Accurate and efficient simulation of quasi-brittle fracture remains challenging due to the intricate interplay among distributed damage, softening behaviour, and strongly localised crack evolution, which demands high spatial resolution within evolving fracture process zones. Therefore, this work proposes an adaptive computational framework that integrates the cell-based smoothed finite element with the phase-field cohesive zone model (a-CSFEM-PFCZM) for quasi-brittle fracture simulation. The formulation is implemented on arbitrary polygonal meshes and incorporates a damage-driven adaptive mesh refinement strategy that dynamically refines regions undergoing active fracture processes. It enables efficient resolution of evolving crack paths while controlling the growth of degrees of freedom across the domain. The use of CSFEM further enhances numerical robustness on adaptive polygonal meshes and facilitates seamless coupling between coarse and refined regions without requiring transition elements or additional compatibility constraints. Based on these features, a simple and effective procedure is developed for transferring and mapping field and history variables during mesh adaptation, thereby supporting flexible treatment of complex mesh topologies and evolving fracture processes. Several benchmark problems, including homogeneous structural components and meso-scale heterogeneous materials involving complex crack initiation and propagation, are investigated to assess the performance of the proposed approach. The results demonstrate that the method accurately reproduces crack patterns and load-displacement responses while exhibiting negligible sensitivity to mesh topology. Compared with uniformly refined simulations, the adaptive framework achieves comparable fidelity with substantially fewer degrees of freedom and markedly reduced computational cost. These results indicate that the proposed a-CSFEM-PFCZM framework provides a robust, accurate, and flexible computational tool for quasi-brittle fracture analysis.

Die Lage eines Punkte P im Raum wird durch den Ortsvektor r(t) beschrieben.

In this work, we introduce the Projection Enhanced Triangular Finite Element Method (PET-FEM), a finite element formulation for polygonal meshes. The method relies on a FEM sub-mesh, while the internal degrees of freedom are recovered by a least-squares projection operator. This yields an implementation that is simple, flexible, and free of problem-dependent parameters. For higher-order PET-FEM, the formulation admits a serendipity-style reduction of internal degrees of freedom and shows improved robustness under mesh distortion compared to classical FEM serendipity elements. We further propose a first-order element that blends VEM and PET-FEM to obtain a computationally inexpensive, locking-free discretization. We benchmark our approach for the Poisson equation and for standard benchmarks in structural mechanics, including linear and nonlinear cases (e.g., Cook’s membrane and a punch test). The method achieves optimal convergence across all tests, with improved accuracy of the first-order element in locking-dominated problems.

This work presents a novel Virtual Element Method (VEM) based on a divergence-free projection for the numerical simulation of two-dimensional frictionless contact problems. The proposed formulation belongs to a new class of stabilization-free VEMs, where the stiffness matrix is constructed without introducing any stabilization terms. Unlike conventional stabilization-free VEMs (Berrone et al., 2023), the projection operator is defined in a divergence-free space, leading to a formulation that completely avoids stabilization. Since no stabilization terms are required, contact constraints can be imposed in a more natural and consistent manner. To the best of the author's knowledge, there has been no previous work applying a stabilization-free VEM-type method to the field of contact mechanics. In addition, fracture phenomena induced by contact interactions are also investigated by coupling the proposed VEM with phase field models. The intrinsic flexibility of polygonal meshes in VEM is fully exploited to develop an adaptive mesh refinement strategy, which is applied in the vicinity of the contact interfaces and crack surfaces. This adaptive strategy significantly enhances computational efficiency and accuracy in capturing localized deformation, stress concentration, and crack evolution. Several numerical examples involving frictionless contact and contact-induced fracture are presented to demonstrate the accuracy and robustness of the proposed method.

The third medium contact (TMC) has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, this methodology introduces a third medium between two contacting bodies, thereby avoiding the complex treatment of the contact constraints. The approach has been successfully applied for different problems in the framework of the finite element method (FEM). As a generalization of the finite element method, the virtual element method (VEM) can handle arbitrary polygonal elements, providing greater flexibility for modeling third medium contact. However, due to the introduction of the projection operator, VEM requires additional stabilization terms to control the rank of the stiffness matrix. Moreover, the regularization term in the third medium contact formulation requires a second-order numerical scheme, which further complicates the application of classical virtual element schemes to such problems. In this work, the stabilization-free virtual element method (SFVEM) is adopted to TMC and applied to solve contact problems undergoing large deformations. Different from the traditional VEM, SFVEM does not require additional stabilization terms, which simplifies the construction of necessary regularization terms in third medium contact. Building upon the traditional second-order FEM framework, we present the specific format of SFVEM for solving third medium contact, including the construction of high-order projection operator and the tangent stiffness matrix. Numerical examples are provided to demonstrate the effectiveness and applicability of SFVEM in solving complex 2D contact problems with the TMC approach.

