This study presents the application of a 3D Finite Fracture Mechanics (FFM) criterion for predicting fatigue life estimation of laminates exhibiting free edge effects. The proposed 3D FFM fatigue criterion incorporates interface properties such as the critical interlaminar stress and the incremental energy release rate as functions of the number of cycles. Material constants calibration involves computing critical interlaminar stress using effective stress distribution over an average delamination onset width while assuming a quadratic relation between critical incremental energy release rate and nominal remote maximum stress cycle. The 3D FFM fatigue criterion system of equations consists of two inequalities solved for a unique solution by assuming homothetic crack extension and utilising a non-linear constraint optimisation. The proposed methodology predicts that lower angles of ply orientation in angle-ply laminates exhibit greater finite fatigue life for a given remote cyclic load. Predictions of fatigue life estimation align well with the experimental results from the literature.

Measuring mode II fracture toughness at a dissimilar interface using the Transverse Crack Tensile may be challenging, particularly if geometric and elastic symmetry conditions are not maintained during crack propagation. Building on previous results, the authors propose to extend the modified Transverse Crack Tensile test setup to hybrid interfaces. A preliminary parametric calibration was carried out to determine key design parameters. The proposed method was experimentally validated through mechanical testing with the assistance of DIC to evaluate the full-field strain. A Finite Element model was appropriately implemented to study the extension of potential plastic zones. The results obtained for the chosen metal-composite interface demonstrate that the proposed test setup can be successfully extended to hybrid interfaces, confirming its robustness. Additionally, guidelines for the design of the test samples are provided.

Graded lattice structures have garnered significant attention for their ability to combine lightweight properties with superior mechanical performance. Their tailored structures/properties under in-plane loading make them ideal for impact resistance and energy absorption (EA) applications in aerospace, automotive, and biomedical engineering. Despite the research advances in this field, research into out-of-plane of graded lattice structures is relatively limited. This study investigates the out-of-plane EA performance of three common lattice structures, namely, hexagonal honeycomb (HEX), auxetic re-entrant (REE), and double arrowhead (DAH). Unique grade patterns including bottom thick (BOT), mid thick (MID), and ends thick (EDG), were introduced in the lattices' out-of-plane direction and their mechanical behavior was examined under quasi-static compression conditions using both experimental and finite element analysis. Parametric investigations were conducted to examine the effects of grade ratio, cell wall thickness, and grade patterns, aiming to optimize mechanical EA and crashworthiness of each structure. Results show that the specific energy absorption (SEA) of all structures follows the trend MID > EDGE > BOT > UNI and HEX_MID demonstrated the highest SEA value amongst all designs. On the other hand, all graded lattice structures demonstrated significantly enhanced crash force efficiency, with HEX_BOT, REE_EDGE, and DAH_EDGE approaching similar to 90% of the maximum performance, showcasing their potential for efficient EA.

The material mismatch between the dissimilarly oriented plies within laminated structures induces localised singular interlaminar stresses at free edges, under various loading conditions such as mechanical, moisture, or thermal. These interlaminar stresses lead to premature interlaminar cracking. This study introduces the application of Finite Fracture Mechanics (FFM) for predicting free edge delamination in angle-ply laminates under uniform thermal loading. The current framework assumes nucleation of semi-elliptically shaped crack at the dissimilar interface, resulting in a 3D FFM criterion. For a given material intrinsic properties, e.g. interlaminar fracture toughness and strength, calculation of quantities such as interlaminar stresses and incremental energy release rates are required. These quantities, necessary for the evaluation of the FFM criterion, are determined semi-analytically through expressions derived from dimensional analysis and finite element models. Dimensional analysis facilitates the finding of these quantities only once using non-dimensionalised functions. The resulting non-dimensionalised functions for stresses and energy release rates are not a function of thermal load and ply thickness. This eliminates the requirement to re-solve the underlying boundary value problem for varying loads and ply thicknesses. The accuracy of finite element models is confirmed against results from models available in literature and dimensional analysis is validated against numerical solutions. The 3D FFM system is solved by assuming a homothetic crack extension and is implemented as a standard constrained nonlinear optimisation problem. In addition to the 3D FFM, another model based on the Theory of Critical Distances (TCD) is employed for validation purposes. The predictions from both the 3D FFM and TCD are compared to those from models available in the literature.

