Authors:Daniel Giraldo; Doriam Restrepo Pages: 883 - 903 Abstract: This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr–Coulomb and Drucker–Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials ( \(p \ge 3\) ) require mesh resolutions above of \(PPW \ge \) 10 to ensure displacement errors below 10%. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1454-8 Issue No:Vol. 60, No. 6 (2017)

Authors:Ferdinando Auricchio; Giulia Scalet; Peter Wriggers Pages: 905 - 922 Abstract: The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1437-9 Issue No:Vol. 60, No. 6 (2017)

Authors:Hannes Erdle; Thomas Böhlke Pages: 923 - 942 Abstract: The implementation of novel material models in the microscale gives a deeper understanding of inner and intercrystalline effects of crystalline materials. For future works, this allows more precise predictions of macroscale models. Here, we present a finite gradient crystal plasticity theory which preserves the single crystal slip kinematics. However, the model is restricted to one gradient-stress, associated with the gradient of the accumulated plastic slip, in order to account for long range dislocation interactions in a physically simplified, numerically efficient approach. In order to model the interaction of dislocations with and their transfer through grain boundaries, a grain boundary yield condition is introduced. The grain boundary flow rule is evaluated at sharp interfaces using discontinuous trial functions in the finite element implementation, thereby allowing for a discontinuous distribution of the accumulated plastic slip. Simulations of crystal aggregates are performed under different loading conditions which reproduce well the size dependence of the yield strength. An analytical solution for a one-dimensional single slip supports the numerical results. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1447-7 Issue No:Vol. 60, No. 6 (2017)

Authors:E. T. Ooi; C. Song; S. Natarajan Pages: 943 - 967 Abstract: This manuscript presents an extension of the recently-developed high order complete scaled boundary shape functions to model elasto-static problems in functionally graded materials. Both isotropic and orthotropic functionally graded materials are modelled. The high order complete properties of the shape functions are realized through the introduction of bubble-like functions derived from the equilibrium condition of a polygon subjected to body loads. The bubble functions preserve the displacement compatibility between the elements in the mesh. The heterogeneity resulting from the material gradient introduces additional terms in the polygon stiffness matrix that are integrated analytically. Few numerical benchmarks were used to validate the developed formulation. The high order completeness property of the bubble functions result in superior accuracy and convergence rates for generic elasto-static and fracture problems involving functionally graded materials. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1443-y Issue No:Vol. 60, No. 6 (2017)

Authors:Sylvain Mercier; Serge Gratton; Nicolas Tardieu; Xavier Vasseur Pages: 969 - 982 Abstract: Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1450-z Issue No:Vol. 60, No. 6 (2017)

Authors:Eric Li; Z. C. He; G. Wang; G. R. Liu Pages: 983 - 996 Abstract: The phononics crystals (PCs) are periodic man-made composite materials. In this paper, a mass-redistributed finite element method (MR-FEM) is formulated to study the wave propagation within liquid PCs with hard inclusion. With a perfect balance between stiffness and mass in the MR-FEM model, the dispersion error of longitudinal wave is minimized by redistribution of mass. Such tuning can be easily achieved by adjusting the parameter r that controls the location of integration points of mass matrix. More importantly, the property of mass conservation in the MR-FEM model indicates that the locations of integration points inside or outside the element are immaterial. Four numerical examples are studied in this work, including liquid PCs with cross and circle hard inclusions, different size of inclusion and defect. Compared with standard finite element method, the numerical results have verified the accuracy and effectiveness of MR-FEM. The proposed MR-FEM is a unique and innovative numerical approach with its outstanding features, which has strong potentials to study the stress wave within multi-physics PCs. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1451-y Issue No:Vol. 60, No. 6 (2017)

Authors:M. A. Celigueta; S. Latorre; F. Arrufat; E. Oñate Pages: 997 - 1010 Abstract: The Discrete Element Method (DEM) has been used for modelling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear elastic behavior of a continuum modelled via the classical force-displacement relationships at the contact interfaces between particles. In this work we propose a new way for computing the contact forces between discrete particles. The newly proposed forces take into account the surroundings of the contact, not just the contact itself. This brings in the missing terms that provide an accurate approximation to an elastic continuum, and avoids calibration of the DEM parameters for the purely linear elastic range. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1453-9 Issue No:Vol. 60, No. 6 (2017)

