Computer Methods in Applied Mechanics and Engineering最新文献

Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the development of a generalized framework capable of handling topological changes and transitioning implicitly from fluid–structure interaction (FSI) conditions to solid–solid contact conditions. We propose a mono-field interface advancing method for handling multibody contact simulations in submerged environments. Given the physical demands of the problem, we adopt a phase-field based fully Eulerian approach to resolve the multiphase and multibody interactions in the system. We employ a stabilized finite element formulation and a partitioned iterative procedure to solve the unified momentum equation comprising solid and fluid dynamics coupled with the Allen-Cahn phase-field equation. The evolution of solid strain in the Eulerian reference frame is governed by the transport of the left Cauchy–Green deformation tensor. We introduce a contact force approach to handle smooth elastic-elastic and elastic-rigid contact based on the overlap of the diffused interfaces of two colliding bodies. We propose a novel approach to extend the model for multibody contact simulations while using a single phase-field function for all the solids. The method is based on updating the solid boundaries at every time step and checking for collisions among them. The developed approach eliminates the need to solve multiple phase field equations and multiple strain equations at every time step. This reduces the overall computational time by nearly 16% compared to a multi phase-field approach. The implemented model is verified for smooth dry contact and FSI contact scenarios. Using the proposed framework, we demonstrate the collision dynamics between multiple bodies submerged in an open liquid tank.

This paper reports a procedure to develop random fields of material properties on a mesoscale level, coarser than the microscale level of heterogeneous material microstructure. Since the anisotropy of properties at the mesoscale level is unavoidable, tensor-valued random fields (TRFs) need to be constructed. The construction satisfies three criteria: (i) the passage from the micro to mesoscale must be conducted according to micromechanics, (ii) any anisotropic properties must be grasped, and (iii) full (spatial) correlation structure must be accounted for. The construction is illustrated in the example of a linear elastic microstructure modeling a planar interpenetrating phase composite (IPC), where each phase is interconnected throughout the microstructure. The most general representation of a statistically homogeneous and isotropic correlation structure of the TRFs of stiffness and compliance is employed. Four material functions of the representation are determined through scale-dependent homogenization, which grasps any auto- and cross-correlations within/among different components of TRFs. The Gaussianity of the TRFs is also assessed with a finding that, overall, the smaller is the mesoscale and the more pronounced is the microstructural randomness, the more non-Gaussian are the mesoscale TRFs.

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards’ equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

Multimaterial problems in linear and nonlinear elasticity are some of the least explored using mixed finite element formulations with higher-order elements. The fundamental issue in adapting the mixed displacement–pressure formulations with linear and higher-order continuous elements for the pressure field is their inability to capture pressure and stress jumps across material interfaces. In this paper, for the first time in literature, we perform comprehensive studies of multimaterial problems in elasticity consisting of compressible and incompressible material models using the mixed displacement–pressure formulation to assess the performance of different element types in accurately resolving pressure fields within the domains and pressure jumps across material interfaces. In particular, inf–sup stable displacement–pressure combinations with element-wise discontinuous pressure for triangular and tetrahedral elements are considered and their performance is assessed along with the Q1/P0 element and Taylor–Hood elements using several numerical examples. The results show that Taylor–Hood elements fail to capture the stress jumps due to the continuity of DOFs across elements, the Crouzeix–Raviart (P2b/P1dc) element yields substantially poor pressure fields despite a significant increase in pressure degrees of freedom and that the P3/P1dc element produces superior quality results fields when compared with the P2b/P1dc element.

This study introduces a novel topology optimization approach by employing power law-based material interpolation and adaptive filtering in the framework of the unstructured grids. As an extension of the established Solid Isotropic Material with Penalization (SIMP) method that utilizes the fixed structured mesh, the proposed Colored Body-Fitted Optimization (CBFO) method adopts the body-fitted grids to enhance efficiency, accuracy, and adaptability for diverse engineering applications. Notably, incorporating body-fitted meshes with intermediate density profiles enables improved flexibility in the numerical simulations and eliminates the need for re-meshing in each iteration. The dual re-meshing strategy drastically reduces computational costs, with only two re-meshing procedures required throughout the optimization process. This approach facilitates the generation of dense mesh regions around critical boundaries to augment solution accuracy while enabling sparse mesh configurations in the low-sensitivity regions, thereby boosting computational efficiency without compromising performance. The effectiveness, robustness, and efficiency of the CBFO method are validated through testing on multiple standard minimum compliance and compliant mechanism problems. The proposed optimization method can converge in dozens of iterations, obtain better objective function values, and save computational costs by up to 69 % compared to the previous method using the body-fitted mesh. Additionally, a concise MATLAB script implementing the proposed method using an Object-Oriented Programming (OOP) paradigm is provided in the appendix and the supplementary material, complete with annotations.

