International Journal for Numerical Methods in Engineering最新文献

C. Krüger, V. Curo$��\underset{¸}{s}�$u, and S. Loehnert, “An Extended Phase-Field Approach for the Efficient Simulation of Fatigue Fracture Processes,” International Journal for Numerical Methods in Engineering 125, no. 7 (2024): e7422, https://doi.org/10.1002/nme.7422.

FIGURE 13 | Compact tension specimen: (A) geometry and boundary conditions and (B) identification of Paris-law (dotted) for different load ranges $��\Delta �P�$ (solid lines are XPFM simulations, the dashed line is a standard PFM simulation for comparison).

Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase-field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second-order phase-field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth-order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high-order phase-field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high-order phase-field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use $��{�H�}^{�1�}�$-conforming virtual elements and the generalized-$��\alpha �$ time integration method for the momentum balance equation, and adopt $��{�H�}^{�2�}�$-conforming virtual elements for the high-order phase-field equation. We verify our virtual element framework using classical quasi-static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

Mixed Finite Elements (FEs) with assumed stresses and displacements provide many advantages in analysing shell structures. They ensure good results for coarse meshes and provide an accurate representation of the stress field. The shell FEs within the family designated by the acronym Mixed Isostatic Self-equilibrated Stresses (MISS) have demonstrated high performance in linear and nonlinear problems thanks to a self-equilibrated stress assumption. This article extends the MISS family by introducing an eight nodes solid-shell FE for the analysis of geometrically nonlinear structures. The element, named MISS-4S, features 24 displacement variables and an isostatic stress representation ruled by 18 parameters. The displacement field is described only by translations, eliminating the need for complex finite rotation treatments in large displacements problems. A total Lagrangian formulation is adopted with the Green–Lagrange strain tensor and the second Piola–Kirchhoff stress tensor. The numerical results concerning popular shell obstacle courses prove the accuracy and robustness of the proposed formulation when using regular or distorted meshes and demonstrate the absence of any locking phenomena. Finally, convergences for pointwise and energy quantities show the superior performance of MISS-4S compared to other elements in the literature, highlighting that an isostatic and self-equilibrated stress representation, already used in shell models, also gives advantages for solid-shell FEs.

The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order computational homogenization are required to fully capture their nonlinear behavior, which arises from nonlocal interactions due to the buckling or patterning of the microstructure. In the two-scale formulation, the effective behavior of the microstructure is captured with a representative volume element (RVE), and a homogenized effective continuum is considered on the macroscale. Although an effective continuum formulation is introduced, solving such two-scale models concurrently is still computationally demanding due to the many repeated solutions for each RVE at the microscale level. In this work, we propose a reduced-order model for the microscopic problem arising in second-order computational homogenization, using proper orthogonal decomposition and a novel hyperreduction method that is specifically tailored for this problem and inspired by the empirical cubature method. Two numerical examples are considered, in which the performance of the reduced-order model is carefully assessed by comparing its solutions with direct numerical simulations (entirely resolving the underlying microstructure) and the full second-order computational homogenization model. The reduced-order model is able to approximate the result of the full computational homogenization well, provided that the training data is representative for the problem at hand. Any remaining errors, when compared with the direct numerical simulation, can be attributed to the inherent approximation errors in the computational homogenization scheme. Regarding run times for one thread, speed-ups on the order of 100 are achieved with the reduced-order model as compared to direct numerical simulations.

Flexoelectricity shows promising applications for self-powered devices with its increased power density. This paper presents a second-order computational homogenization strategy for flexoelectric composite. The macro-micro scale transition, Hill–Mandel energy condition, periodic boundary conditions, and macroscopic constitutive tangents for the two-scale electromechanical coupling are investigated and considered in the homogenization formulation. The macrostructure and microstructure are discretized using $��{�C�}^{�1�}�$ triangular finite elements. The second-order multiscale solution scheme is implemented using ABAQUS with user subroutines. Finally, we present numerical examples including parametric analysis of a square plate with holes and the design of piezoelectric materials made of non-piezoelectric materials to demonstrate the numerical implementation and the size-dependent effects of flexoelectricity.

The present study develops a new topology optimization scheme considering the dynamic instability caused by the unsymmetrical properties of system. From a mathematical point of view, the left and right eigenvectors of asymmetric system are observed with the complex eigenvalues. With the dynamic instability, the magnitudes of structural responses are increasing with respect to time and this phenomenon causes many engineering issues. As the dynamic instability is one of the serious problems, the suppression is desired from an engineering point of view. To systematically reduce this dynamic instability, the present study develops a new topology optimization scheme for the reinforcement design. To overcome the numerical difficulties of the mode conversion and the highly nonlinear behavior, this research proposes the summation of the first several complex eigenvalues. To show the issues of the dynamic instability and the validity of the present approach, several topological reinforcement problems are solved.

The unpreconditioned H-TFETI-DP (hybrid total finite element tearing and interconnecting dual-primal) domain decomposition method introduced by Klawonn and Rheinbach turned out to be an effective solver for variational inequalities discretized by huge structured grids. The basic idea is to decompose the domain into non-overlapping subdomains, interconnect some adjacent subdomains into clusters on a primal level, and enforce the continuity of the solution across both the subdomain and cluster interfaces by Lagrange multipliers. After eliminating the primal variables, we get a reasonably conditioned quadratic programming (QP) problem with bound and equality constraints. Here, we first reduce the continuous problem to the subdomains' boundaries, then discretize it using the boundary element method, and finally interconnect the subdomains by the averages of adjacent edges. The resulting QP problem in multipliers with a small coarse grid is solved by specialized QP algorithms with optimal complexity. The method can be considered as a three-level multigrid with the coarse grids split between primal and dual variables. Numerical experiments illustrate the efficiency of the presented H-TBETI-DP (hybrid total boundary element tearing and interconnecting dual-primal) method and nice spectral properties of the discretized Steklov–Poincaré operators as compared with their finite element counterparts.

With the wide application of thermoelastic structures in industries such as the aerospace field, the problem of topology optimization of thermoelastic structures has become a very common and important research topic. It is well known that the thermal environment has a non-negligible influence on the dynamic performance of structures. However, few people consider the influence of the thermal environment on structural stiffness in thermoelastic dynamic topology optimization. In practical engineering applications, the influence of the environment on the structure performance should be considered to obtain the optimal structure. In this paper, we focus on the problem of dynamic topology optimization considering the effect of non-uniform temperature fields on structural stiffness. The influence of non-uniform temperature fields adds on structural stiffness to the topology optimization of thermoelastic dynamic for the first time, thereby comprehensively addressing its effects on structural stiffness in the context of dynamic topology optimization under harmonic vibration and transient load. The proposed method begins by computing the distribution of the non-uniform temperature field within the structure. Subsequently, thermal stresses in the structure are determined through the application of thermoelastic theory. The geometric stiffness matrix of the structure is then calculated using finite element theory. The dynamic topology optimization model, employing a variable density approach, is established in conjunction with the dynamic compliance design objective. Sensitivity analysis is conducted through the adjoint method, and the design variables are updated utilizing the method of moving asymptotes. Numerical examples are presented to validate the efficacy of the proposed method and obtain the influence of different factors on the optimization results. The results show that the dynamic compliance of the optimized structure increases with increasing heat flux. For the optimization under harmonic vibration, the optimization results obtained by different external excitation frequencies are significantly different. For transient optimization, the study discovers that the optimization present transient effect.