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

Authors:Andreas Naumann; Daniel Ruprecht; Joerg Wensch Abstract: Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FE models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit–explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand. PubDate: 2018-01-10 DOI: 10.1007/s00466-018-1540-6

Authors:Alberto Sibileau; Ferdinando Auricchio; Simone Morganti; Pedro Díez Abstract: Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical properties. One may obtain specific macro-scale (or bulk) properties in the resulting architectured material by properly designing the unit-cell. Typically, this is stated as an optimal design problem in which the parameters describing the shape and mechanical properties of the unit-cell are selected in order to produce the desired bulk characteristics. This is especially pertinent due to the ease manufacturing of these complex structures with 3D printers. The proper generalized decomposition provides explicit parametic solutions of parametric PDEs. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen. PubDate: 2018-01-10 DOI: 10.1007/s00466-017-1534-9

Authors:José Manuel Navarro-Jiménez; Manuel Tur; José Albelda; Juan José Ródenas Abstract: This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method. PubDate: 2018-01-03 DOI: 10.1007/s00466-017-1533-x

Authors:C. A. Kantzos; R. W. Cunningham; V. Tari; A. D. Rollett 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: 2017-12-29 DOI: 10.1007/s00466-017-1531-z

Authors:Fadi Aldakheel; Peter Wriggers; Christian Miehe Abstract: The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2–15, 1977). Within a top–down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic–plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486–522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic–plastic solids under finite strain deformation. It combines modified structures of Gurson–Tvergaard–Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157–169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1–17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit–Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup–cone failure mechanism. PubDate: 2017-12-28 DOI: 10.1007/s00466-017-1530-0

Authors:John T. Klein; Eduard G. Karpov Abstract: Negative extensibility metamaterials are able to contract against the line of increasing external tension. A bistable unit cell exhibits several nonlinear mechanical behaviors including the negative extensibility response. Here, an exact form of the total mechanical potential is used based on engineering strain measure. The mechanical response is a function of the system parameters that specify unit cell dimensions and member stiffnesses. A phase diagram is calculated, which maps the response to regions in the diagram using the system parameters as the coordinate axes. Boundary lines pinpoint the onset of a particular mechanical response. Contour lines allow various material properties to be fine-tuned. Analogous to thermodynamic phase diagrams, there exist singular “triple points” which simultaneously satisfy conditions for three response types. The discussion ends with a brief statement about how thermodynamic phase diagrams differ from the phase diagram in this paper. PubDate: 2017-12-27 DOI: 10.1007/s00466-017-1520-2