The nonlocal macro-meso damage (NMMD) model has shown promising results in simulating the fracture process of materials. However, due to the inherent limitations of the nonlocal methods, its stability depends on whether the number of elements/nodes within the nonlocal region is sufficient. This paper proposes a discrepancy-informed quadrature strategy for NMMD to address its inherent limitations. Concretely, two discrepancies are defined to evaluate the uniformity of family point distribution within the nonlocal domain, followed by the introduction of a discrepancy-informed nonlocal quadrature strategy. The proposed strategy refines this by discretizing the nonlocal integral domain into finite circles for 2D or spheres for 3D and the discrete family points are uniformly arranged in each layer. This new quadrature strategy ensures relatively uniform distribution of pair points in the nonlocal space of each real material point, thus significantly enhancing the robustness and computational efficiency of the NMMD model. Numerical examples corroborate the strategy in accurately simulating different fracture modes, achieving an average computational speedup of approximately three times. This discrepancy-informed quadrature strategy effectively addresses the element size constraints of the original NMMD quadrature strategy.

Due to their high specific strength and stiffness, stiffened thin-walled structures are extensively utilized in aerospace applications to maintain a high load-bearing capacity in a complex thermo-mechanical coupled environment. Thermal deformation significantly impacts the intake and exhaust performances, aerodynamic profiles, and even structural safety, hence how to design a reasonable stiffener layout for thermal structures is necessary. Thermoelastic topology optimization is an efficient method. However, to reduce the thermal load and maintain stiffness, design-dependent thermal loading problems such as the grayscale issues and the material-less effect often result. Due to the high proportion of gray elements and a lower penalized element stiffness, thermal deformation magnitude is closely related to the grayscale issues. Therefore, the key challenge is to address the grayscale issues induced by the thermal load. To address this challenge, a thermoelastic topology optimization method via regional strain energy minimization (RSEM) is proposed in this study. The region here means the skin domain of stiffened thin-walled structures. To control the width size of stiffeners consisting of voxels, a maximum size constraint is established through the p-mean aggregation function, employing the Helmholtz-type anisotropic filter to calculate the solid ratio. This study compares three optimization formulations that minimize the compliance, global strain energy and regional strain energy as objective functions, respectively. Two numerical examples are presented to demonstrate the effectiveness of the proposed method in addressing design-dependent thermal loading problems. Compared to conventional methodologies, the proposed method can generate a clear stiffener layout and reduce the thermal deformation by 77% for an engineered thin-walled end cap structure under a thermo-mechanical coupled field.

We propose a novel optimization technique for the automatic construction of interface operators for coupling non-matching 3D meshes. The core of the method lies in the use of localized Lagrange multipliers and least-squares approximation to find the optimal location of additional interface nodes, allowing the problem to be solved without modifying the meshes of the coupled subdomains and passing the patch test. Although many techniques exist in the literature for coupling incompatible meshes, such as the widely accepted Mortar method, which solves the problem exactly, the proposed method brings two crucial advantages: first, it eliminates the need to compute complex surface integrals on the intersection of the boundary meshes (thanks to the use of techniques adapted from the existing method of localized Lagrange multipliers); and second, and more importantly, we achieve this passing the patch test with comparable accuracy to Mortar. The efficiency and accuracy of the proposed coupling technique is demonstrated by comparing its results with other coupling methods and by solving various theoretical and practical examples with exact and experimental solutions in statics and dynamics.

Traditional fatigue assessment methods for new and unexplored metallic alloys is challenging due to very limited experimental data. To address this, we formulate the assessment within a conditional probability framework, allowing us to capture the complexities of uncertainty in fatigue predictions. We employ advanced probabilistic methods to account for both inherent material variability and model uncertainty. We analyse fatigue data of multi-principal element alloys (MPEAs) tested under stress ratios of R = 0.1 and R = −1, including face-centred cubic (FCC) microstructures of CoCrFeMnNi and AlCoCrFeMnNi alloys. Based on results, we found a clear material trend which allows us more reliable predictions and informed decision-making, which is distinct than the conventional fitting. for the future alloy design. As we demonstrate the efficacy of this framework in extracting the intricate relationships between MPEA composition and the trend in fatigue behaviour, we believe that our study will pave the way for enhanced advanced material design and uncertainty quantification in future MPEA research and materials engineering applications.

The main idea of this work is to investigate the uncertainty propagation while homogenizing the periodic fiber-reinforced composites with some structural interface imperfections, and specifically their thermal and mechanical properties in linear elastic regimes. The effective modules method is implemented here with the use of two alternative Finite Element Method (FEM) programs based on its displacement (temperature) formulation. Probabilistic (Shannon) entropy and probabilistic distance are engaged here to quantify uncertainty propagation of effective characteristics as well as their probabilistic distance to the original composite's characteristics. Probabilistic entropies fluctuations are contrasted with the traditional moments-based approach while increasing the input statistical scattering of material characteristics. According to the Maximum Entropy Principle Gaussian input parameters are tested as inducing the largest deviations in effective characteristics, but they are compared against some other symmetric distributions. The entire methodology is based upon the response random polynomials relating homogenized characteristics with material and geometrical parameters of the original composites subjected to randomization. Some series of the FEM experiments serve as the basis for the artificial neural network identification and optimization of these polynomials, whose application in conjunction with the Monte-Carlo simulation enables Shannon entropy determination. Relative entropy as well as the referential probabilistic moments are computed using the iterative generalized stochastic perturbation technique as well as the semi-analytical probabilistic method.