International Journal for Numerical Methods in Engineering最新文献

Accurate modeling of layered composite structures often requires the use of detailed finite element models which can sufficiently resolve the kinematics and material behavior within each layer of the composite. However, individually discretizing each material layer into finite elements presents a prohibitive computational expensive given the large number of thin layers comprising some laminated composites. To address these challenges, an 8-node layered solid hexahedral finite element is formulated with the aim of striking an appropriate balance between efficiency and fidelity. The element is discretized into an arbitrary number of distinct material layers, and employs reduced in-plane integration within each layer. The chosen reduced integration scheme is supplemented by a novel physical stabilization approach which includes layerwise enhancements to mitigate various forms of locking phenomena. The proposed framework additionally supports the inclusion of interlaminar enhanced displacements to better represent the kinematics of general layered composite materials. The described element formulation has been implemented in the ParaDyn finite element code, and its efficacy for modeling laminated composite structures is demonstrated on a variety of verification problems.

In this work, a low-order virtual element method (VEM) with adaptive meshing is applied for thermodynamic topology optimization with linear elastic material for the two-dimensional case. VEM has various significant advantages compared to other numerical discretization techniques, for example the finite element method (FEM). One advantage is the flexibility to use arbitrary shaped elements including the possibility to add nodes on the fly during simulation, which opens a new variety of application fields. The latter mentioned feature is used in this publication to propose an adaptive mesh-refinement strategy during the thermodynamic optimization procedure and investigate its feasibility. The thermodynamic topology optimization (TTO) includes a efficient gradient-enhanced approach to regularization of the otherwise ill-posed density based topology optimization approach and was already applied to various material models in combination with finite elements. However, the special numerical treatment leading to efficiency of the regularization approach within the TTO has to be modified to be applicable to VEM, which is presented in the publication. We show the performance of this framework by investigating several numerical results on benchmark problems.

This work presents large-scale elasto-plastic topology optimization for design of structures with maximized energy absorption and tailored mechanical response. The implementation uses parallel computations to address multi million element three-dimensional problems. Design updates are generated using the gradient-based method of moving asymptotes and the material is modeled using small strain, nonlinear isotropic hardening wherein the coaxiality between the plastic strain rate and stress is exploited. This formulation renders an efficient state solve and we demonstrate that the adjoint sensitivity scheme resembles that of the state update. Furthermore, the KKT condition is enforced directly into the path dependent adjoint sensitivity analysis which eliminates the need of monitoring the elasto-plastic switches when calculating the gradients and provides a straight forward framework for elasto-plastic topology optimization. Numerical examples show that structures discretized using several millions degrees of freedom and loaded in multiple load steps can be designed within a reasonable time frame.

We introduce the fused sequential addition and migration (fSAM) algorithm for generating microstructures of fiber composites with long, flexible, nonoverlapping fibers and industrial volume fractions. The proposed algorithm is based on modeling the fibers as polygonal chains and enforcing, on the one hand, the nonoverlapping constraints by an optimization framework. The connectivity constraints, on the other hand, are treated via constrained mechanical systems of d'Alembert type. In case of straight, that is, nonflexible, fibers, the proposed algorithm reduces to the SAM (Comput. Mech., 59, 247–263, 2017) algorithm, a well-established method for generating short fiber-reinforced composites. We provide a detailed discussion of the equations governing the motion of a flexible fiber and discuss the efficient numerical treatment. We elaborate on the integration into an existing SAM code and explain the selection of the numerical parameters. To capture the fiber length distributions of long fiber reinforced composites, we sample the fiber lengths from the Gamma distribution and introduce a strategy to incorporate extremely long fibers. We study the microstructure generation capabilities of the proposed algorithm. The computational examples demonstrate the superiority of the novel microstructure-generation technology over the state of the art, realizing large fiber aspect ratios (up to 2800) and high fiber volume fractions (up to $��32�\%�$ for an aspect ratio of 150) for experimentally measured fiber orientation tensors.

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

An improved naturally stabilized nodal integration (NSNI) is presented for resolving displacement locking concerned with highly orthotropic and nearly incompressible materials in the linear setting. It is recognized that the original NSNI is susceptible to the locking when dealing with these types of materials. The proposed method utilizes spectral decomposition to split the elasticity matrix into stiff and nonstiff parts. The terms associated with the stiff modes in the bilinear form are sampled by nodal integration (NI) without stabilization, whereas the other terms are integrated with NSNI. This approach leads to a unified implementation to handle locking in both types of materials. The performance and convergence of the proposed formulation are verified through several two- and three-dimensional numerical examples, illustrating the advantages of the presented method over its standard counterpart.

The phase-field formulation for fracture propagation is widely adopted due to its capability of naturally treating complex crack geometries. The challenges of the phase-field crack simulation include the non-convexity of the underlying energy functional and the expensive computational cost associated with the fine mesh required to resolve the phase-field length-scale around the crack region. We present a novel phase-field monolithic scheme based on the limited-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, or the L-BFGS method, to address the convergence difficulties usually encountered by a Newton-based approach because of the non-convex energy functional. Comparing with the conventional BFGS method, the L-BFGS monolithic scheme avoids to store the fully dense Hessian approximation matrix. This feature is critical in the context of finite element simulations. To alleviate the expensive computational cost, we integrate the proposed L-BFGS monolithic scheme with an adaptive mesh refinement (AMR) technique. We provide the algorithmic details about the proposed L-BFGS monolithic scheme, especially about how to handle the hanging-node constraints generated during the AMR process as extra linear constraints. Several two-dimensional (2D) and three-dimensional (3D) numerical examples are provided to demonstrate the capabilities of the proposed monolithic scheme, including the accuracy, the robustness, and the computational efficiency regarding the memory consumption and the wall-clock time. Particularly, we emphasize the importance of the appropriately chosen convergence criteria for brute crack propagation. The proposed L-BFGS phase-field monolithic scheme combined with the AMR technique offers an accurate, robust, and efficient approach to model brittle crack propagation in both 2D and 3D problems.

The cover image is based on the Research Article Stabilization-free virtual element method for 2D elastoplastic problems by Bing-Bing Xu et al., https://doi.org/10.1002/nme.7490.