The layered structures exhibit a weakly singular stress state in the vicinity of free edges, attributable to the elastic mismatch of adjacent plies, thereby promoting delamination. In the present study, this so-called free edge effect is investigated for symmetric angle-ply laminates in the framework of the Finite Fracture Mechanics (FFM). For a given intrinsic properties, such as fracture toughness and strength, the computation of the interlaminar stresses and energy release rate is imperative for the evaluation of coupled FFM criterion. These quantities are determined in terms of non-dimensionalised functions employing a comprehensive three-dimensional Finite Element Method (FEM) model. Dimensional analysis facilitates finding these functions for all laminate configurations only once while preserving the generality of functions. A semi-elliptically shaped crack is presumed to nucleate at the dissimilar interface post-crack initiation. Given that, the considered crack has two dimensions, the solution of 3D FFM model leads to an optimisation problem. It is hypothesised that homothetic crack extensions occur, i.e., cracks extend only in a self-similar manner, maintaining a constant aspect ratio of semi-ellipse. For validation purposes, the prediction of the laminate fracture using proposed 3D FFM fracture criterion is compared with the experimental test results found in the literature for various laminate types (AS1/3501-6, T800/914, G947/M18) and layups ([±10n]s, [±15n]s, [±20n]s, [±30n]s). It is observed that close agreement can be achieved between prediction and experiments when intrinsic properties are known.

This study investigated the fracture characteristics of hybrid laminates consisting of CorTen steel and carbon fibre-reinforced polymer composites under quasi-static loading, both experimentally and numerically. The hybrid laminates are classified into two groups: one featuring alternative overlaying of steel and composite, and the other with symmetric cross-ply and angle-ply configurations overlaid within steel layers. The effects of layup sequence and composite-layer ply orientation on the fracture behaviour are examined. Experimental results revealed these factors influenced the fracture behaviour and load-carrying capacity. A semi-analytical framework is developed to determine the interlaminar stresses and assess interfaces susceptible to delamination, identifying whether these stresses are primary or secondary factors (combined with other fracture modes) in the experimentally observed fracture mechanisms. Angle-ply laminates, known for exhibiting mode III delamination at dissimilar interfaces, served as a baseline configuration to establish a “characteristic distance” for the average stress fracture criterion. This criterion is first utilised to predict mode III delamination in angle-ply laminates and subsequently, using the same characteristic distance in the quadratic average stress criterion, for mixed-mode I/III delamination in hybrid laminates. The predicted fracture stresses closely agreed the experimental results.

Traditional approaches that rely on stress or energy-based criteria to predict delamination require the determination of stresses before crack onset or energy release rates after crack initiation, respectively. While a relatively new coupled criterion, Finite Fracture Mechanics, necessitates the computation of both stresses and energy release rates. This study discusses the numerical determination of the interlaminar stresses and energy release rates of interlaminar semi-elliptical cracks emanating at the free edge in carbon fibre-reinforced polymer materials. The method establishes a new semi-analytical framework, based on dimensional analysis, which permits obtaining a functional expression for the stresses and the energy release rates in function of material and geometrical parameters. This framework eliminates the need to re-solve the underlying boundary value problem for a different material, geometry, and load. The non-dimensional functions are obtained by performing careful interpolation from a set of finite element solutions, ensuring predictions are accurate and within acceptable numerical limits. The influence of material contrast and relative ply thickness on interlaminar stresses and energy release rates are investigated using the semi-analytical framework. Additionally, the fracture mechanics analysis is also conducted to investigate the influence of semi-axes of semi-elliptical crack on energy release rate distributions. Understanding the interlaminar stresses and energy release rates is essential for applying either stress, energy, or coupled criterion to predict the structural strength of a layered body.

