Authors:Shih-Po Lin; Jiun-Shyan Chen; Shixue Liang Abstract: After publication of the original article [1], it has come to our attention that a citation of article [2] was missed. PubDate: 2018-02-26 DOI: 10.1007/s00466-017-1526-9

Authors:A. R. Khoei; B. Bahmani Abstract: In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton–Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature. PubDate: 2018-02-20 DOI: 10.1007/s00466-018-1555-z

Authors:Konstantinos Agathos; Eleni Chatzi; Stéphane P. A. Bordas Abstract: A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity. PubDate: 2018-02-19 DOI: 10.1007/s00466-017-1532-y

Authors:Kai Ke Yang; Ji Hong Zhu; Chuang Wang; Dong Sheng Jia; Long Long Song; Wei Hong Zhang Abstract: The purpose of this paper is to investigate the structures achieved by topology optimization and their fabrications by 3D printing considering the particular features of material microstructures and macro mechanical performances. Combining Digital Image Correlation and Optical Microscope, this paper experimentally explored the anisotropies of stiffness and strength existing in the 3D printed polymer material using Stereolithography (SLA) and titanium material using Selective Laser Melting (SLM). The standard specimens and typical structures obtained by topology optimization were fabricated along different building directions. On the one hand, the experimental results of these SLA produced structures showed stable properties and obviously anisotropic rules in stiffness, ultimate strengths and places of fractures. Further structural designs were performed using topology optimization when the particular mechanical behaviors of SLA printed materials were considered, which resulted in better structural performances compared to the optimized designs using ‘ideal’ isotropic material model. On the other hand, this paper tested the mechanical behaviors of SLM printed multiscale lattice structures which were fabricated using the same metal powder and the same machine. The structural stiffness values are generally similar while the strength behaviors show a difference, which are mainly due to the irregular surface quality of the tiny structural branches of the lattice. The above evidences clearly show that the consideration of the particular behaviors of 3D printed materials is therefore indispensable for structural design and optimization in order to improve the structural performance and strengthen their practical significance. PubDate: 2018-02-14 DOI: 10.1007/s00466-018-1537-1

Authors:Z. H. Teng; F. Sun; S. C. Wu; Z. B. Zhang; T. Chen; D. M. Liao Abstract: By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications. PubDate: 2018-02-10 DOI: 10.1007/s00466-018-1553-1

Authors:Xia Yan; Zhaoqin Huang; Jun Yao; Yang Li; Dongyan Fan; Kai Zhang Abstract: In this paper, a numerical model is developed for coupled analysis of deforming fractured porous media with multiscale fractures. In this model, the macro-fractures are modeled explicitly by the embedded discrete fracture model, and the supporting effects of fluid and fillings in these fractures are represented explicitly in the geomechanics model. On the other hand, matrix and micro-fractures are modeled by a multi-porosity model, which aims to accurately describe the transient matrix–fracture fluid exchange process. A stabilized extended finite element method scheme is developed based on the polynomial pressure projection technique to address the displacement oscillation along macro-fracture boundaries. After that, the mixed space discretization and modified fixed stress sequential implicit methods based on non-matching grids are applied to solve the coupling model. Finally, we demonstrate the accuracy and application of the proposed method to capture the coupled hydro-mechanical impacts of multiscale fractures on fractured porous media. PubDate: 2018-02-07 DOI: 10.1007/s00466-018-1541-5

Authors:Yung C. Shin; Neil Bailey; Christopher Katinas; Wenda Tan Abstract: This paper presents an overview of vertically integrated comprehensive predictive modeling capabilities for directed energy deposition processes, which have been developed at Purdue University. The overall predictive models consist of vertically integrated several modules, including powder flow model, molten pool model, microstructure prediction model and residual stress model, which can be used for predicting mechanical properties of additively manufactured parts by directed energy deposition processes with blown powder as well as other additive manufacturing processes. Critical governing equations of each model and how various modules are connected are illustrated. Various illustrative results along with corresponding experimental validation results are presented to illustrate the capabilities and fidelity of the models. The good correlations with experimental results prove the integrated models can be used to design the metal additive manufacturing processes and predict the resultant microstructure and mechanical properties. PubDate: 2018-01-30 DOI: 10.1007/s00466-018-1545-1

