Journal: International Journal for Numerical Methods in Engineering

Abbreviation

Int. J. Numer. Meth. Engng

Publisher

Wiley

Journal Volumes

ISSN

1097-0207
0029-5981

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Publications1 - 10 of 19
  • Lagrangian-Eulerian multidensity topology optimization with the material point method
    Item type: Journal Article
    Li, Yue; Li, Xuan; Li, Minchen; et al. (2021)
    International Journal for Numerical Methods in Engineering
    In this paper, a hybrid Lagrangian–Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature points. This transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature points act as MPM particles embedded in a lower-resolution grid and enable a subcell multidensity resolution of intricate structures with a reduced computational cost. A quadrature-level connectivity graph-based method is adopted to avoid the artificial checkerboard issues commonly existing in multiresolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.
  • Parametrized reduced order modeling for cracked solids
    Item type: Journal Article
    Agathos, Konstantinos; Bordas, Stéphane P.A.; Chatzi, Eleni (2020)
    International Journal for Numerical Methods in Engineering
    A parametrized reduced order modeling methodology for cracked two dimensional solids is presented, where the parameters correspond to geometric properties of the crack, such as location and size. The method follows the offline‐online paradigm, where in the offline, training phase, solutions are obtained for a set of parameter values, corresponding to specific crack configurations and a basis for a lower dimensional solution space is created. Then in the online phase, this basis is used to obtain solutions for configurations that do not lie in the training set. The use of the same basis for different crack geometries is rendered possible by defining a reference configuration and employing mesh morphing to map the reference to different target configurations. To enable the application to complex geometries, a mesh morphing technique is introduced, based on inverse distance weighting, which increases computational efficiency and allows for special treatment of boundaries. Applications in linear elastic fracture mechanics are considered, with the extended finite element method being used to represent discontinuous and asymptotic fields.
  • An assessment of numerical techniques to find energy-minimizing microstructures associated with nonconvex potentials
    Item type: Journal Article
    Kumar, Siddhant; Vidyasagar, Ananthan; Kochmann, Dennis M. (2020)
    International Journal for Numerical Methods in Engineering
    Microstructural patterns emerge ubiquitously during phase transformations, deformation twinning, or crystal plasticity. Challenges are the prediction of such microstructural patterns and the resulting effective material behavior. Mathematically, the experimentally observed patterns are energy‐minimizing sequences produced by an underlying non‐(quasi)convex strain energy. Therefore, identifying the microstructure and effective response is linked to finding the quasiconvex, relaxed energy. Due to its nonlocal nature, quasiconvexification has traditionally been limited to (semi‐)analytical techniques or has been dealt with by numerical techniques such as the finite element method (FEM). Both have been restricted to primarily simple material models. We here contrast three numerical techniques—FEM, a Fourier‐based spectral formulation, and a meshless maximum‐entropy (max‐ent) method. We demonstrate their performance by minimizing the energy of a representative volume element for both hyperelasticity and finite‐strain phase transformations. Unlike FEM, which fails to converge in most scenarios, the Fourier‐based spectral formulation (FFT) scheme captures microstructures of intriguingly high resolution, whereas max‐ent is superior at approximating the relaxed energy. None of the methods are capable of accurately predicting both microstructures and relaxed energy; yet, both FFT and max‐ent show significant advantages over FEM. Numerical errors are explained by the energy associated with microstructural interfaces in the numerical techniques compared here.
  • An unbiased computational contact formulation for 3D friction
    Item type: Journal Article
    Sauer, Roger A.; De Lorenzis, Laura (2015)
    International Journal for Numerical Methods in Engineering
  • An augmented Lagrangian algorithm for contact mechanics based on linear regression
    Item type: Journal Article
    De Lorenzis, Laura; Zavarise, Giorgio (2012)
    International Journal for Numerical Methods in Engineering
  • A general high-order finite element formulation for shells at large strains and finite rotations
    Item type: Journal Article
    Başar, Y.; Hanskötter, U.; Schwab, C. (2003)
    International Journal for Numerical Methods in Engineering
  • A three‐dimensional hybrid finite element – spectral boundary integral method for modeling earthquakes in complex unbounded domains
    Item type: Journal Article
    Albertini, Gabriele; Elbanna, Ahmed E.; Kammer, David S. (2021)
    International Journal for Numerical Methods in Engineering
    We present a 3D hybrid method which combines the finite element method (FEM) and the spectral boundary integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex, heterogeneous, and nonlinear part— such as the dynamic rupture along a fault with near fault plasticity—and the high accuracy and computational efficiency of SBIM is used to simulate the exterior half spaces perfectly truncating all incident waves. The exact truncation allows us to greatly reduce the domain of spatial discretization compared to a traditional FEM approach, leading to considerable savings in computational time and memory requirements. The coupling of FEM and SBIM is achieved by the exchange of traction and displacement boundary conditions at the computationally defined boundary. The method is suited to implementation on massively parallel computers. We validate the developed method by means of a benchmark problem. Three more complex examples with a low velocity fault zone, low velocity off-fault inclusion, and interaction of multiple faults, respectively, demonstrate the capability of the hybrid scheme in solving problems of very large sizes. Finally, we discuss potential applications of the hybrid method for problems in geophysics and engineering.
  • Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics
    Item type: Journal Article
    Studer, C.; Leine, R. I.; Glocker, Ch. (2008)
    International Journal for Numerical Methods in Engineering
  • Formulation for wave propagation in dissipative media and its application to absorbing layers in elastoplastic analysis using mathematical programming
    Item type: Journal Article
    Wang, Liang; Zhang, Xue; Tinti, Stefano (2023)
    International Journal for Numerical Methods in Engineering
    In this article, we propose a new solution scheme for modeling elastoplastic problems with stress wave propagation in dissipative media. The scheme is founded on a generalized Hellinger-Reissner (HR) variational principle. The principle renders the discretized boundary-value problem into an equivalent second-order cone programming (SOCP) problem that can be resolved in mathematical programming using the advanced optimization algorithm-the interior point method. In such a way, the developed method not only inherits admirable features of the SOCP-based finite element method in solving elastoplastic problems but also enables the enforcement of absorbing layers (i.e., Caughey absorbing layer), which is essential in modeling stress wave propagation problems, to absorb wave energy. The proposed scheme is validated via the comparison between analytical and numerical results for seismic wave propagation in dissipative media. Its application to elastoplastic dynamic problems with stress wave propagation is also illustrated to demonstrate its efficiency.
  • A numerical study of steady plane granular chute flows using the Jenkins-Savage model and its extension
    Item type: Journal Article
    Szidarovszky, Ferenc; Hutter, Kolumban; Yakowitz, Sydney (1987)
    International Journal for Numerical Methods in Engineering
    The granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour. We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom-near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non-linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non-dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two-point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins–Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.
Publications1 - 10 of 19