3D woven composites, known for their exceptional structural integrity, are highly attractive for aeronautical applications, particularly in critical components such as aero-engine fan blades. Despite their promising potential, a comprehensive understanding of their mechanical behaviour remains essential for optimised design and application. Significant nonlinear behaviour well before the ultimate failure of 3D woven composites with a layer-to-layer angle interlock fibre architecture under warp tension has been observed in experiments. Although the same experimental observation for this type of material had been reported in the literature previously, the fundamental mechanisms of nonlinearity were not fully studied. In this work, the contributing factors that lead to this severe nonlinearity are investigated and their effects on modelling the response of 3D woven composites are characterised. An appropriately defined mesoscale single-layer unit cell is adopted for this purpose to simplify the finite element modelling, along with a justification performed. Fibre tow/matrix debonding, damage in neat matrix and nonlinear shear in fibre tows have been identified as the most significant sources of nonlinearity and their modelling strategies are discussed. In comparison with the experiments, the results demonstrate the specific effects of each identified factor on the nonlinear behaviour of the material. As modelling of 3D woven composites is computationally costly, this study would provide important insights into the choice of appropriate modelling strategies for 3D woven composites in a design process.

Geometric scaling has been defined as means of producing equivalent 3D layer-to-layer angle interlock woven composite configurations that have different reinforcement geometries but identical, or very similar, effective elastic properties. Scaling rules have been derived under condition that the key geometric properties of the weave: the interlocking angle, global fibre volume fraction and weft to warp tow volume ratio, should not be affected by scaling. The role of tow sizes as designable parameters directly associated with scaling has been established for the first time. With scaling method in place, design of 3D woven composites can be defined as a two-stage process, where the effective elastic properties are varied via systematic variation of tow densities, while scaling is applied at a post-processing stage to ensure the practicality of design. The design process is comprehensive in a sense that it involves all the designable parameters, explicitly defining their roles and contribution.

Modeling progressive damage in laminated composite aerostructures is computationally demanding due to the explicit definitions of unidirectional lamina required to apply failure criteria and the numerous iterations needed to capture nonlinear behavior, especially for large-scale models. To address this challenge, the primary novelty of this paper lies in the development of an explicitly differentiable data-driven section-level shell constitutive model aimed at accelerating such analysis. In the offline phase, mesoscale 3D solid unit cells subjected to rigorous shell deformation boundary conditions are utilized. This strategy extracts 3D laminate’s nonlinear responses at the mesoscale and homogenizes them into a macroscopic shell representation. Subsequently, artificial neural networks (ANNs) are employed to construct a regression model for the generalized stress–strain relationship and a classification model for damage states. The training efficiency is significantly enhanced by a Boosted Region Adaptive Sampling (BRAS) strategy, which autonomously densifies sampling data exclusively in highly nonlinear regimes. Crucially, to guarantee implicit nonlinear convergence during online simulations, the analytical Jacobian matrix is derived from the ANN via the chain rule. Implemented into a user subroutine, this framework allows instantaneous section-level updates. Validation on a representative omega-section stiffened laminated plate, through a like-for-like comparison with established 3D finite element reference models, demonstrates that the proposed framework retains predictive fidelity while substantially reducing computational costs.

The interlaced architecture of 2D woven composites is commonly regarded as a source of increased anisotropic complexity in mechanical characterization compared with tape laminates, whereas it in fact offers an opportunity for simplification that has not been recognized in existing studies. In this work, a material symmetry analysis, explicitly accounting for the rotational symmetries of the weave architecture, is performed to identify the principal axes of woven laminae. The analysis reveals that a 2D woven lamina exhibits orthotropic behavior along both the warp/weft (0 degrees/90 degrees) and the +45 degrees/- 45 degrees directions, thus establishing the theoretical foundation for direct tensile characterization of the in-plane shear response of woven composite laminae. Leveraging this insight, a simple off-axis tension method is proposed for characterizing the in-plane shear behavior of woven composites using unidirectionally oriented woven plies, without the need for specially laminated +/- 45 degrees layups required by ASTM D3518, which is derived from classical laminate theory, or complex V-notched fixtures such as ASTM D7078. When the loading direction is oriented at 45 degrees with respect to the principal axes to be characterized, the proposed approach enables the determination of both the shear modulus and the full in-plane shear stressstrain response from a tension test. Experimental results obtained from twill woven composites, which possess a more complex interlaced architecture than plain weaves, demonstrate that the off-axis tension method reliably captures shear behavior, showing good agreement with V-notched shear tests. These results highlight the proposed method as a rigorous and efficient alternative for in-plane shear characterization of woven laminae.

