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Computer Methods in Applied Mechanics and Engineering

Computer Methods in Applied Mechanics and Engineering

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Scaled Boundary Perfectly Matched Layer (SBPML): A novel 3D time-domain artificial boundary method for wave problem in general-shaped and heterogeneous infinite domain
Guoliang Zhang; Mi Zhao; Junqi Zhang; Xiuli Du;
Abstracts:Artificial boundary method is widely used in the numerical modeling of unbounded wave problem. However, the accurate modeling of truncated infinite domain with general geometry and heterogeneous materials is still a challenging task, especially for direct time-domain analysis in three dimensions (3D). In this paper, a novel 3D time-domain artificial boundary method, called Scaled Boundary Perfectly Matched Layer (SBPML), is proposed. This method is a generalization of the Perfectly Matched Layer (PML) based on a scaled boundary coordinates transformation inspired by the Scaled Boundary Finite Element Method (SBFEM), which is capable of using artificial boundary of general geometry (not necessarily convex) and considering plane physical surfaces and interfaces extending to infinity in the truncated infinite domain. Local scaled boundary coordinates are firstly introduced on the element-level into the truncated infinite domain to describe general geometry properties of the infinite domain. Then, a complex stretching function from PML is applied to radial direction of the local scaled boundary coordinates to map the physical space onto the complex space, resulting in a SBPML domain. The spatial discretization of the SBPML domain produces semi-discrete mixed displacement–stress​ unsplit-field formulations of third orders in time. The order of the obtained formulation can be reduced by one, enabling a seamless coupling with the standard displacement-based finite element formulation of the interior domain. The coupled system can be solved by an explicit time integration algorithm efficiently. The validation of the SBPML is demonstrated through several benchmark tests, including wave problems in unbounded domains with general geometries and heterogeneous material properties. Furthermore, the application of the SBPML in dynamic soil–structure interaction (SSI) is demonstrated using two engineering problems, including an impact analysis of soft rock-nuclear island system and a vibration analysis of soil-lined tunnel system.
Versatile benchmark model reproducing snap-through, asymmetric, symmetric unstable/stable, and multiple bifurcation including hill-top branching in structural instability
Masato Tanaka; Kiyohiro Ikeda; Fumio Fujii;
Abstracts:This paper proposes a simple yet innovative two degrees of freedom (2-DoFs) benchmark model for structural instability. The proposed rigid-body-spring model is versatile in that it reproduces various kinds of instability phenomena. Its parameter combinations comprehensively realize snap-through, asymmetric, symmetric unstable/stable, and multiple bifurcation including hill-top branching in structural stability problems. Governing equations including the total potential energy, nonlinear equilibrium equations, stiffness matrix (Jacobian), and stability information are all explicitly formulated. For post-buckling analysis, path branching is visualized for intuitive diagnosis. The versatile benchmark model is expected to yield a qualitative understanding of the instability mechanism depending on the model parameters. The benchmark model also contributes to the phenomenological understanding of stability design.
Damage identification in fiber metal laminates using Bayesian analysis with model order reduction
Nanda Kishore Bellam Muralidhar; Carmen Gräßle; Natalie Rauter; Andrey Mikhaylenko; Rolf Lammering; Dirk A. Lorenz;
Abstracts:Fiber metal laminates (FML) are composite structures consisting of metals and fiber reinforced plastics (FRP) which have experienced an increasing interest as the choice of materials in aerospace and automobile industries. Due to a sophisticated built up of the material, not only the design and production of such structures is challenging but also its damage detection. This research work focuses on damage identification in FML with guided ultrasonic waves (GUW) through an inverse approach based on the Bayesian paradigm. As the Bayesian inference approach involves multiple queries of the underlying system, a parameterized reduced-order model (ROM) is used to closely approximate the solution with considerably less computational cost. The signals measured by the embedded sensors and the ROM forecasts are employed for the localization and characterization of damage in FML. In this paper, a Markov Chain Monte-Carlo (MCMC) based Metropolis–Hastings (MH) algorithm and an Ensemble Kalman filtering (EnKF) technique are deployed to identify the damage. Numerical tests illustrate the approaches and the results are compared in regard to accuracy and efficiency. It is found that both methods are successful in multivariate characterization of the damage with a high accuracy and were also able to quantify their associated uncertainties. The EnKF distinguishes itself with the MCMC-MH algorithm in the matter of computational efficiency. In this application of identifying the damage, the EnKF is approximately thrice faster than the MCMC-MH.
Machine learning-based multi-objective optimization for efficient identification of crystal plasticity model parameters
Khem Veasna; Zhangxi Feng; Qi Zhang; Marko Knezevic;
Abstracts:A set of constitutive model parameters along with crystallography governs the activation of deformation mechanisms in crystal plasticity. The constitutive parameters are typically established by fitting of mechanical data, while microstructural data is used for verification. This paper develops a Pareto-based multi-objective machine learning methodology for efficient identification of crystal plasticity constitutive parameters. Specifically, the methodology relays on a Gaussian processes-based surrogate model to limit the number of calls to a given crystal plasticity model, and, consequently, to increase the computational efficiency. The constitutive parameters pertaining to an Elasto-Plastic Self-Consistent (EPSC) crystal plasticity model including a dislocation density-based hardening law, a backstress law, and a phase transformations law are identified for two materials, a dual phase (DP) steel, DP780, subjected to load reversals and a stainless steel (SS), 316L, subjected to strain rate and temperature sensitive deformation. The latter material undergoes plasticity-induced martensitic phase transformations. The optimization objectives were the quasi static flow stress data for the DP steel case study, while a set of strain-rate and temperature sensitive flow stress and phase volume fraction data for the SS case study. The procedure and results for the two case studies are presented and discussed illustrating advantages and versatility of the developed methodology. In particular, the efficiency of the developed methodology over an existing genetic algorithm methodology is discussed. Additionally, the parameters identified for the SS case study were utilized to simulate three biaxial tensile loading paths using a finite element implementation of EPSC for further verification.
