluid forces in compliant liquid seals
Authors: Bäuerle Simon , Hetzler Hartmut
Published: October 2015

This contribution discusses the influence of fluid forces, stemming from compliant, contact‐free annular rotor seals, on the steady state stability and bifurcation behaviour of a rotor. The model used in this work consists of a Laval‐Rotor where the disc runs in a turbulently streamed seal. The compliance of the seal is reduced to a visco‐elastically supported outer seal ring. In order to account for the fluid seal forces the Childs‐Hirs‐model is used. An investigation of the eigenvalues shows that the compliance of the seal support may lead to a significant increase in the stable operating range. A stability‐loss via Hopf‐, Hopf‐Hopf or secondary Hopf‐Bifurcations can occur depending on the system parameters. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal Impedance Load of a Bistable Energy Harvester
Authors: Heymanns Matthias , Hagedorn Peter
Published: October 2015

In this contribution we investigate a bistable energy harvester with regard to its optimal impedance load. A bistable energy harvester exhibits three different types of oscillation: Single‐well (about a stable equilibrium), cross‐well (between the wells) and inter‐well (about the unstable equilibrium). The occurring oscillation type depends, for instance, on the excitation parameters and the initial conditions. It has already been observed ( [1]) that the optimal impedance, which allows to maximize the power output, varies for each oscillation type. In our investigations we complement these findings with analytical and numerical calculations. For our analysis we examine the non‐dimensionalized coupled equations of a bistable energy harvester. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A DAE formulation for geared rotor dynamics including frictional contact between the teeth
Authors: Jehle Georg , Fidlin Alexander
Published: October 2015

A DAE approach is presented for geared rotor dynamics simulations with rigid helical evolvent gears. It includes the normal contact force between the teeth as well as tangential components.

Given the evolvent tooth flank geometry of gear 1 and gear 2 [1], the contact line and the velocity difference in the contact are found. The requirement of no penetration of the teeth yields a non‐holonomic constraint and the contact normal force. The friction caused force and moment are obtained by applying Coulomb's friction model.

This approach is used to investigate the dynamics of two ideal rotors with translational DoFs, which are connected by gears to one another. The driving rotor has a given angular speed, while the driven rotates unrestrainedly and is connected to a rotational damper. Because of the periodic friction terms, the solution is periodic. A direct time integration or a harmonic approach can be used for the numerical computation. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)