Authors:Ziyu Zhang; Wen Jiang; John E. Dolbow; Benjamin W. Spencer Abstract: We present a strategy for the numerical integration of partial elements with the eXtended finite element method (X-FEM). The new strategy is specifically designed for problems with propagating cracks through a bulk material that exhibits inelasticity. Following a standard approach with the X-FEM, as the crack propagates new partial elements are created. We examine quadrature rules that have sufficient accuracy to calculate stiffness matrices regardless of the orientation of the crack with respect to the element. This permits the number of integration points within elements to remain constant as a crack propagates, and for state data to be easily transferred between successive discretizations. In order to maintain weights that are strictly positive, we propose an approach that blends moment-fitted weights with volume-fraction based weights. To demonstrate the efficacy of this simple approach, we present results from numerical tests and examples with both elastic and plastic material response. PubDate: 2018-01-29 DOI: 10.1007/s00466-018-1544-2

Authors:Ling Li; Luming Shen; Giang D. Nguyen; Abbas El-Zein; Federico Maggi Abstract: A smoothed particle hydrodynamics (SPH) framework is developed for modelling multiphase interactions at meso-scale, including the liquid–solid interaction induced deformation of the solid phase. With an inter-particle force formulation that mimics the inter-atomic force in molecular dynamics, the proposed framework includes the long-range attractions between particles, and more importantly, the short-range repulsive forces to avoid particle clustering and instability problems. Three-dimensional numerical studies have been conducted to demonstrate the capabilities of the proposed framework to quantitatively replicate the surface tension of water, to model the interactions between immiscible liquids and solid, and more importantly, to simultaneously model the deformation of solid and liquid induced by the multiphase interaction. By varying inter-particle potential magnitude, the proposed SPH framework has successfully simulated various wetting properties ranging from hydrophobic to hydrophilic surfaces. The simulation results demonstrate the potential of the proposed framework to genuinely study complex multiphase interactions in wet granular media. PubDate: 2018-01-27 DOI: 10.1007/s00466-018-1551-3

Authors:Alexander Schlüter; Charlotte Kuhn; Ralf Müller Abstract: In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61–69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated. PubDate: 2018-01-24 DOI: 10.1007/s00466-018-1550-4

Authors:R. Kruse; N. Nguyen-Thanh; P. Wriggers; L. De Lorenzis Abstract: This paper presents an isogeometric formulation for frictionless contact between deformable bodies, based on the recently proposed concept of the third medium. This concept relies on continuum formulations not only for the contacting bodies but also for a fictitious intermediate medium in which the bodies can move and interact. Key to the formulation is a suitable definition of the constitutive behavior of the third medium. In this work, based on a number of numerical tests, the role of the material parameters of the third medium is systematically assessed. We also assess the rate of spatial convergence for higher-order discretizations, stemming from the regularization of the non-smooth contact problem inherent to the third medium approach. Finally, problems with self contact are considered and turn out to be an attractive application of the method. PubDate: 2018-01-23 DOI: 10.1007/s00466-018-1547-z

Authors:Tao He; Hexin Zhang; Kai Zhang Abstract: In this paper the cell-based smoothed finite element method (CS-FEM) is introduced into two mainstream aspects of computational fluid dynamics: incompressible flows and fluid–structure interaction (FSI). The emphasis is placed on the fluid gradient smoothing which simply requires equal numbers of Gaussian points and smoothing cells in each four-node quadrilateral element. The second-order, smoothed characteristic-based split scheme in conjunction with a pressure stabilization is then presented to settle the incompressible Navier–Stokes equations. As for FSI, CS-FEM is applied to the geometrically nonlinear solid as usual. Following an efficient mesh deformation strategy, block-Gauss–Seidel procedure is adopted to couple all individual fields under the arbitrary Lagriangian–Eulerian description. The proposed solvers are carefully validated against the previously published data for several benchmarks, revealing visible improvements in computed results. PubDate: 2018-01-23 DOI: 10.1007/s00466-018-1549-x

Authors:Z. C. He; J. Y. Hu; Eric Li Abstract: Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully. PubDate: 2018-01-22 DOI: 10.1007/s00466-018-1548-y

Authors:Mickaël Abbas; Alexandre Ern; Nicolas Pignet Abstract: We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order \(k\ge 1\) on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime. PubDate: 2018-01-20 DOI: 10.1007/s00466-018-1538-0