Unit cell modeling of plain woven composites is essential for characterizing their mechanical properties, yet conventional unit cell models, defined by translational symmetry alone, include additional geometric symmetries that result in large degrees of freedom and high computational cost, limiting their practicality for extensive repeated analyses in applications such as optimization and uncertainty quantification studies. This work formulates a minimum single fiber tow unit cell for plain woven composites with rigorously defined relative displacement boundary conditions by applying all symmetries in a plain weave. Building on this simplification, a parametric geometric model is developed that can accommodate high fiber tow volume fractions, which conventional methods struggle to achieve due to fiber tow interference. Finite element simulations, including sanity checks and comparisons of effective properties, verify the accuracy of the minimum single fiber tow unit cell. The results show that it reproduces the effective properties of the complete unit cell with negligible errors, while substantially reducing computational cost. The proposed unit cell model enables significantly more efficient repeated evaluations of plain woven composites.

A linear stability model based on a phase-field method is established to study the formation of ripples on the ice surface. The pattern on horizontal ice surfaces, e.g. glaciers and frozen lakes, is found to be originating from a gravity-driven instability by studying ice–water–air flows with a range of water and ice thicknesses. Contrary to gravity, surface tension and viscosity act to suppress the instability. The results demonstrate that a larger value of either water thickness or ice thickness corresponds to a longer dominant wavelength of the pattern, and a favourable wavelength of 90 mm is predicted, in agreement with observations from nature. Furthermore, the profiles of the most unstable perturbations are found to be with two peaks at the ice–water and water–air interfaces whose ratio decreases exponentially with the water thickness and wavenumber.

This paper is intended to reconcile the stress-based and strain-based formulations for material failure criteria, where a longstanding and deep division is present. The two approaches do not naturally agree with each other, and they not genuinely complement each other, either. Most popular criteria are stress-based when originally proposed, including the maximum stress, Tresca, von Mises, Raghava-Caddell-Yeh and the Mohr criteria. Their formulations are unique and self-consistent, i.e., capable of reproducing the input data. Their strain-based counterparts, with the maximum strain criterion being considered as the strain-based counterpart of the maximum stress criterion, are neither unique nor necessarily self-consistent. It has been proven that the self-consistent ones reproduce their respective stress-based counterparts identically in effect with a disadvantage of requiring an additional material property to apply, without a single benefit. For the Mohr criterion as a special case, a strain-based counterpart is simply infeasible in general. All undesirable features of strain-based criteria are rooted in a single source: The failure strains can only be measured under a uniaxial stress state, which corresponds to a combined strain state in general, not a uniaxial strain state! Given the arguments presented, the reconciliation proves to be biased completely towards the stress-based side if mathematics, logic and common sense prevail over perception and prejudice.

The uncertainty quantification is crucial to the high-precision prediction of composites’ effective properties. However, the unclear input uncertainties of multiscale parameters, complex uncertainty propagations of inter-scale correlations, and unaffordable computational cost of massive simulations are three primary problems at present. In this work, an innovative model with high accuracy and feasible cost for the mechanical property prediction of plain woven composites is developed encompassing minimum-size unit cells and multi-scale uncertainty quantification. For the accuracy holding, an uncertainty analysis process consists of the traceability description, inter-scale propagation and quantification is established. The uncertainties of geometry are described by uniform distributions for fiber, fiber bundle and composite scales, respectively; that of constituent properties is described by normal distributions for fiber and matrix, and its propagations to bundle and composite scales are realized by Nataf transformation methods with the consideration of parameter correlations. For the cost control, minimum-size unit cells are formulated by exhaustive analysis of structural symmetries to reduce the computational cost without accuracy compromising for the single simulation, and 1/8 and 1/16 unit cells compared with traditional full-size ones are obtained. The evolution convergence for statistical uncertainties of effective properties is finally obtained with totally reduced computational cost of 89%.