Emerging innovative materials with multifunctionality are revolutionizing the design, development, and manufacturing of electronics. Through a novel machine learning approach, this study addresses computational challenges in modeling size-dependent free vibration of smart sandwich nanoplates with a carbon nanotube-reinforced core and multifunctional thermal-magneto-electroelastic face sheets supported by a Winkler-Pasternak foundation. A nonlocal strain gradient theory plate model quantifies dual-scale effects of nonlocal and material length scale parameters, while incorporating carbon nanotube interphase layer and agglomeration effects, as well as the multiphysics field couplings in the thermal-magneto-electro-elastic layer. To overcome the prohibitive computational cost of traditional Galerkin-based solution in high-dimensional parametric spaces, a backpropagation neural network surrogate is developed for predicting natural frequencies. Verification studies validate the accuracy of the proposed machine-learning-based surrogate approach against analytical solutions. Additionally, extensive parametric analyses using the surrogate evaluate the impact of key factors, including nonlocal and material length scale parameters, boundary conditions, carbon nanotube agglomeration states, electric voltage, magnetic potentials, thermal gradients, and elastic foundation parameters, on the free vibration response. The backpropagation neural network surrogate model enables a systematic statistical evaluation of parameter interactions and sensitivity trends, providing new insights into the relationships among multiphysics variables that influence the size-dependent dynamic behavior of smart, multifunctional nanoplates.

As a key enabling technology for fourth-generation interconnects, Through-silicon via (TSV) has been widely adopted in advanced electronic packaging. However, performance degradation of TSV in service remains a significant challenge in engineering practice. To accurately characterize and effectively evaluate the performance of TSV structures under multi-physics service conditions, a cross-scale analysis method of the TSV performance degradation is proposed based on thermodynamic irreversible entropy production, which can also reveal the structural evolving process from the microscopic viewpoint. First, the electro-thermo-mechanical coupled response of the TSV structure is modeled and analyzed under generalized low-frequency signal excitation. Temperature and stress distributions under multi-physics coupling effects are obtained, while the entropy production process within the structure is simultaneously tracked. Subsequently, based on the theory of thermodynamic theory, a local entropy production model for the TSV structure is developed by incorporating plastic work and heat conduction mechanisms. This model reveals the thermodynamic mechanisms driving performance degradation and damage evolution in TSVs. Finally, a numerical example is provided to validate the effectiveness of the proposed method and model, yielding several important conclusions.

Hypersonic magnetohydrodynamic (MHD) control has considerable potential for optimizing the aerodynamic and thermal characteristics of hypersonic vehicles and managing flows such as boundary layer transitions. As key factors influencing MHD control, magnetic field parameters are a central focus of research. To address the challenges in simulating 3D magnetic fields and assessing their impact on MHD control, this study employed a 3D, low-magnetic-Reynolds-number MHD model to conduct numerical simulations. These simulations helped investigate hypersonic MHD control under various magnetic field types and configurations and analyze the underlying mechanisms and their effects on the flow field and thermal/force distributions. The results indicate that the direction of the Lorentz force is jointly determined by the orientations of the magnetic field and the flow field. Different Lorentz force directions influence the shock stand-off distance through distinct mechanisms, near-wall Lorentz forces can effectively regulate the increase or decrease in surface heat flux. Under the computational conditions of this study, considering both MHD thermal protection performance and the MHD shock control effectiveness, the optimal magnetic control parameters for the two-dimensional solenoid model are determined as LM = 0.26 m and x0 = 0.04 m. Through three-dimensional magnetic field analysis, the optimal magnetic configuration for the three-dimensional model is identified as M9. The external flow fields generated by spatial magnetic configurations M4, M5, M7, and M8 exhibit significant asymmetry, and the numerical simulation results provide theoretical support for the application of magnetic field in hypersonic vehicle attitude control.

