International Journal for Numerical Methods in Engineering最新文献

Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: inconsistent volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing in meshfree collocation methods. Using these, we introduce an artificial compressibility in the fluid to reduce errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour in meshfree collocation methods, even for complex industrial test cases such as automotive water crossing.

Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e., components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are modeled using a fully coupled non-linear thermo-mechanical finite element framework. To obtain the intricate heat transfer response, the components leverage self-contact, which is modeled using a third medium contact method. The effective heat transfer properties of the regulators are tuned by solving a topology optimization problem using a traditional gradient-based algorithm. Several designs of thermo-mechanical regulators in the form of switches, diodes, and triodes are presented.

Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase-field fracture poor convergence is found or, in the case of using staggered algorithms, leads to the presence of jumps in the evolution of the cracks. In this work, a novel method is proposed to perform micromechanical simulations with phase-field fracture imposing monotonic increases of crack length and allowing the use of monolithic implementations, being able to resolve all the snap-backs during the unstable propagation phases. The method is derived for FFT-based solvers in order to exploit its very high numerical performance in micromechanical problems, but an equivalent method is also developed for Finite Elements (FE) showing the equivalence of both implementations. It is shown that the stress-strain curves and the crack paths obtained using the crack control method are superposed in stable propagation regimes to those obtained using strain control with a staggered scheme. J-integral calculations confirm that during the propagation process in the crack control method, the energy release rate remains constant and equal to an effective fracture energy that has been determined as a function of the concretization for FFT simulations. Finally, to show the potential of the method, the technique is applied to simulate crack propagation through the microstructure of composites and porous materials providing an estimation of the effective fracture toughness.

This paper focuses upon the single-step multi-stage time integration methods for second-order time-dependent systems. Firstly, a new and novel generalization of the Runge-Kutta (RK) and Runge-Kutta-Nyström (RKN) methods is proposed, featuring an advanced Butcher table for designing new and optimal algorithms. It encompasses not only the classical multi-stage methods as subsets, but also introduces novel designs with enhanced accuracy, stability, and numerical dissipation/dispersion properties. Secondly, to sharpen the focus on the present developments, several existing multi-stage explicit time integration methods (which are of interest and the focus of this paper) are revisited within the proposed unified mathematical framework, such that it highlights the differences, advantages, and disadvantages of various existing methods. Thirdly, the consistency analysis is rigorously demonstrated using both single-step and multi-step local truncation errors, addressing the order reduction problem observed in existing methods when applied to nonlinear dynamics problems. Finally, two sets of single-step, two-stage, third-order time-accurate schemes with controllable numerical dissipation/dispersion at the bifurcation point are presented. In contrast to existing methods, these newly proposed schemes preserve third-order time accuracy in nonlinear dynamics applications and exhibit improved stability in cases involving physical damping. Numerical examples are demonstrated to verify the theoretical analysis and the superior performance of the proposed schemes compared to existing methods.

Implicit-explicit (IMEX) time integration schemes are well suited for non-linear structural dynamics because of their low computational cost and high accuracy. However, the stability of IMEX schemes cannot be guaranteed for general non-linear problems. In this article, we present a scalar auxiliary variable (SAV) stabilization of high-order IMEX time integration schemes that leads to unconditional stability. The proposed IMEX-BDFk-SAV schemes treat linear terms implicitly using kth-order backward difference formulas (BDFk) and non-linear terms explicitly. This eliminates the need for iterations in non-linear problems and leads to low computational costs. Truncation error analysis of the proposed IMEX-BDFk-SAV schemes confirms that up to kth-order accuracy can be achieved and this is verified through a series of convergence tests. Unlike existing SAV schemes for first-order ordinary differential equations (ODEs), we introduce a novel SAV for the proposed schemes that allows direct solution of the second-order ODEs without transforming them into a system of first-order ODEs. Finally, we demonstrate the performance of the proposed schemes by solving several non-linear problems in structural dynamics and show that the proposed schemes can achieve high accuracy at a low computational cost while maintaining unconditional stability.

This paper introduces a modified displacement-driven approach for contact mechanics between rigid and deformable bodies within the finite element framework. This modification enhances efficiency, addressing the limitations of the original formulation, which resulted in an overdetermined system of equations. The proposed enhancement aims to resolve this issue by forming a determined system of equations while providing accurate results. Additionally, using an advanced solver significantly reduces computation time, making it well-suited for handling large-scale problems. The performance of the enhanced formulation is demonstrated by several numerical examples and compared to the results from the initial model. The results show that the enhanced formulation satisfies numerical stability and exhibits quadratic convergence behavior. These results are validated using both an analytical solution and a penalty method. Furthermore, a spatial convergence study confirms the accuracy and reliability of the algorithms.