Abstract: A coupling peridynamic approach is developed for the consolidation and dynamic analyses of saturated porous media. In this method, the coupling state-based peridynamic equations of solid skeleton and pore fluid are derived based on the u–p form governing equations. Then, the corresponding implicit incremental formulations are obtained according to the linearization method on the basis of the first-order Taylor’s expansion technique and the Newton–Raphson method. There are two advantages of the present implicit algorithm comparing with the explicit one. First, the former can handily deal well with various boundary conditions without setting up additional boundary layers. Next, the former is more reasonable and efficient to solve the consolidation problems whereas it often needs very small time step for the explicit peridynamic method combining with an additional damping under a quasi-static loading. Finally, both the consolidation and dynamic examples are given out and the results certify the validity and accuracy of the developed method by comparing it with the finite element method. PubDate: 2019-03-20

Abstract: This paper proposes a new efficient stochastically adapted spectral finite element method to simulate fault dislocation and its wave propagation consequences. For this purpose, a dynamic form of the split node technique is formulated and developed to stochastic spectral finite element method in order to model fault dislocation happening within a random media without increasing computational demand caused by discontinuities. As discontinuities are not modeled explicitly herein, no additional degrees of freedom are implemented in the proposed method due to the discontinuities, while effects of these discontinuities are preserved. Therefore, the present method simultaneously includes merits of stochastic finite element method, spectral finite element method and the spilt node technique, thereby providing a new numerical tool for analysis of wave propagation under fault dislocation in random media. Several numerical simulations are solved by the proposed method, which present stochastic analysis of fault slip-induced wave propagation in layered random media. Formulations and numerical results demonstrate capability, application and efficiency of this novel method. PubDate: 2019-03-16

Abstract: Computational homogenization techniques nowadays are extensively used to gain a better understanding of the links between complex microstructural features in materials and their corresponding (evolving) macroscopic properties. This requires robust tools to discretize complex microstructural geometries and enable simulations. To achieve this, the present contribution presents an integrated approach for the conformal discretization of complex inclusion-based RVE geometries defined implicitly based on experimental techniques or through computational RVE generation methodologies. The conforming mesh generator extends the Persson–Strang truss analogy in order to deal with complex periodic heterogeneous RVEs. Such an approach, based on signed distance fields, carries the advantage that the level set information maintained in previously presented RVE generation methodologies (Sonon et al. in Comput Methods Appl Mech Eng 223:103–122, 2012. https://doi.org/10.1016/j.cma.2012.02.018) can seamlessly be used in the discretization procedure. This provides a natural link between the RVE geometry generation and the mesh generator to obtain high quality optimized FEM meshes exploitable in regular codes and softwares. PubDate: 2019-03-15

Abstract: This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order virtual element method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both homogeneous problems, in which the plane of isotropy is fixed; and non-homogeneous problems, in which the fibre direction defining the isotropy plane varies with position, are explored. In the latter case various options are considered for approximating the non-homogeneous fibre directions at an element level. Through a range of numerical examples the VEM approximations are shown to be robust and locking-free for several element geometries and for fibre directions that correspond to both mild and strong non-homogeneity. Further, the convergence rate of the VEM is shown to be comparable to classical low-order standard finite element approaches. PubDate: 2019-03-05

Abstract: Metal powder-based Additive Manufacturing (AM) processes are increasingly used in industry and science due to their unique capability of building complex geometries. However, the immense computational cost associated with AM predictive models hinders the further industrial adoption of these technologies for time-sensitive applications, process design with uncertainties or real-time process control. In this work, a novel approach to accelerate the explicit finite element analysis of the transient heat transfer of AM processes is proposed using Graphical Processing Units. The challenges associated with this approach are enumerated and multiple strategies to overcome each challenge are discussed. The performance of the proposed algorithms is evaluated on multiple test cases. Speed-ups of about 100 ×–150 × compared to an optimized single CPU core implementation for the best strategy were achieved. PubDate: 2019-03-01