Discretization techniques for large-displacement analyses of shear-deformable 3D beams should ideally introduce a minimal number of unknowns with a clear physical interpretation and that should possibly be approximated through polynomials of generic degree. Moreover, numerical formulations should be objective, locking-free and singularity-free for arbitrarily large rotations. In this context, the Virtual Element (VE) method offers significant potential that remains to be fully explored. In this work, we propose a novel VE formulation that enables the construction of new nonlinear 3D beam elements of arbitrary polynomial interpolation order. The proposed formulation introduces displacements and rotations at the element endpoints as the only unknowns, even in the case of high-order interpolation functions, as the additional internal degrees of freedom are statically condensed at the element level. The consistency, robustness, and accuracy of this new formulation are assessed through a series of well-established benchmark tests. Numerical results confirm that the developed 3D beam virtual elements are computationally efficient, locking-free, and highly accurate, particularly when high-order ansatz functions are used.

Metal components operating in high-temperature environments are prone to creep damage due to the combined effects of continuous constant stress and thermal loading, which may ultimately lead to structural failure. Conventional creep life prediction models, such as the Larson–Miller parameter and θ‑projection method, are largely empirical, ignoring energy dissipation and micro‑damage mechanisms, which makes them inherently limited for accurate creep failure prediction. To overcome the above limitations, this work develops two models which take thermodynamics as the theoretical basis and regard entropy generation as the core characterization indicator. Specifically, the first‑type model couples energy dissipation with temperature to quantify entropy generation from irreversible processes. The second‑type model uses creep strain as the dominant variable, links macroscopic stress to mesoscopic plastic deformation, and the thermodynamic state index (TSI) is introduced as a failure criterion. Finally, the proposed method is validated using material strain data obtained from high-temperature creep experiments. The results reveal that both models exhibit good predictive performance, and the second-type model achieves better accuracy under high-temperature conditions.

Accurate prediction of ductile fracture in elastoplastic and pseudo-elastoplastic materials, including metals and Ultra-High-Performance Cementitious Composites (UHPC), is essential for structural design. Conventional phase-field models for ductile fracture are limited by excessive sensitivity to the regularisation length scale, reliance on ad hoc plastic work thresholds, and incomplete representation of softening behaviour. To overcome these issues, we propose a phase-field model that incorporates both elastic energy and plastic work as fracture driving forces, introducing separate intrinsic thresholds via dedicated degradation functions to ensure thermodynamically consistent crack initiation without arbitrary adjustments. Stiffness degradation is decoupled from the phase-field variable through an independent variable, removing geometric constraints on the length scale parameter and enhancing computational flexibility. The framework supports arbitrary softening laws through tailored characteristic functions, capturing post-peak stress-strain responses and eliminating the need for damage history variables. A semi-explicit numerical scheme, combining an explicit equilibrium algorithm with a neighboured element method for phase-field evolution, is implemented in ABAQUS/Explicit. Benchmark validations confirm minimal influence of the length scale parameter across various softening laws. By adjusting threshold values, the model reproduces a wide range of failure modes—including the transition between (quasi-)brittle and ductile fracture—while accurately capturing strain hardening and fracture in both dislocation-mediated metals and fibre-bridging-dominated pseudo-elastoplastic UHPC at the macroscopic level, thereby demonstrating broad applicability and robustness for ductile fracture analyses.

ZusammenfassungDie Bewegung eines Massenpunktes unter der Wirkung von Kräften wird beschrieben durch $$ \boxed{\frac{{d(mv)}}{{dt}} = \dot{p} = F}, $$ mit F = ∑ F i und dem Impuls $$ p = mv. $$

This work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. proposed third-medium formulation embeds a third medium between potentially interacting ies, enabling a unified and robust treatment of hyperelastic contact and self-contact without need for discretization of the contact interface. In this work, we propose a new regularization term for three-dimensional problems to ensure element quality in a third medium. Due to need for higher-order elements for the regularization term, this paper details the linearization process of this problem within the finite element framework. In addition, pneumatically actuated systems are considered by introducing a pneumatic term to represent pneumatic loading (pressure or suction) and inducing contact caused by internal inflation. This approach is suitable complex hyperelastic contact and self-contact, and has potential applications in the fields of robotics and flexible mechanisms. The framework is developed in a fully three-dimensional ting, making it also suitable for isogeometric methods and meshless methods. Several benchmark and application-level simulations demonstrate the accuracy, robustness, and versatility of proposed approach. The results highlight the capability of the three-dimensional third-medium model to handle challenging nonlinear contact scenarios relevant to soft materials, soft actuators, and emerging multifunctional structures.

