International Journal for Numerical Methods in Engineering最新文献

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.

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.

A backward stable numerical calculation of a function with condition number $��\kappa �$ will have a relative accuracy of $��\kappa �{�ϵ�}_{�\text{machine}�}�$. Standard formulations and software implementations of finite-strain elastic materials models make use of the deformation gradient $��F�=�I�+�\partial �u�/�\partial �X�$ and Cauchy-Green tensors. These formulations are not numerically stable, leading to loss of several digits of accuracy when used in the small strain regime, and often precluding the use of single precision floating point arithmetic. We trace the source of this instability to specific points of numerical cancellation, interpretable as ill-conditioned steps. We show how to compute various strain measures in a stable way and how to transform common constitutive models to their stable representations, formulated in either initial or current configuration. The stable formulations all provide accuracy of order $��{�ϵ�}_{�\text{machine}�}�$. In many cases, the stable formulations have elegant representations in terms of appropriate strain measures and offer geometric intuition that is lacking in their standard representation. We show that algorithmic differentiation can stably compute stresses so long as the strain energy is expressed stably, and give principles for stable computation that can be applied to inelastic materials.