Abstract: Shear transformation zone dynamics models of metallic glass deformation access experimentally-relevant time scales by using the kinetic Monte Carlo method to simulate small, fast, often discrete events, while the finite element method calculates macroscopic shape change and continuum-level interactions within samples. The most time-consuming portion of these models is the finite element method calculation on each step. However, in cases where the finite element mesh geometry and element elastic properties do not change from step to step, the finite element stiffness matrix (and its Cholesky factors) from previous steps can be reused. This strategy improves the asymptotic complexity of these models and in practice accelerates their execution by nearly 200 \(\times \) . This enables simulation of larger samples in more reasonable time. A set of three-dimensional shear transformation zone dynamics simulations, with larger length scales than any currently in the literature, illustrates the utility of this approach. PubDate: 2019-03-01

Abstract: One of the most employed strategies in finite element analysis of fluid–structure interaction (FSI) problems involves using an arbitrary Lagrangian–Eulerian (ALE) method for the fluid, requiring an additional step to the partitioned coupling algorithm: the dynamic mesh moving. Mesh moving techniques need to avoid excessive element distortion or inversion. In this work, we develop a partitioned FSI algorithm for large displacement shell structures-incompressible flow interaction analysis using the finite element method (FEM). The coupling is performed by a block Gauss–Seidel implicit approach and the fluid mesh is updated by a linear Laplacian smoothing. To save computing time and avoid element inversion during the mesh deformation procedure, we introduce a coarse higher-order auxiliary mesh, which is used only to capture the structural deformation and extend it to the fluid domain. The shell structure is modeled by a FEM formulation with nodal positions and components of an unconstrained vector as degrees of freedom, which avoids the need for dealing with large rotations approximations. We solve the fluid dynamics equations in the ALE description using an implicit time marching temporal integrator and stabilized mixed FEM spatial discretization. Finally, the accuracy and robustness of the proposed method are tested with numerical examples compared to the literature results. PubDate: 2019-03-01

Abstract: Regenerative medicine is one of the most promising future approaches for the treatment of damaged tissues and organs. Its methodologies are based on a good understanding and control of cellular behavior within in-vivo tissues, and this represents an important challenge. Cell behavior can be controlled, among other stimuli, by changing the mechanical properties of the extracellular matrix, applying external/internal forces, and/or reproducing an electric stimulus. To remotely control the local cell micro-environment, we consider in this work a microsphere of cell size made of a piezoelectric material and charged with nanomagnetic particles. This microsphere is integrated within an extracellular matrix, in such a way that internal forces can be generated within the microsphere by means of an external magnetic field. As a result, a stiffness gradient and an electric field are generated around the microsphere. These stimuli can be controlled externally by changing the magnetic field intensity and direction. To fine-tune this process and achieve the desired cell numbers, a computational numerical simulation has been developed and employed for several cell phenotypes using the ABAQUS software with the user-define subroutine UEL. The 3D numerical model presented can successfully predict the fundamental aspects of cell maturation, differentiation, proliferation, and apoptosis within a nonlinear substrate. The results obtained, which are in agreement with previous experimental and computational works, show that the generated stiffness gradient as well as the electric field within the cell micro-environment can play a highly significant role in remotely controlling the lineage specification of the Mesenchymal Stem Cells and accelerating cell migration and proliferation, which opens the door to new methodologies of tissue regeneration. PubDate: 2019-03-01

Abstract: In this work, we propose a new decomposed subspace reduction (DSR) method for reduced-order modeling of fracture mechanics based on the integrated singular basis function method (ISBFM) with reproducing kernel approximation enriched by crack-tip basis functions. It is shown that the standard MOR approach based on modal analysis (ISBFM-MA) with a direct employment of the crack-tip enrichment functions yields an inappropriate scaling effect to the stiffness matrix, and results in the loss of essential crack features and the erroneous representation of inhomogeneous Dirichlet boundary conditions in the reduced subspace. On the other hand, the solution of ISBFM-DSR is not affected by the arbitrary scaling of the enrichment functions, and it properly captures the singularity and discontinuity properties of fracture problems in its low-dimensional reduced-order approximation. It is also shown that the inhomogeneous boundary conditions can be accurately represented in the ISBFM-DSR solution. Validations are given in the numerical examples. PubDate: 2019-03-01