A novel Overset Improved Element-Free Galerkin-Finite Element Method (Ov-IEFG-FEM) for solving transient heat conduction problems with concentrated moving heat sources is introduced in this communication. The method is a mesh-less/mesh-based chimera-type approach that utilises a coarse finite element mesh to discretise the problem geometry, while a separate set of overlapping nodes (patch nodes) moves with the heat source to capture the marked thermal gradients with higher accuracy using the Improved Element-Free Galerkin (IEFG) technique. Outside of the heat source area, where accuracy requirements are significantly lower, the thermal problem is solved using the Finite Element Method (FEM). The approach involves solving the problem over these two overlapping computational domains and transferring numerical information between the approximations performed on both. Such transfer of information occurs through immersed boundaries that are properly defined, enabling straightforward achievement of accurate results. The proposed Ov-IEFG-FEM is conceived to provide an enriched solution by appropriately coupling the temperature fields computed on the patch nodes and the coarse background mesh using IEFG and FEM, respectively. A comprehensive explanation concerning the appropriate coupling between the temperature fields of both the coarse background finite element mesh and the fine arrangement of moving patch nodes for the IEFG computations, is also provided in this communication. Numerical experiments demonstrate the method effectiveness in accurately and efficiently solving transient heat conduction problems with concentrated moving heat sources.

Laminates experience three-dimensional singular stress near their free edges due to elastic mismatches between layers, which can cause delamination. This paper critically evaluates methods for predicting free edge delamination and highlights the limitations of conventional strength-of-materials and fracture mechanics approaches. The Theory of Critical Distances (TCD) uses a material-dependent critical distance parameter, while Finite Fracture Mechanics (FFM) employs a combined stress-energy criterion without needing a predefined length parameter. This review compares TCD and FFM, also discussing Cohesive Zone Models and Phase-Field Models, and aims to guide the selection of appropriate methods for analyzing free edge delamination.

This paper presents volume-constrained stress minimization-based, topology optimization. The maximum entropy (maxent) basis functions-based meshless method for two-dimensional linear elastic structures is explored. This work focuses to test the effectiveness of the meshless method in handling the stress singularities during the topology optimization process. The commonly used moving least square basis functions are replaced with maximum entropy basis functions, as the latter possess weak Kronecker delta property which leads to the finite element method (FEM) like displacement boundary conditions imposition. The maxent basis functions are calculated once at the beginning of the simulation and then used in optimization at every iteration. Young’s modulus for each background cell is interpolated using the modified solid isotropic material with penalization approach. An open source pre-processor CUBIT is used. A comparison of the proposed approach with the FEM is carried out using a diverse set of problems with simple and complex geometries of structured and unstructured discretization, to establish that maxent-based meshless methods perform better in tackling the stress singularities due to its smooth stress field.

This study presents a data-driven, probability embedded approach for the failure prediction of IM7/8552 unidirectional carbon fibre reinforced polymer (CFRP) composite materials under biaxial stress states based on micromechanical modelling and artificial neural networks (ANNs). High-fidelity 3D representative volume element (RVE) finite element models were used for the generation of failure points. Fibre failure and the friction between fibres and matrix after fibre/matrix debonding were taken into consideration and implemented as VUMAT subroutines, respectively. Uncertainty quantification was conducted based on a coupled experimental–numerical approach and failure probabilities were inserted into the failure points to generate the database for the training of ANNs. A total of 15 biaxial stress combinations were considered for the generation of datasets. Two strategies were considered for the construction of form-free failure criteria based on the ANNs for regression and classification problems. It is found that for the regression problems, an ANN model with 2 hidden layers and 64 neurons can achieve a mean square error (MSE) of 0.027% and a mean absolute error (MAE) of 0.78%. For the classification problems, an ANN model with 3 hidden layers and 32 neurons, presents an excellent performance in the prediction with a probability of 98.1%. A good agreement was observed between the failure strength of composites under transverse and in-plane shear predicted by these ANNs and failure envelopes theoretically predicted by Tsai–Wu and Hashin failure criteria.