Authors:Junpu Li; Wen Chen; Zhuojia Fu Abstract: A modified dual-level algorithm is proposed in the article. By the help of the dual level structure, the fully-populated interpolation matrix on the fine level is transformed to a local supported sparse matrix to solve the highly ill-conditioning and excessive storage requirement resulting from fully-populated interpolation matrix. The kernel-independent fast multipole method is adopted to expediting the solving process of the linear equations on the coarse level. Numerical experiments up to 2-million fine-level nodes have successfully been achieved. It is noted that the proposed algorithm merely needs to place 2–3 coarse-level nodes in each wavelength per direction to obtain the reasonable solution, which almost down to the minimum requirement allowed by the Shannon’s sampling theorem. In the real human head model example, it is observed that the proposed algorithm can simulate well computationally very challenging exterior high-frequency harmonic acoustic wave propagation up to 20,000 Hz. PubDate: 2018-01-16 DOI: 10.1007/s00466-018-1536-2

Authors:Yanping Lian; Stephen Lin; Wentao Yan; Wing Kam Liu; Gregory J. Wagner Abstract: In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments. PubDate: 2018-01-12 DOI: 10.1007/s00466-017-1535-8

Authors:Mengqi Zhang; Ning Zhao; Zhanjiang Wang; Qian Wang Abstract: Semi-analytical models have been developed to analyze the contact of inhomogeneous materials based on the equivalent inclusion method. It is important to pursue a higher efficiency in numerical implementation of the semi-analytical models. This paper reports the development of a dual-grid computational scheme for further improving the efficiency of the current semi-analytical modeling. Parametric studies show that the new method can save at least 50% of the execution time with respect to the original algorithm in a considerably wide range of conditions. The new method is applied to investigate the influence of inhomogeneities on contact pressure distributions. Data regression is performed to obtain the amplitudes of contact pressure disturbances as a function of inhomogeneitys elastic modulus, size and location. Then, a criterion is developed based on the values of contact pressure disturbances to determine the circumstances in which the coupling between inhomogeneities and surface contact be ignored. PubDate: 2018-01-12 DOI: 10.1007/s00466-018-1543-3

Authors:Wentao Yan; Stephen Lin; Orion L. Kafka; Yanping Lian; Cheng Yu; Zeliang Liu; Jinhui Yan; Sarah Wolff; Hao Wu; Ebot Ndip-Agbor; Mojtaba Mozaffar; Kornel Ehmann; Jian Cao; Gregory J. Wagner; Wing Kam Liu Abstract: Additive manufacturing (AM) possesses appealing potential for manipulating material compositions, structures and properties in end-use products with arbitrary shapes without the need for specialized tooling. Since the physical process is difficult to experimentally measure, numerical modeling is a powerful tool to understand the underlying physical mechanisms. This paper presents our latest work in this regard based on comprehensive material modeling of process–structure–property relationships for AM materials. The numerous influencing factors that emerge from the AM process motivate the need for novel rapid design and optimization approaches. For this, we propose data-mining as an effective solution. Such methods—used in the process–structure, structure–properties and the design phase that connects them—would allow for a design loop for AM processing and materials. We hope this article will provide a road map to enable AM fundamental understanding for the monitoring and advanced diagnostics of AM processing. PubDate: 2018-01-12 DOI: 10.1007/s00466-018-1539-z

Authors:Xiaoyang Xu; Peng Yu Abstract: When smoothed particle hydrodynamics (SPH) is directly applied for the numerical simulations of transient viscoelastic free surface flows, a numerical problem called tensile instability arises. In this paper, we develop an optimized particle shifting technique to remove the tensile instability in SPH. The basic equations governing free surface flow of an Oldroyd-B fluid are considered, and approximated by an improved SPH scheme. This includes the implementations of the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation. To verify the effectiveness of the optimized particle shifting technique in removing the tensile instability, the impacting drop, the injection molding of a C-shaped cavity, and the extrudate swell, are conducted. The numerical results obtained are compared with those simulated by other numerical methods. A comparison among different numerical techniques (e.g., the artificial stress) to remove the tensile instability is further performed. All numerical results agree well with the available data. PubDate: 2018-01-12 DOI: 10.1007/s00466-018-1542-4