Authors:Christopher Zimmermann; Roger A. Sauer Pages: 1011 - 1031 Abstract: A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis. For a convenient embedding into general finite element codes, the Bézier extraction operator for LR NURBS is formulated. An automatic remeshing technique is presented that allows adaptive local refinement and coarsening of LR NURBS. In this work, LR NURBS are applied to contact computations of 3D solids and membranes. For solids, LR NURBS-enriched finite elements are used to discretize the contact surfaces with LR NURBS finite elements, while the rest of the body is discretized by linear Lagrange finite elements. For membranes, the entire surface is discretized by LR NURBS. Various numerical examples are shown, and they demonstrate the benefit of using LR NURBS: Compared to uniform refinement, LR NURBS can achieve high accuracy at lower computational cost. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1455-7 Issue No:Vol. 60, No. 6 (2017)

Authors:Hossein Ahmadian; Bowen Liang; Soheil Soghrati Pages: 1033 - 1055 Abstract: A new computational framework is introduced for the automated finite element (FE) modeling of fiber reinforced composites and simulating their micromechanical behavior. The proposed methodology relies on a new microstructure reconstruction algorithm that implements the centroidal Voronoi tessellation (CVT) to generate an initial uniform distribution of fibers with desired volume fraction and size distribution in a repeating unit cell of the composite. The genetic algorithm (GA) is then employed to optimize locations of fibers such that they replicate the target spatial arrangement. We also use a non-iterative mesh generation algorithm, named conforming to interface structured adaptive mesh refinement (CISAMR), to create FE models of the CFRPC. The CVT–GA–CISAMR framework is then employed to investigate the appropriate size of the composite’s representative volume element. We also study the strength and failure mechanisms in the CFRPC subject to varying uniaxial and mixed-mode loadings. PubDate: 2017-12-01 DOI: 10.1007/s00466-017-1457-5 Issue No:Vol. 60, No. 6 (2017)

Authors:M. S. Pigazzini; Y. Bazilevs; A. Ellison; H. Kim Abstract: In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on isogeometric analysis, where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff–Love thin shell. Continuum damage mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff–Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff–Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations. PubDate: 2017-11-24 DOI: 10.1007/s00466-017-1514-0

Authors:Azahar Monge; Philipp Birken Abstract: We consider the Dirichlet–Neumann iteration for partitioned simulation of thermal fluid–structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations with jumps in the material coefficients across the interface. The heat equations are discretized using an implicit Euler scheme in time, whereas a finite element method on one domain and a finite volume method with variable aspect ratio on the other one are used in space. We provide an exact formula for the spectral radius of the iteration matrix. The formula indicates that for large time steps, the convergence rate is the aspect ratio times the quotient of heat conductivities and that decreasing the time step will improve the convergence rate. Numerical results confirm the analysis and show that the 1D formula is a very good estimator in 2D and even for nonlinear thermal FSI applications. PubDate: 2017-11-23 DOI: 10.1007/s00466-017-1511-3

Authors:Boumediene Nedjar; Herbert Baaser; Robert J. Martin; Patrizio Neff Abstract: We investigate a finite element formulation of the exponentiated Hencky-logarithmic model whose strain energy function is given by $$\begin{aligned} W_\mathrm {eH}(\varvec{F}) = \dfrac{\mu }{k}\, e^{\displaystyle k \left \text{ dev }_n \log \varvec{U}\right ^2} + \dfrac{\kappa }{2 \hat{k}}\, e^{\displaystyle \hat{k} [\text{ tr } (\log \varvec{U})]^2 }, \end{aligned}$$ where \(\mu >0\) is the (infinitesimal) shear modulus, \(\kappa >0\) is the (infinitesimal) bulk modulus, k and \(\hat{k}\) are additional dimensionless material parameters, \(\varvec{U}=\sqrt{\varvec{F}^T\varvec{F}}\) is the right stretch tensor corresponding to the deformation gradient \(\varvec{F}\) , \(\log \) denotes the principal matrix logarithm on the set of positive definite symmetric matrices, \(\text{ dev }_n \varvec{X} = \varvec{X}-\frac{\text{ tr } \varvec{X}}{n}\varvec{1}\) and \( \varvec{X} = \sqrt{\text{ tr }\varvec{X}^T\varvec{X}}\) are the deviatoric part and the Frobenius matrix norm of an \(n\times n\) -matrix \(\varvec{X}\) , respectively, and \(\text{ tr }\) denotes the trace operator. To do so, the equivalent different forms of the constitutive equation are recast in terms of the principal logarithmic stretches by use of the spectral decomposition together with the undergoing properties. We show the capability of our approach with a number of relevant examples, including the challenging “eversion of elastic tubes” problem. PubDate: 2017-11-22 DOI: 10.1007/s00466-017-1518-9

