Authors:Bo Mi Lee; Kenneth J. Loh; Yuan-Sen Yang Pages: 39 - 49 Abstract: Abstract Nanomaterial-based thin films, particularly those based on carbon nanotubes (CNT), have brought forth tremendous opportunities for designing next-generation strain sensors. However, their strain sensing properties can vary depending on fabrication method, post-processing treatment, and types of CNTs and polymers employed. The objective of this study was to derive a CNT-based thin film strain sensor model using inputs from nano-/micro-scale experimental measurements of nanotube physical properties. This study began with fabricating ultra-low-concentration CNT-polymer thin films, followed by imaging them using atomic force microscopy. Image processing was employed for characterizing CNT dispersed shapes, lengths, and other physical attributes, and results were used for building five different types of thin film percolation-based models. Numerical simulations were conducted to assess how the morphology of dispersed CNTs in its 2D matrix affected bulk film electrical and electromechanical (strain sensing) properties. The simulation results showed that CNT morphology had a significant impact on strain sensing performance. PubDate: 2017-07-01 DOI: 10.1007/s00466-017-1391-6 Issue No:Vol. 60, No. 1 (2017)

Authors:Y. Bazilevs; K. Kamran; G. Moutsanidis; D. J. Benson; E. Oñate Pages: 83 - 100 Abstract: Abstract In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a Meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework. PubDate: 2017-07-01 DOI: 10.1007/s00466-017-1394-3 Issue No:Vol. 60, No. 1 (2017)

Authors:Tong Shen; Franck Vernerey Pages: 143 - 161 Abstract: Abstract When immersed in solution, surface-active particles interact with solute molecules and migrate along gradients of solute concentration. Depending on the conditions, this phenomenon could arise from either diffusiophoresis or the Marangoni effect, both of which involve strong interactions between the fluid and the particle surface. We introduce here a numerical approach that can accurately capture these interactions, and thus provide an efficient tool to understand and characterize the phoresis of soft particles. The model is based on a combination of the extended finite element—that enable the consideration of various discontinuities across the particle surface—and the particle-based moving interface method—that is used to measure and update the interface deformation in time. In addition to validating the approach with analytical solutions, the model is used to study the motion of deformable vesicles in solutions with spatial variations in both solute concentration and temperature. PubDate: 2017-07-01 DOI: 10.1007/s00466-017-1399-y Issue No:Vol. 60, No. 1 (2017)

Authors:M. A. Celigueta; S. Latorre; F. Arrufat; E. Oñate Abstract: 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: 2017-08-01 DOI: 10.1007/s00466-017-1453-9

Authors:Daniel Giraldo; Doriam Restrepo Abstract: 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: 2017-08-01 DOI: 10.1007/s00466-017-1454-8

Authors:Eric Li; Z. C. He; G. Wang; G. R. Liu Abstract: 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: 2017-07-31 DOI: 10.1007/s00466-017-1451-y

Authors:Zhen Hu; Sankaran Mahadevan; Dan Ao Abstract: Abstract An uncertainty aggregation and reduction framework is presented for structure–material performance prediction. Different types of uncertainty sources, structural analysis model, and material performance prediction model are connected through a Bayesian network for systematic uncertainty aggregation analysis. To reduce the uncertainty in the computational structure–material performance prediction model, Bayesian updating using experimental observation data is investigated based on the Bayesian network. It is observed that the Bayesian updating results will have large error if the model cannot accurately represent the actual physics, and that this error will be propagated to the predicted performance distribution. To address this issue, this paper proposes a novel uncertainty reduction method by integrating Bayesian calibration with model validation adaptively. The observation domain of the quantity of interest is first discretized into multiple segments. An adaptive algorithm is then developed to perform model validation and Bayesian updating over these observation segments sequentially. Only information from observation segments where the model prediction is highly reliable is used for Bayesian updating; this is found to increase the effectiveness and efficiency of uncertainty reduction. A composite rotorcraft hub component fatigue life prediction model, which combines a finite element structural analysis model and a material damage model, is used to demonstrate the proposed method. PubDate: 2017-07-28 DOI: 10.1007/s00466-017-1448-6

Authors:Mohammad Rezaul Karim; Micheal Kattoura; Seetha R. Mannava; Vijay K. Vasudevan; Arif S. Malik; Dong Qian Abstract: Abstract A multiscale simulation method is established to study the microstructural responses of near-surface grain boundary structures of copper subjected to ultrashort femtosecond laser pulse. By integrating a two-temperature model with molecular dynamics, the presented approach allows for incorporation of both laser processing parameters and microstructures, enabling systematic simulation studies on the process-properties link. Following a brief introduction of the simulation methodology, a detailed modeling study on the ultrashort laser-material interaction is presented. In particular, we highlight the effects of laser process parameters on the near-surface response and corresponding phase change, formation of voids and their growth, and mechanism of dislocation nucleating and propagating from grain boundary. PubDate: 2017-07-28 DOI: 10.1007/s00466-017-1449-5