A range of nonlinear factors were investigated based on a novel unit cell model with a reduced domain to characterize the mechanical nonlinearity exhibited by braided composites in this study. These factors include geometric nonlinearity, nonlinear shear behaviour, plasticity within the matrix and transverse fibre direction, as well as failure and damage evolution. This novel size-reduced unit cell for braided composites, based on nonorthogonal translational symmetry principles, has been developed to streamline the analysis and tackle convergence challenges. This novel size-reduced unit cell is formulated by leveraging geometric features, as well as the symmetry and anti-symmetry of relative displacement boundary conditions. In order to evaluate the efficacy of these unit cells in characterizing elastic and strength properties, a benchmark study was conducted. The results demonstrate that the novel size-reduced unit cell has the ability to reliably predict the stiffness and strength responses of the 2D3A braided composite at the mesoscale. The unit cell's predictions, which include nonlinear stress-strain curves, modulus, and strength, exhibit a robust analytical performance and a satisfactory agreement with experimental results.

A phase-field model for three-phase flows is established by combining the Navier-Stokes (NS) and the energy equations, with the Allen-Cahn (AC) and Cahn-Hilliard (CH) equations and is demonstrated analytically to satisfy the energy dissipation law. A finite difference scheme is then established to discretize the model and this numerical scheme is proved to be unconditionally stable. Based on this scheme, the droplet icing process with phase changing is numerically simulated and the pointy tip of the icy droplet is obtained and analyzed. The influence of the temperature of the supercooled substrate and the ambient air on the droplet freezing process is studied. The results indicate that the formation of the droplet pointy tip is primarily due to the expansion in the vertical direction during the freezing process. Lower substrate temperatures can accelerate this process. Changes in air temperature have a relatively minor impact on the freezing process, mainly affecting its early stages. Moreover, our results demonstrate that the ice front transitions from an approximately horizontal shape to a concave one. Dedicated physical experiments were conducted and the measured solidification process matches the results of the proposed phase-field method very well.

A phase-field model for three-phase flows with cylindrical/spherical interfaces is established by combining the Navier-Stokes (NS), the continuity, and the energy equations, with an explicit form of curvature-dependent modified Allen-Cahn (AC) and Cahn-Hilliard (CH) equations. These modified AC and CH equations are proposed to solve the inconsistency of the phase-field method between flat and curved interfaces, which can result in “phase-vanishing” problems and the break of mass conservation during the phase-changing process. It is proved that the proposed model satisfies the energy dissipation law (energy stability). Then the icing process with three phases, i.e., air, water, and ice, is simulated on the surface of a cylinder and a sphere, respectively. It is demonstrated that the modification of the AC and CH equations remedies the inconsistency between flat and curved interfaces and the corresponding “phase-vanishing” problem. The evolution of the curved water-air and the water-ice interfaces are captured simultaneously, and the volume expansion during the solidification owing to the density difference between water and ice agrees with the theoretical results. A two-dimensional icing case with bubbles rising is simulated. The movement and deformation of bubbles, as well as the evolution of the interfaces, effectively illustrate the complex interactions between different phases in the icing process with phase changes.

The Hashin criterion is one the most popular failure criteria for fibre reinforce composites. It is critically appraised in this paper. The most significant feature of the criterion is failure modes introduced and the assumption that failure is determined by the traction on the failure plane. For this assumption, there has never been any justification provided in the literature, except the available arguments in the Mohr criterion, where the concept of plane failure as opposed to point failure was first introduced based on this assumption. However, the arguments there were applicable only to isotropic materials and, even so, they are not without exceptions. As contradictions to the assumption in the context of composite failure, three relatively simple cases have been considered in this paper, supported by physical evidence. In each case, failure is observed in a plane on which traction vanishes completely, to which the failure cannot be attributed. The assumption is therefore unfounded both theoretically and physically for anisotropic materials, which dismisses the validity of the Hashin criterion in turn.

A novel damage evolution model for unidirectional (UD) composites is established in this paper in the context of continuum damage mechanics (CDM). It addresses matrix cracking and it is to be applied along with the damage representation established previously. The concept of damage driving force is employed based on the Helmholtz free energy. It is shown that the damage driving force can be partitioned into three parts, resembling closely three conventional modes of fracture, respectively. A damage evolution law is derived accordingly based on the newly obtained expressions of the damage driving force. The fully rationalised Tsai-Wu criterion is employed in the model for predicting the initiation of matrix cracking damage and fibre failure, assisted with the rationalised maximum stress criterion for identifying the damage modes. A mechanism is introduced to describe the unloading behaviour as a part of the proposed model. The predictions were validated against experimental results, showing good agreement with the experiments and demonstrating the capability and effectiveness of the proposed model.