Authors:A. Esmaeili; P. Steinmann; A. Javili Abstract: Surfaces of solids behave differently from the bulk due to different atomic rearrangements and processes such as oxidation or aging. Such behavior can become markedly dominant at the nanoscale due to the large ratio of surface area to bulk volume. The surface elasticity theory (Gurtin and Murdoch in Arch Ration Mech Anal 57(4):291–323, 1975) has proven to be a powerful strategy to capture the size-dependent response of nano-materials. While the surface elasticity theory is well-established to date, surface plasticity still remains elusive and poorly understood. The objective of this contribution is to establish a thermodynamically consistent surface elastoplasticity theory for finite deformations. A phenomenological isotropic plasticity model for the surface is developed based on the postulated elastoplastic multiplicative decomposition of the surface superficial deformation gradient. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and the consistent elastoplastic tangent of the surface contribution is derived. Finally, a series of numerical examples provide further insight into the problem and elucidate the key features of the proposed theory. PubDate: 2017-11-22 DOI: 10.1007/s00466-017-1517-x

Authors:Ashraf Idkaidek; Seid Koric; Iwona Jasiuk Abstract: Fracture analysis of a cortical bone sample from a tibia of a 70 years-old human male donor is conducted computationally using an extended finite element method. The cortical bone microstructure is represented by several osteons arranged based on bone microscopy image. The accuracy of results is examined by comparing a linear elastic fracture mechanics approach with a cohesive segment approach and varying the finite element model mesh density, element type, damage evolution, and boundary conditions. Microstructural features of cortical bone are assumed to be linear elastic and isotropic. We find that the accuracy of results is influenced by the finite element model mesh density, simulation increment size, element type, and the fracture approach type. Using a relatively fine mesh or small simulation increment size gives inaccurate results compared to using an optimized mesh density and simulation increment size. Also, mechanical properties of cortical bone phases influence the crack propagation path and speed. PubDate: 2017-11-16 DOI: 10.1007/s00466-017-1491-3

Authors:Riccardo Broglia; Danilo Durante Abstract: This paper focuses on the analysis of a challenging free surface flow problem involving a surface vessel moving at high speeds, or planing. The investigation is performed using a general purpose high Reynolds free surface solver developed at CNR-INSEAN. The methodology is based on a second order finite volume discretization of the unsteady Reynolds-averaged Navier–Stokes equations (Di Mascio et al. in A second order Godunov—type scheme for naval hydrodynamics, Kluwer Academic/Plenum Publishers, Dordrecht, pp 253–261, 2001; Proceedings of 16th international offshore and polar engineering conference, San Francisco, CA, USA, 2006; J Mar Sci Technol 14:19–29, 2009); air/water interface dynamics is accurately modeled by a non standard level set approach (Di Mascio et al. in Comput Fluids 36(5):868–886, 2007a), known as the single-phase level set method. In this algorithm the governing equations are solved only in the water phase, whereas the numerical domain in the air phase is used for a suitable extension of the fluid dynamic variables. The level set function is used to track the free surface evolution; dynamic boundary conditions are enforced directly on the interface. This approach allows to accurately predict the evolution of the free surface even in the presence of violent breaking waves phenomena, maintaining the interface sharp, without any need to smear out the fluid properties across the two phases. This paper is aimed at the prediction of the complex free-surface flow field generated by a deep-V planing boat at medium and high Froude numbers (from 0.6 up to 1.2). In the present work, the planing hull is treated as a two-degree-of-freedom rigid object. Flow field is characterized by the presence of thin water sheets, several energetic breaking waves and plungings. The computational results include convergence of the trim angle, sinkage and resistance under grid refinement; high-quality experimental data are used for the purposes of validation, allowing to compare the hydrodynamic forces and the attitudes assumed at different velocities. A very good agreement between numerical and experimental results demonstrates the reliability of the single-phase level set approach for the predictions of high Froude numbers flows. PubDate: 2017-11-16 DOI: 10.1007/s00466-017-1505-1