A Bernstein–Bézier Lagrange–Galerkin method for three-dimensional advection-dominated problems
Mofdi El-Amrani; Abdellah El Kacimi; Bassou Khouya; Mohammed Seaid;
Abstracts:We present a high-order Bernstein–Bézier finite element discretization to accurately solve three-dimensional advection-dominated problems on unstructured tetrahedral meshes. The key idea consists of implementing a modified method of characteristics to discretize the advection terms in a Bernstein–Bésier finite element framework. The proposed Bernstein–Bézier Lagrange–Galerkin method has been designed so that the Courant–Friedrichs–Lewy condition is strongly relaxed using semi-Lagrangian time discretization. A low complexity procedures in building finite element matrices and load vectors is also achieved in the present work by both the analytical rule and the sum factorization method using the tensorial feature of Bernstein polynomials. Several numerical examples including advection–diffusion equations with known analytical solutions and the viscous Burgers problem are considered to illustrate the accuracy, robustness and performance of the proposed approach. The computed results support our expectations for a stable and highly accurate Bernstein–Bézier Lagrange–Galerkin finite element method for three-dimensional advection-dominated problems.
Machine learning of nonlocal micro-structural defect evolutions in crystalline materials
Eduardo A. Barros de Moraes; Marta D’Elia; Mohsen Zayernouri;
Abstracts:The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to avalanche, strain bursts, intermittent energy spikes, and nonlocal interactions producing anomalous features across different time- and length-scales, directly affecting plasticity, void and crack nucleation. Discrete Dislocation Dynamics (DDD) simulations are often used at the meso-level, but the cost and complexity increase dramatically with simulation time. To further understand how the anomalous features propagate to the continuum, we develop a probabilistic model for dislocation motion constructed from the position statistics obtained from DDD simulations. We obtain the continuous limit of discrete dislocation dynamics through a Probability Density Function for the dislocation motion, and propose a nonlocal transport model for the PDF. We develop a machine-learning framework to learn the parameters of the nonlocal operator with a power-law kernel, connecting the anomalous nature of DDD to the origin of its corresponding nonlocal operator at the continuum, facilitating the integration of dislocation dynamics into multi-scale, long-time material failure simulations.
C0-nonconforming virtual element methods for the vibration and buckling problems of thin plates">A C0-nonconforming virtual element methods for the vibration and buckling problems of thin plates
Dibyendu Adak; David Mora; Iván Velásquez;
Abstracts:In this work, we study the C0-nonconforming VEM for the fourth-order eigenvalue problems modeling the vibration and buckling problems of thin plates with clamped boundary conditions on general shaped polygonal domain, possibly even nonconvex domain. By employing the enriching operator, we have derived the convergence analysis in discrete H2 seminorm, and H1, L2 norms for both problems. We use the Babuška–Osborn spectral theory (Babuška and Osborn, 1991), to show that the introduced schemes provide well approximation of the spectrum and prove optimal order of rate of convergence for eigenfunctions and double order of rate of convergence for eigenvalues. Finally, numerical results are presented to show the good performance of the method on different polygonal meshes.
An accelerated subspaces recycling strategy for the deflation of parametric linear systems based on model order reduction
Dionysios Panagiotopoulos; Wim Desmet; Elke Deckers;
Abstracts:Krylov subspace recycling has been extensively used to facilitate the solution of sequences of linear systems by constructing a deflation subspace and accelerating the convergence of a corresponding iterative solver. However, most existing techniques update the recycled subspace sequentially for each system, thus inducing a potentially high computational cost. In that context, this work proposes a method to accelerate the above procedure for the case of multiresolution analyses of affine parametric systems, by decoupling the solution of the system from the construction of the recycled subspace. The proposed method follows the projection based Model Order Reduction (MOR) logic that splits operations into an offline and an online phase and therefore proves particularly beneficial in case of affine parametrizations that involve multiple affine coefficients. In the offline phase of the method an especially tailored version of the Automatic Krylov subspaces Recycling (AKR) algorithm (Panagiotopoulos et al., 2021), proposed within this work and denoted as AKR-D, is employed. In brief, AKR-D constructs a high quality recycling basis W for a predefined parameter interval Ψ by targeting a desirable convergence rate at an automatically generated set of parameter values Ω⊂Ψ. The upfront construction of W enables an a-priori Galerkin projection of the affinely described full parametric system to yield a reduced order model (ROM). This ROM can be leveraged in the online phase of the proposed recycling method to accelerate the construction of the corresponding projector P onto W=span{W}, whose implicit assembly is required in most recycling based deflation schemes. The effectiveness of the proposed strategy is investigated in terms of algorithmic complexity and is demonstrated on a densely parametrized system arising within the boundary integral solver of the Helmholtz equation and a random sparse parametrization example.
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