Abstract: This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the multi-dimensional uncertainty problem. However, we significantly decrease its huge computational burden whilst keeping its universality and accuracy at the same time. This is accomplished by coupling POD with MCS in the IGA stochastic analysis. Namely, we reduce the full order system whose DOFs is N to a much smaller DOF s. Several examples validate that the proposed scheme is general, effective and efficient; and the larger the scale and/or the number of the samples of the problem, the more advantageous the method will inherit. PubDate: 2019-03-01

Abstract: Quasi-incompressible behavior is a desired feature in several constitutive models within the finite elasticity of solids, such as rubber-like materials and some fiber-reinforced soft biological tissues. The Q1P0 finite element formulation, derived from the three-field Hu–Washizu variational principle, has hitherto been exploited along with the augmented Lagrangian method to enforce incompressibility. This formulation typically uses the unimodular deformation gradient. However, contributions by Sansour (Eur J Mech A Solids 27:28–39, 2007) and Helfenstein et al. (Int J Solids Struct 47:2056–2061, 2010) conspicuously demonstrate an alternative concept for analyzing fiber reinforced solids, namely the use of the (unsplit) deformation gradient for the anisotropic contribution, and these authors elaborate on their proposals with analytical evidence. The present study handles the alternative concept from a purely numerical point of view, and addresses systematic comparisons with respect to the classical treatment of the Q1P0 element and its coalescence with the augmented Lagrangian method by means of representative numerical examples. The results corroborate the new concept, show its numerical efficiency and reveal a direct physical interpretation of the fiber stretches. PubDate: 2019-03-01

Abstract: This study proposes a scale-dependent finite difference method (S-FDM) to approximate the time fractional differential equations (FDEs), using Hausdroff metric to conveniently link the order of the time fractional derivative (α) and the non-uniform time intervals. The S-FDM is unconditional stable and exhibits a convergence rate on the order of 2-α. Numerical tests show that the S-FDM is superior to the standard methods with either uniform or non-uniform time steps in computing time or cost, accuracy, and convergence rate, especially for a large time range. Hence, although many numerical schemes have been developed in the last decades for various FDEs, the unique S-FDM proposed in this study fits the requirement of calculating anomalous transport in natural systems involving a large spatiotemporal scale, which might be the future direction to extend the application of FDEs especially in Earth sciences, the ideal testbed for FDEs. PubDate: 2019-03-01

Abstract: New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. These results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations. PubDate: 2019-03-01

Abstract: A novel wavelet multiresolution interpolation formula is developed for approximating continuous functions defined on an arbitrary two-dimensional domain represented by a set of scattered nodes. The present wavelet interpolant is created explicitly without the need for matrix inversion. It possesses the Kronecker delta function property and does not contain any ad-hoc parameters, leading to an excellent stability and usefulness for function approximation. Using the wavelet multiresolution interpolant to construct trial and weight functions, a wavelet multiresolution interpolation Galerkin method (WMIGM) is proposed for solving elasticity problems. In this WMIGM, the essential boundary conditions can be imposed with ease as in the conventional finite element method. The stiffness matrix can be efficiently obtained through semi-analytical integration using an underlying general database, instead of the numerical integration usually requiring a mesh. The accuracy of the WMIGM is examined through theoretical analysis and benchmark problems. Results demonstrate that the proposed WMIGM has an excellent accuracy, optimal rate of convergence and competitive efficiency, as well as an excellent stability against irregular nodal distribution. Most importantly, by adding more nodes into local region only, a high resolution of localized steep gradients can be achieved as desired without changing the existing nodes. PubDate: 2019-03-01