Here you can find input mesh files, parameter files, output files and animations for numerical examples considered in the paper entitled "A computational framework for crack propagation along contact interfaces and surfaces under load" submitted to Computer Methods in Applied Mechanics and Engineering.

We present the first implicit computational framework for simulating crack propagation along contact interfaces and surfaces under load in three-dimensional bodies, which is distinct from modelling the contact interaction associated with crack closure. We restrict ourselves to brittle fracture and frictionless contact and focus on numerical challenges associated with the coupling of unilateral constraints emerging from the Griffith’s criterion and the contact conditions. The formulation is based on the configurational mechanics framework and is solved using the finite element method. The approach utilises a monolithic Arbitrary Lagrangian–Eulerian formulation permitting simultaneous resolution of crack propagation and unilateral contact constraints. Contact is embedded in the model using the well-known mortar contact formulation. Evolving cracks are explicitly modelled as displacement discontinuities within the mesh. Heterogeneous approximation of arbitrary order is used to discretise spatial displacements, enabling hp-adaptive refinement around the crack front and the contact interfaces traversed by the crack. The result is a holistic approach which handles issues associated with thermodynamic consistency, numerical accuracy and robustness of the computational scheme. Several numerical examples are presented to verify the model formulation and implementation; they also highlight how contact pressure and load applied on surfaces traversed by cracks influence their propagation. The robustness of the approach is validated by comparison of our simulations with existing numerical results and an industrial experiment involving cracks of complex morphologies propagating along contact interfaces between multiple deformable bodies.

Topology optimization is a renowned structural optimization approach used to compute the optimal topology for the enhancement of structural performance. It has been in common practice in different engineering fields such as automobile and aerospace. However, there still exist gaps between topology optimization and its engineering operations, which considerably impedes topology optimization’s applications. One of these gaps is how to make (especially finite element-based) topology optimization results machine-readable, which means, how to transform these into computer-aided design (CAD) models, which are ready-to-use models for manufacturing. In the proposed work the authors adopted a unique methodology that plugs the gap between topology optimization and manufacturing. This methodology seamlessly integrates the structural analysis tool, boundary description tool and standard CAD geometry representation; equipped with the Hausdorff distance approach for 3D printing/additive manufacturing of optimal structures. Initially, we extract the skeleton of the optimal design (in the form of a points cloud) using the level set method, followed by an interpolation technique with shape preservation property, the extracted skeleton is made dense. Incorporating the shape and curvature information of the data set, an adaptive B-spline approximation is devised for fitting a smooth curve through the points cloud. This approach interprets topology optimization results as a parametric CAD model with minimum possible control points and minimum approximation error. The CAD-based optimal designs are then used for additive manufacturing. The numerical results exhibit in detail the validity and accuracy of the proposed method.

Inter-fibre failure analysis of carbon fibre-reinforced polymer (CFRP) composites, under biaxial loading conditions, has been a longstanding challenge and is addressed in this study. Biaxial failure analysis of IM7/8552 CFRP unidirectional (UD) composites is conducted under various stress states. Two widely accepted failure criteria, the interactive Tsai-Wu and non-interactive Hashin failure criteria, are comprehensively assessed with finite element-based micromechanical analysis. High-fidelity three-dimensional representative volume elements (RVEs) are subjected to biaxial loadings with imposed periodic boundary conditions. Carbon fibres are assumed to be transversely isotropic and linearly elastic. The Drucker-Prager plastic damage constitutive model and cohesive zone model are utilised to simulate the mechanical response of the matrix and fibre-matrix interface, respectively. Coulomb friction is assumed between the fibres and matrix after interface failure. Two sets of biaxial loading scenarios (i.e. transverse stress dominated and shear stress dominated) with the associated failure modes are selected for the failure analysis and assessment of these failure criteria. A data-driven failure envelope for the composites under biaxial loadings is developed using a univariate cubic spline function. Failure mode transition points are determined under biaxial loadings. It is found that the micromechanics-based numerical model is effective in assessing these two existing criteria.