Authors:T. I. Zohdi Abstract: There are many emerging manufacturing processes whereby surface structures are processed by spatially laser patterning of an entire feature at a time, as opposed to rastering a small beam. It is important to ascertain and ideally control the induced thermal fields underneath the pattern. This paper develops a computational framework to rapidly evaluate the induced thermal fields due to application of a laser on the surface. The aggregate thermal fields are efficiently computed by superposing individual “beamlet” heat-kernel solutions, based on Green’s functions, to form complex surface patterns. The utility of the approach is that laser-process designers can efficiently compute the results of selecting various system parameters, such as spatially-variable laser intensity within a pattern. This allows one to rapidly compute system parameter studies needed in the manufacturing of new products. Included are: A computational framework to compute the time-transient thermal response from a spatio-temporally non-uniform laser beam in an arbitrary spatial pattern and An analysis of how the results can be used to track the evolution of the thermal gradients and their correlation to thermal stresses. Three-dimensional examples are provided to illustrate the technique. The utility of the approach is that an analyst can efficiently ascertain a large number of laser-input scenarios without resorting to computationally-intensive numerical procedures, such the Finite Element Method. PubDate: 2017-11-14 DOI: 10.1007/s00466-017-1503-3

Authors:K. Wisniewski; E. Turska Abstract: The 9-node quadrilateral shell element MITC9i is developed for the Reissner-Mindlin shell kinematics, the extended potential energy and Green strain. The following features of its formulation ensure an improved behavior: 1. The MITC technique is used to avoid locking, and we propose improved transformations for bending and transverse shear strains, which render that all patch tests are passed for the regular mesh, i.e. with straight element sides and middle positions of midside nodes and a central node. 2. To reduce shape distortion effects, the so-called corrected shape functions of Celia and Gray (Int J Numer Meth Eng 20:1447–1459, 1984) are extended to shells and used instead of the standard ones. In effect, all patch tests are passed additionally for shifts of the midside nodes along straight element sides and for arbitrary shifts of the central node. 3. Several extensions of the corrected shape functions are proposed to enable computations of non-flat shells. In particular, a criterion is put forward to determine the shift parameters associated with the central node for non-flat elements. Additionally, the method is presented to construct a parabolic side for a shifted midside node, which improves accuracy for symmetric curved edges. Drilling rotations are included by using the drilling Rotation Constraint equation, in a way consistent with the additive/multiplicative rotation update scheme for large rotations. We show that the corrected shape functions reduce the sensitivity of the solution to the regularization parameter \( \gamma \) of the penalty method for this constraint. The MITC9i shell element is subjected to a range of linear and non-linear tests to show passing the patch tests, the absence of locking, very good accuracy and insensitivity to node shifts. It favorably compares to several other tested 9-node elements. PubDate: 2017-11-14 DOI: 10.1007/s00466-017-1510-4

Authors:Dennis Schurr; Philip Holzwarth; Peter Eberhard Abstract: Stresses in gear contact simulations, performed using elastic multibody systems, are recovered. A single gear pair is used for stress investigations and an impact is chosen as simulation case representing an extremely dynamical situation. The gears are modeled as a reduced elastic multibody system allowing a fast computation of the dynamical problem. Depending on the projection matrix which is used for model order reduction, stresses can sometimes not be recovered accurately throughout the whole gear. Thus, the main focus in this paper lies on the selection of the functions which make up the projection matrix and, therefore, determine the elastic deformations and the quality of recovered stresses. However, the chosen set of modes does not only affect stress calculation, it also strongly affects the computation of the dynamics of the gear system and, thus, the computational effort, and may lead to serious drawbacks. This issue is discussed, too. Upon that, several different mode sets are analyzed trying to minimize the computational effort of the elastic multibody system for the given problem while still being able to recover accurate stress values on distinct geometric areas. The stress values are compared with a finite element reference computation. The novel contribution of this paper is the determination of a minimal set of modes including ones assigned to the nodes of the gear contact surface, which are able to accurately recover stresses but minimize the numerical drawbacks. PubDate: 2017-11-13 DOI: 10.1007/s00466-017-1507-z

Authors:T. I. Zohdi; B. E. Abali Abstract: Electrical high voltage (HV) machines are prone to corona discharges leading to power losses as well as damage of the insulating layer. Many different techniques are applied as corona protection and computational methods aid to select the best design. In this paper we develop a reduced-order model in 1D estimating electric field and temperature distribution of a conductor wrapped with different layers, as usual for HV-machines. Many assumptions and simplifications are undertaken for this 1D model, therefore, we compare its results to a direct numerical simulation in 3D quantitatively. Both models are transient and nonlinear, giving a possibility to quickly estimate in 1D or fully compute in 3D by a computational cost. Such tools enable understanding, evaluation, and optimization of corona shielding systems for multilayered coils. PubDate: 2017-11-12 DOI: 10.1007/s00466-017-1504-2