Abstract The role of fatigue in the design of concrete structures has increased significantly in recent years, particularly due to the expansion of offshore wind energy systems, where especially the moisture content plays a decisive role. Despite some contradictions in the literature, one trend is clear: Submerged concrete (wet) exhibits significantly lower fatigue resistance than air-stored concrete (dry). The underlying damage mechanisms responsible for this phenomenon yet remain unclear. In this chapter, the main results obtained from a joint project are reported. The results showed that the water in the microstructure, i.e. at a size of ≤ 10 nm, is primarily responsible for the water-induced fatigue damage. Additionally – and even more relevant for design – the effect of the water-induced damage is more significant at low load frequencies. The results provide clear indications that the threshold beyond which the water-induced damage mechanisms become decisive may be well in the range of storage at 85% relative humidity. Comprehensive microscopic investigations traced the water-induced damage mechanisms back to a water redistribution process at a scale of only a few nanometres. This leads to pore pressure, causing loosening effects (damages) in the dense structure of the calcium silicate hydrate phases.

The third medium contact has recently emerged as an effective approach for simulating contact problems, particularly in cases involving complex self-contact problems and extended optimization applications. By introducing a third medium between potential contact surfaces, contact constraints can be enforced through the constitutive response of the auxiliary material, thereby avoiding the explicit treatment of contact conditions. However, existing third medium formulations typically rely on regularization terms involving higher-order derivatives of the deformation field, which complicates the numerical implementation and significantly increases the computational cost. The Virtual Element Method (VEM) offers greater flexibility in mesh design for the third medium contact problems. However, the projection operators in VEM become significantly more complex due to the presence of higher-order derivatives. In this work, a first-order virtual element method is proposed for third medium contact problems in finite elasticity. To make third-medium contact compatible with a first-order VEM discretization, the auxiliary-field-based first-order regularization is incorporated into the VEM framework, enabling the entire problem to be discretized using only first-order derivatives with the first-order VEM framework. The resulting method retains the geometric flexibility of VEM while achieving higher computational efficiency. Several numerical examples involving complex self-contact are presented to demonstrate the performance of the proposed approach, including self-contact in flexible structures, deformation of auxetic metamaterials, and simulations of pneumatic soft robotic actuators. The results show that the proposed method provides stable and accurate contact simulations while significantly reducing the computational complexity compared with conventional higher-order regularization approaches.

In this work, a three-dimensional (3D) second-order serendipity virtual element method (S-VEM) is developed for the static and dynamic analysis of hyperelastic materials. The VEM framework is based on the projection of unknown basis functions onto polynomial spaces, allowing for flexible discretization with arbitrary polyhedral meshes. While most existing VEM formulations for 3D mechanical problems are discretized using first-order formulations, higher-order schemes offer improved precision, especially for nonlinear problems. However, conventional second-order VEM formulations introduce additional degrees of freedom (DOFs), such as body and surface moments, which complicate the implementation and reduce computation efficiency. To address this challenge, we propose a novel 3D second-order serendipity VEM that avoids any extra moment-related DOFs. This is the first application of a serendipity VEM to 3D static and dynamic problems in hyperelasticity. Furthermore, by integrating advanced mesh generation techniques, the proposed method enables hybrid simulations that combine second-order serendipity VEM and FEM to efficiently handle complex geometries.

To account for the reduction in fatigue life observed under the same equivalent strain range with increasing load path non-proportionality, this study proposes a modified ASME equivalent strain range model by introducing a life reduction factor and a non-proportionality factor. The determination method for the life reduction factor is proposed by integrating with the Fatemi-Socie model. For thin-walled specimen under symmetric cyclic loadings, the proposed method enables multiaxial fatigue life prediction without requiring complex multiaxial constitutive relationships. Furthermore, under asymmetric cyclic loadings, a fatigue life prediction model is proposed on the basis of the critical plane theory and Smith-Watson-Topper mean stress correction criterion. Notably, when the mean stress is zero, this model reduces to the equivalent strain model established in this study. Comprehensive validation using 1325 data points from 28 materials under 28 loading conditions (including 18 symmetric and 10 asymmetric cyclic loadings) confirms the model’s universal prediction capability, demonstrating high prediction accuracy for both uniaxial/multiaxial and symmetric/asymmetric loading paths.