Authors:J. M. Rodriguez Prieto; J. M. Carbonell; J. C. Cante; J. Oliver; P. Jonsén Pages: 639 - 655 Abstract: The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1442-z Issue No:Vol. 61, No. 6 (2018)

Authors:Jörg Schröder; Markus von Hoegen; Patrizio Neff Pages: 657 - 685 Abstract: In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \({{\varvec{F}}}\) to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1466-4 Issue No:Vol. 61, No. 6 (2018)

Authors:Jin He; Harold S. Park Pages: 687 - 697 Abstract: We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young–Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young–Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1474-4 Issue No:Vol. 61, No. 6 (2018)

Authors:Yuval Tal; Bradford H. Hager Pages: 699 - 716 Abstract: This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal–dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1475-3 Issue No:Vol. 61, No. 6 (2018)

Authors:Oliver Schmitt; Paul Steinmann Pages: 717 - 727 Abstract: We introduce a manufacturing constraint for controlling the minimum member size in structural shape optimization problems, which is for example of interest for components fabricated in a molding process. In a parameter-free approach, whereby the coordinates of the FE boundary nodes are used as design variables, the challenging task is to find a generally valid definition for the thickness of non-parametric geometries in terms of their boundary nodes. Therefore we use the medial axis, which is the union of all points with at least two closest points on the boundary of the domain. Since the effort for the exact computation of the medial axis of geometries given by their FE discretization highly increases with the number of surface elements we use the distance function instead to approximate the medial axis by a cloud of points. The approximation is demonstrated on three 2D examples. Moreover, the formulation of a minimum thickness constraint is applied to a sensitivity-based shape optimization problem of one 2D and one 3D model. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1477-1 Issue No:Vol. 61, No. 6 (2018)

Authors:Julian Kochmann; Stephan Wulfinghoff; Lisa Ehle; Joachim Mayer; Bob Svendsen; Stefanie Reese Pages: 751 - 764 Abstract: Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871–883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89–110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton–Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1476-2 Issue No:Vol. 61, No. 6 (2018)

Authors:Shih-Po Lin; Jiun-Shyan Chen; Shixue Liang Pages: 765 - 765 Abstract: After publication of the original article [1], it has come to our attention that a citation of article [2] was missed. PubDate: 2018-06-01 DOI: 10.1007/s00466-017-1526-9 Issue No:Vol. 61, No. 6 (2018)

Authors:J.-M. Mencik Pages: 767 - 767 Abstract: In the original published article, Eqs. (40) and (41) are incorrect. PubDate: 2018-06-01 DOI: 10.1007/s00466-018-1566-9 Issue No:Vol. 61, No. 6 (2018)

Authors:C. A. Kantzos; R. W. Cunningham; V. Tari; A. D. Rollett Pages: 575 - 580 Abstract: Characterizing complex surface topologies is necessary to understand stress concentrations created by rough surfaces, particularly those made via laser power-bed additive manufacturing (AM). Synchrotron-based X-ray microtomography ( \(\upmu \hbox {XCT}\) ) of AM surfaces was shown to provide high resolution detail of surface features and near-surface porosity. Using the CT reconstructions to instantiate a micromechanical model indicated that surface notches and near-surface porosity both act as stress concentrators, while adhered powder carried little to no load. Differences in powder size distribution had no direct effect on the relevant surface features, nor on stress concentrations. Conventional measurements of surface roughness, which are highly influenced by adhered powder, are therefore unlikely to contain the information relevant to damage accumulation and crack initiation. PubDate: 2018-05-01 DOI: 10.1007/s00466-017-1531-z Issue No:Vol. 61, No. 5 (2018)

Authors:Tore A. Helgedagsrud; Yuri Bazilevs; Kjell M. Mathisen; Ole A. Øiseth Abstract: A modified rigid-object formulation is developed, and employed as part of the fluid–object interaction modeling framework from Akkerman et al. (J Appl Mech 79(1):010905, 2012. https://doi.org/10.1115/1.4005072) to simulate free vibration and flutter of long-span bridges subjected to strong winds. To validate the numerical methodology, companion wind tunnel experiments have been conducted. The results show that the computational framework captures very precisely the aeroelastic behavior in terms of aerodynamic stiffness, damping and flutter characteristics. Considering its relative simplicity and accuracy, we conclude from our study that the proposed free-vibration simulation technique is a valuable tool in engineering design of long-span bridges. PubDate: 2018-06-04 DOI: 10.1007/s00466-018-1587-4

Authors:Xinzeng Feng; David A. Hormuth; Thomas E. Yankeelov Abstract: We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0. PubDate: 2018-06-02 DOI: 10.1007/s00466-018-1589-2

Authors:Heng Peng; Yinghua Liu; Haofeng Chen Abstract: In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm. PubDate: 2018-05-15 DOI: 10.1007/s00466-018-1581-x