Authors:Sylvain Mercier; Serge Gratton; Nicolas Tardieu; Xavier Vasseur Abstract: 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: 2017-07-28 DOI: 10.1007/s00466-017-1450-z

Authors:E. T. Ooi; C. Song; S. Natarajan Abstract: 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: 2017-07-24 DOI: 10.1007/s00466-017-1443-y

Authors:Hannes Erdle; Thomas Böhlke Abstract: 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: 2017-07-21 DOI: 10.1007/s00466-017-1447-7

Authors:Ferdinando Auricchio; Giulia Scalet; Peter Wriggers Abstract: 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: 2017-07-20 DOI: 10.1007/s00466-017-1437-9

Authors:Simeon Hubrich; Paolo Di Stolfo; László Kudela; Stefan Kollmannsberger; Ernst Rank; Andreas Schröder; Alexander Düster Abstract: Abstract A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy. PubDate: 2017-07-18 DOI: 10.1007/s00466-017-1441-0

Authors:Lucio de Abreu Corrêa; Juan Carlos Quezada; Régis Cottereau; Sofia Costa d’Aguiar; Charles Voivret Abstract: Abstract This paper proposes a description of a granular medium as a stochastic heterogeneous continuum medium. The heterogeneity of the material properties field recreates the heterogeneous stress field in a granular medium. The stochastic approach means that only statistical information, easily available, is required to construct the model. The heterogeneous continuum model is Calibrated with respect to discrete simulations of a set of railway ballast samples. As they are continuum-based, the equilibrium equations can be solved on a large scale using a parallel implementation of an explicit time discretization scheme for the Finite Element Method. Simulations representative of the influence on the environment of the passage of a train on a ballasted railway track clearly show the influence of the heterogeneity. These simulations seem to correlate well with previously unexplained overly damped measurements in the free field. PubDate: 2017-07-15 DOI: 10.1007/s00466-017-1446-8

Authors:Thiago Milanetto Schlittler; Régis Cottereau Abstract: Abstract We present in this paper a new implementation of a multi-scale, multi-model coupling algorithm, with a proposed parallelization scheme for the construction of the coupling terms between the models. This allows one to study such problems with a fully scalable algorithm on large computer clusters, even when the models and/or the coupling have a high number of degrees of freedom. As an application example, we will consider a system composed by an homogeneous, macroscopic Elastic model and an anisotropic polycrystalline material model, with a volume coupling based on the Arlequin framework. PubDate: 2017-07-14 DOI: 10.1007/s00466-017-1445-9

Authors:Paul Oumaziz; Pierre Gosselet; Pierre-Alain Boucard; Stéphane Guinard Abstract: Abstract A non-invasive implementation of the Latin domain decomposition method for frictional contact problems is described. The formulation implies to deal with mixed (Robin) conditions on the faces of the subdomains, which is not a classical feature of commercial software. Therefore we propose a new implementation of the linear stage of the Latin method with a non-local search direction built as the stiffness of a layer of elements on the interfaces. This choice enables us to implement the method within the open source software Code_Aster, and to derive 2D and 3D examples with similar performance as the standard Latin method. PubDate: 2017-07-13 DOI: 10.1007/s00466-017-1444-x

Authors:Ruben Ibañez; Domenico Borzacchiello; Jose Vicente Aguado; Emmanuelle Abisset-Chavanne; Elias Cueto; Pierre Ladeveze; Francisco Chinesta Abstract: Abstract The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, \(\ldots \) ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work. PubDate: 2017-07-13 DOI: 10.1007/s00466-017-1440-1

Authors:M. Cervera; G. B. Barbat; M. Chiumenti Abstract: Abstract This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force–displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson’s ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem. PubDate: 2017-07-10 DOI: 10.1007/s00466-017-1438-8

Authors:Rolf Berthelsen; Ralf Denzer; Philip Oppermann; Andreas Menzel Abstract: Abstract Metal forming processes require wear-resistant tool surfaces in order to ensure a long life cycle of the expensive tools together with a constant high quality of the produced components. Thermal spraying is a relatively widely applied coating technique for the deposit of wear protection coatings. During these coating processes, heterogeneous coatings are deployed at high temperatures followed by quenching where residual stresses occur which strongly influence the performance of the coated tools. The objective of this article is to discuss and apply a thermo-mechanically coupled simulation framework which captures the heterogeneity of the deposited coating material. Therefore, a two-scale finite element framework for the solution of nonlinear thermo-mechanically coupled problems is elaborated and applied to the simulation of thermoviscoplastic material behaviour including nonlinear thermal softening in a geometrically linearised setting. The finite element framework and material model is demonstrated by means of numerical examples. PubDate: 2017-07-08 DOI: 10.1007/s00466-017-1436-x

Authors:Sahir N. Butt; Jithender J. Timothy; Günther Meschke Abstract: Abstract Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone. PubDate: 2017-07-06 DOI: 10.1007/s00466-017-1439-7