Abstract: This paper proposes a novel method to accurately and efficiently reduce a microstructural mechanical model using a wavelet based discretisation. The model enriches a standard reduced order modelling (ROM) approach with a wavelet representation. Although the ROM approach reduces the dimensionality of the system of equations, the computational complexity of the integration of the weak form remains problematic. Using a sparse wavelet representation of the required integrands, the computational cost of the assembly of the system of equations is reduced significantly. This wavelet-reduced order model (W-ROM) is applied to the mechanical equilibrium of a microstructural volume as used in a computational homogenisation framework. The reduction technique however is not limited to micro-scale models and can also be applied to macroscopic problems to reduce the computational costs of the integration. For the sake of clarity, the W-ROM will be demonstrated using a one-dimensional example, providing full insight in the underlying steps taken. PubDate: 2019-03-01

Abstract: An efficient solution algorithm has been developed for space–time finite element method that is derived from time discontinuous Galerkin (TDG) formulation. The proposed algorithm features an iterative solver accelerated by a novel and efficient preconditioner. This preconditioner is constructed based on the block structure of coupled space–time system matrix, which is expressed as addition of Kronecker products of temporal and spatial submatrices. With this unique decomposition, the most computationally intensive operations in the iterative solver, i.e. matrix operations, are subsequently optimized and accelerated employing the inverse property of Kronecker product. Theoretical analysis and numerical examples both demonstrate that the proposed algorithm provides significantly better performance than the already developed implementations for TDG-based space–time FEM. It reduces the computational cost of solving space–time equations to the same order of solving stiffness equations associated with regular FEM, thereby enabling practical implementation of the space–time FEM for engineering applications. PubDate: 2019-03-01

Abstract: Phase-field formulations to fracture and sophisticated mortar contact formulations are well established techniques nowadays. For a wide range of applications, these two variationally consistent approaches could already demonstrate their superiority compared with more traditional methods in terms of generality, performance and accuracy. In the present contribution we combine both methodologies in a unified computational framework to deal with large deformation thermo-fracture mechanical contact problems. In particular, a temperature dependent model for the critical fracture energy density as well as a phase-field dependent model for the heat conduction are taken into account along with a temperature dependent contact model. To be specific, an adhesive anisotropic friction model is considered for the contact in tangential direction, whereas an exponential adhesion model is applied for the normal contact definition. These models are incorporated within the thermal phase-field approach in a thermodynamically consistent formulation. Eventually, a variety of representative numerical examples demonstrates the capabilities of this novel framework. PubDate: 2019-03-01

Abstract: This work presents a new finite element treatment of the coupled problem of Darcy–Biot-type fluid transport in porous media undergoing large deformations, that is free from any stabilization techniques. The formulation bases on an incremental two-field minimization principle that is constrained by the equation of continuity for the fluid mass content and determines at a given state the deformation and the fluid mass flux vector. The big advantage of the minimization formulation over classical saddle point principles of poroelasticity is the omission of the inf-sup condition—a condition that makes the construction of stable and computationally efficient finite element formulations difficult. Due to the \(H(\hbox {Div}, {\mathcal B}_0)\) variational structure of the minimization principle on the fluid side, lowest order Raviart–Thomas elements are used for the conforming approximation of the fluid mass flux. Furthermore, a standard nodal-based element using bilinear interpolation for both fields combined with a reduced numerical integration of the (volumetric) coupling term is analyzed and used for the solution of the minimization principle. Representative numerical examples demonstrate the performance of the proposed finite element designs of the minimization principle and clearly underline advantages over finite element formulations of the classical two-field saddle point principle formulated in deformation and fluid potential. PubDate: 2019-02-27

Abstract: We introduce a comprehensive framework for the efficient implementation of finite deformation gradient-regularised damage formulations in existing finite element codes. The numerical implementation is established within a thermo-mechanically fully coupled finite element formulation, where the heat equation solution capabilities are utilised for the damage regularisation. The variationally consistent, gradient-extended and geometrically non-linear damage formulation is based on an overall free energy function, where the standard local free energy contribution is additively extended by two non-local terms. The first additional term basically contains the referential gradient of the non-local damage variable. Secondly, a penalty term is added to couple the local damage variable—the evolution of which is governed by an ordinary differential equation—and the non-local damage field variable that is governed by an additional balance equation of elliptic type. PubDate: 2019-02-27

Abstract: In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn–Hilliard–Cook equation. The Ciarlet–Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler–Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures. PubDate: 2019-02-25