A novel finite element modelling approach is presented which incorporates representative binder yarn compaction, for simulating the low-velocity impact (LVI) and compression after impact (CAI) response of 3D woven layer-to-layer carbon/epoxy composite architectures. Simulations of out-of-plane drop-weight impact tests were performed at energies of 32 J and 42 J. Warp and weft layers were modelled as continuous plies and three different approaches were explored to model the binder reinforcement; (i) with a rectangular cross-section and non-compacted, (ii) with an elliptical cross-section and non-compacted, and (iii) an elliptical cross-section which accounts for compaction. Predictions were compared with experimental results from literature and it is shown that modelling the binder reinforcement as an elliptical cross-section with compaction leads to a predicted damage area, on the impacted side, which is within 2%, and the non-impacted side within 6% of experimental measurements. The predicted CAI strength is within 11% of the experimental values.

In this paper, proportional topology optimisation (PTO) with maximum entropy (maxent)-based meshless method is presented for two-dimensional linear elastic structures for both minimum compliance (PTOc) and stress constraint (PTOs) problems. The computation of maxent basis functions is efficient as compared to the standard moving least square (MLS) and possesses a weak Kronecker delta property leading to straightforward imposition of Dirichlet boundary conditions. The PTO is a simple, non-gradient, accurate, and efficient method compared to the standard topology optimisation methods. A detailed and efficient implementation of the computational algorithms for both PTOc and PTOs is presented. The maxent basis functions are calculated only once at the start of simulation and used in each optimisation iteration. Young's modulus for each background cells is calculated using the modified solid isotropic material with penalisation (SIMP) method. A parametric study is also conducted on the degree of proportionality and history dependence of both PTOc and PTOs algorithms. A variety of numerical examples with simple and complex geometries, and structured and unstructured discretisations are presented to show the accuracy, efficiency, and robustness of the developed computational algorithms. Both PTOc and PTOs algorithms can handle large topological changes, and provide excellent optimisation convergence characteristics.

This paper presents a meshless element-free Galerkin method coupled with the radial basis functions (RBFs)-based level set algorithm for topology optimization. The meshless approach provides the structural response and corresponding sensitivities at nodal/grid points, and the solution of RBFs-based level set formulation updates the structural geometry accordingly. Thus, this unique and novel approach allows solution of the optimization problems using a single discretization scheme for both the meshless and the level set methods. A special technique is proposed for the identification of meshless nodal points within the solid and void regions of the structural geometry. The present method handles the appropriate topological modifications, i.e. hole creation, splitting, merging, etc., affectively. Optimal solutions of the benchmark problems suggest reliability and compatibility of the proposed approach versus the mesh-based techniques available within the structural optimization literature.

This paper focuses on the utilization of local radial basis functions (LRBFs) based level set method (LSM) for topology optimization of two-dimensional thermal problems using both concentrated as well as uniformly distributed heat generation. The design domain is embedded implicitly into a higher-dimensional function, which is parametrized with the LRBFs through an explicit scheme. This novel combination of LRBFs and LSM has the capability of controlling the topological variations automatically, i.e., hole insertion, merging with each other and with the boundary. The governing equations of heat conduction system are solved with the finite element method to obtain the sensitivities at level set grid points as a velocity field for evolution of the structural geometry. The objective function is set to the heat transfer potential with the maximum material volume as the design constraint. Several experiments are conducted on benchmark test problems and the resulting optimal solutions reveals efficiency, convergence and good agreement with those reported in the literature.