Authors:H. R. Atri; S. Shojaee Abstract: In this paper truncated hierarchical B-spline (THB-spline) is coupled with reproducing kernel particle method (RKPM) to blend advantages of the isogeometric analysis and meshfree methods. Since under certain conditions, the isogeometric B-spline and NURBS basis functions are exactly represented by reproducing kernel meshfree shape functions, recursive process of producing isogeometric bases can be omitted. More importantly, a seamless link between meshfree methods and isogeometric analysis can be easily defined which provide an authentic meshfree approach to refine the model locally in isogeometric analysis. This procedure can be accomplished using truncated hierarchical B-splines to construct new bases and adaptively refine them. It is also shown that the THB–RKPM method can provide efficient approximation schemes for numerical simulations and represent a promising performance in adaptive refinement of partial differential equations via isogeometric analysis. The proposed approach for adaptive locally refinement is presented in detail and its effectiveness is investigated through well-known benchmark examples. PubDate: 2018-05-11 DOI: 10.1007/s00466-018-1580-y

Authors:Alexander Paolini; Stefan Kollmannsberger; Ernst Rank; Thomas Horger; Barbara Wohlmuth Abstract: In order to reduce the transfer of sound and vibrations in structures such as timber buildings, thin elastomer layers can be embedded between their components. The influence of these elastomers on the response of the structures in the low frequency range can be determined accurately by using conforming hexahedral finite elements. Three-dimensional mesh generation, however, is yet a non-trivial task and mesh refinements which may be necessary at the junctions can cause a high computational effort. One remedy is to mesh the components independently from each other and to couple them using the mortar method. Further, the hexahedral mesh for the thin elastomer layer itself can be avoided by integrating its elastic behavior into the mortar formulation. The present paper extends this mortar formulation to take damping into account such that frequency response analyses can be performed more accurately. Finally, the proposed method is verified by numerical examples. PubDate: 2018-05-11 DOI: 10.1007/s00466-018-1582-9

Authors:D. Beli; J.-M. Mencik; P. B. Silva; J. R. F. Arruda Abstract: The wave finite element method has proved to be an efficient and accurate numerical tool to perform the free and forced vibration analysis of linear reciprocal periodic structures, i.e. those conforming to symmetrical wave fields. In this paper, its use is extended to the analysis of rotating periodic structures, which, due to the gyroscopic effect, exhibit asymmetric wave propagation. A projection-based strategy which uses reduced symplectic wave basis is employed, which provides a well-conditioned eigenproblem for computing waves in rotating periodic structures. The proposed formulation is applied to the free and forced response analysis of homogeneous, multi-layered and phononic ring structures. In all test cases, the following features are highlighted: well-conditioned dispersion diagrams, good accuracy, and low computational time. The proposed strategy is particularly convenient in the simulation of rotating structures when parametric analysis for several rotational speeds is usually required, e.g. for calculating Campbell diagrams. This provides an efficient and flexible framework for the analysis of rotordynamic problems. PubDate: 2018-05-07 DOI: 10.1007/s00466-018-1576-7

Authors:Raphael Araújo Cardoso; David Néron; Sylvie Pommier; José Alexander Araújo Abstract: The aim of this work is to improve the performance of fretting simulations making use of an enrichment approach. The idea is to take advantage of the fact that the mechanical fields around the contact edges in cylindrical contact configurations under fretting conditions are similar to the ones found close to the crack tip in linear elastic fracture mechanics problems. This similarity makes attractive the idea of enriching finite element fretting simulations through the X-FEM framework, which enables us to work with coarser meshes while keeping a good accuracy. As it will be shown in this work, it is possible to work with meshes up to 10 times coarser than it should be if a conventional FE method was used allowing a strong improvement of the computational performances. PubDate: 2018-05-02 DOI: 10.1007/s00466-018-1577-6

Authors:Hachmi Ben Dhia; Shuimiao Du Abstract: The surface micro-interaction model of Lennard-Jones (LJ) is used for adhesive contact problems (ACP). To address theoretical and numerical pitfalls of this model, a sequence of partitions of contact models is adaptively constructed to both extend and approximate the LJ model. It is formed by a combination of the LJ model with a sequence of shifted-Signorini (or, alternatively, -Linearized-LJ) models, indexed by a shift parameter field. For each model of this sequence, a weak formulation of the associated local ACP is developed. To track critical localized adhesive areas, a two-step strategy is developed: firstly, a macroscopic frictionless (as first approach) linear-elastic contact problem is solved once to detect contact separation zones. Secondly, at each shift-adaptive iteration, a micro-macro ACP is re-formulated and solved within the multiscale Arlequin framework, with significant reduction of computational costs. Comparison of our results with available analytical and numerical solutions shows the effectiveness of our global strategy. PubDate: 2018-05-02 DOI: 10.1007/s00466-018-1578-5

Authors:Jonathan Köbler; Matti Schneider; Felix Ospald; Heiko Andrä; Ralf Müller Abstract: For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in \({\mathbb {R}}^2\) . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery’s collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®. PubDate: 2018-04-13 DOI: 10.1007/s00466-017-1478-0