Validating a failure criterion under complex stress states is important because composites often encounter multiaxial stress in practical applications, but it also helps to expose any deficiencies of the criterion in failure prediction in the presence of stress interactions. This study examines the recently formulated fully rationalized Tsai-Wu criterion for unidirectional laminates under multiaxial stress states created by ring-on-ring loading. Distinct stress distributions under this loading condition are exhibited and quantified by numerical modeling, featuring critical biaxial tension on the bottom surface and triaxial compression on the top surface. The fully rationalized Tsai-Wu criterion and the original Tsai-Wu criterion are used to predict failure, with the results indicating good agreement between the former and experimental data. In comparison with the latter, quadric failure surfaces of the two criteria are constructed to analyze differences in prediction. The findings demonstrate the validity of the rationalization work for the Tsai-Wu criterion and its potential in predicting failure under multiaxial stress states.

Existing failure criteria for orthotropic materials are subject to an underlying assumption which cause contradictions when applied to genuinely orthotropic materials that are significantly anisotropic in elasticity as well as in strengths. For such materials, there is lack of consistent failure criteria to support their applications in engineering structures. A general quadratic failure criterion tends to leave undetermined coefficients for interactive terms. A rational approach is adopted in this paper based on mathematical and logical considerations to determine these coefficients as the objective of this paper. Considerations are based on the intrinsic characteristics of the quadric surfaces introduced by the quadratic failure criterion. These coefficients must take the values as obtained, leaving no alternatives if logic prevails. The obtained criterion integrates for the first time a range of criteria separately formulated for materials of different degrees of anisotropy, from genuinely orthotropic, through transversely isotropic, cubically symmetric, to completely isotropic ones with different or identical tensile and compression strengths.

When stress invariants up to the second order are employed to construct failure criterion for brittle materials, it involves three independent terms and therefore there are three coefficients to be determined. However, there are only two conditions available associated with the strengths under uniaxial tension and compression. Systematic examinations have given to the invariants of the failure envelope as a quadric surface according to analytic geometry. For the failure envelope to meet the basic assumptions, in particular, infinite strength under and only under hydrostatic compression, one of the coefficients can be eliminated based on rigorous mathematical inferences. As a result, it reproduces the Raghava-Caddell-Yeh criterion, which has never been rationally established before but is now in this paper. The failure envelope takes the form of circular paraboloid for brittle materials in general. The criterion degenerates to the von Mises criterion, giving a circular cylindrical failure envelope for ductile materials as a special case. It is as rational as the von Mises criterion in the sense that the assumptions made and the conditions available are logically sufficient for the complete establishment of the failure criterion without any ambiguity.

This article is intended to reconcile the stress-based and strain-based formulations for material failure criteria, where a long-standing and deep division is present. The two approaches do not naturally agree with each other, and they do not genuinely complement each other, either. Most popular criteria are stress-based when originally proposed, including the maximum stress, Tresca, von Mises, Raghava–Caddell–Yeh and the Mohr criteria. Their formulations are unique and self-consistent, i.e. capable of reproducing the input data. Their strain-based counterparts, with the maximum strain criterion being considered as the strain-based counterpart of the maximum stress criterion, are neither unique nor necessarily self-consistent. It has been proven in this article that the self-consistent ones reproduce their respective stress-based counterparts identically in effect with a disadvantage of requiring an additional material property to apply, without a single benefit. For the Mohr criterion as a special case, a strain-based counterpart is simply infeasible in general. All undesirable features of strain-based criteria are rooted in a single source: the failure strains can only be measured under a uniaxial stress state, which corresponds to a combined strain state in general, not a uniaxial strain state! Given the arguments presented, the reconciliation proves to be biased completely towards the stress-based side if mathematics, logic and common sense prevail over perception and prejudice.

Weft tows in 3D woven composites are commonly approximated as perfectly straight, but their undulations are inevitable in reality, although the extent of undulations in the weft tows is not as pronounced as in the warp tows. Such minor undulations in weft tows have been simulated in this paper. A previously established parametrised modelling and analysis tool for 3D woven composites has been extended to reproduce the varying geometry of the weft tows. Two novel models have been proposed to introduce the undulations, allowing their effects to be simulated. The analysis reveals that, compared to the model with straight weft tows, the effective elastic properties can be affected by the weft tow undulations. In addition, the procedure for defining varying intra-tow fibre orientation was formulated and implemented, addressing lack of consistent and robust functionalities of this kind in modern finite element solvers.