When simulating pressure-driven fracture with the Finite Element Method (FEM), significant difficulties can arise upon representing newly formed complex damage surfaces and their concurrent crack face loading. Application of this loading can also be required when additional physics is involved as in the case of hydraulic fracture where fluid physics inside a damage need to be considered. This paper presents a new Finite Element based practical numerical framework which can model pressure-driven fractures as they form on-the-fly without remeshing. The exact location of physical discontinuities passing through the element domain can be represented in the numerical model. The numerical framework can be implemented as a user-defined element and can be integrated into any FE package. A new element (called pressure element) is formulated with the capability to apply pressure and associated forces onto the crack surfaces in an adaptive manner. This element is verified using relevant examples from literature. The framework can also be configured for multi-physics problems where crack face loading is dictated by an additional physics. The element formulation is then extended for multi-physics problems involving fluid–solid interaction. The formulation provides the capability for multi-physics coupling adaptively as the crack propagates. The element is used to successfully simulate a test case from literature using different solution procedures (iterative and simultaneous). This element is also used to model failure in different pressure vessel problems to demonstrate its potential use in structural applications. A new higher-scale vessel element is developed which can represent different size, partitioning and failure states of composite vessel systems at element level. Composite vessel failure involving high number of pressurized cracks and delaminations as well as their interaction is modelled, and burst pressures are predicted for different vessel systems. The proposed numerical framework can be used towards designing more damage-tolerant vessels critical for the sustainable propulsion technologies.

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The objective of this work is to develop a microstructure-based simulation approach to assess the fatigue life of solder joints that are used by the microelectronics industry. The developed approach can generate solder joints with random grain morphologies by means of 3D Voronoi tessellation. The anisotropic material behavior of each grain is described by the Garofalo creep equation combined with Hill's definition of the equivalent stress for anisotropic materials. Grain boundaries are implemented as interface elements, with an isotropic creep constitutive model. The stochastic variability in the creep response of solder joints was qualitatively estimated by generating 100 unique solder joints containing 5 to 9 grains, each having a random material orientation. These joints were independently loaded with a realistic stress level for microelectronic products during thermal cycling. The volume-averaged creep strain energy density in the solder joints was used to predict the fatigue life of the solder joints. The results showed a factor of ~4 difference in expected lifetime of the individual solder joints. Next, nine randomly picked solder joints from the above-mentioned pool of 100 were sandwiched between a silicon die and a printed circuit board to form a simulation model of a Wafer-Level Chip-Scale package (WLCSP). The creep strain energy density in the joints was computed for 34 unique cases of the WLCSP. A factor of ~2.5 between the highest and lowest estimate for the solder joint life was found. The slope of the corresponding Weibull distribution equals ~6, which falls within the slopes typical reported for solder joint reliability of WLCSPs.

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This study aims to develop a model to predict the burst pressure of a dry filament wound cord-rubber composite pressure vessel under hydrostatic internal pressurization using a submodelling based global–local FEA model. The model links the global displacements of a rebar-based model to obtain the local deformation state in a single rhomboidal representative volume. Emphasis is placed on capturing the local stress concentrations in the fibers due to the unique filament winding mosaic pattern. Fiber damage is included in the local model using a maximum principle strain criteria. Verification of the created model is done experimentally on industrially manufactured burst-test specimens. Measurements for displacement during the experiments are taken photographically, while the burst pressure is captured using a pressure transducer. The final error between the burst pressure of the samples and the experimental demonstrators is approximately 6.5%, a marked improvement over conventional models with truss and rebar elements as fibers.

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The wide adoption of composite structures in the aerospace industry requires reliable numerical methods to account for the effects of various damage mechanisms, including delamination. Cohesive elements are a versatile and physically representative way of modelling delamination. However, using their standard form which conforms to solid substrate elements, multiple elements are required in the narrow cohesive zone, thereby requiring an excessively fine mesh and hindering the applicability in practical scenarios. The present work focuses on the implementation and testing of triangular thin plate substrate elements and compatible cohesive elements, which satisfy C¹-continuity in the domain. The improved regularity meets the continuity requirement coming from the Kirchhoff Plate Theory and the triangular shape allows for conformity to complex geometries. The overall model is validated for mode I delamination, the case with the smallest cohesive zone. Very accurate predictions of the limit load and crack propagation phase are achieved, using elements as large as 11 times the cohesive zone.

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As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters, which is typically the second phase in a common bi-level optimization procedure for minimizing the weight of composite structures. To adapt stacking sequence retrieval for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed numerical state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For the DMRG algorithm, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.

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With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem is the discrete truss sizing problem—the goal is to select the best size for each truss member so as to minimize a stress-based objective function. To make the problem compatible with quantum annealing devices, the objective function must be translated into a quadratic unconstrained binary optimization (QUBO) form. This work focuses on exploring the feasibility of making this translation. The practicality of using a quantum annealer for such optimization problems is also assessed. A method is eventually established to translate the objective function into a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger problems faces some challenges that would require further research to address@en

A numerical study on the feasibility of using patches of interface weakening or toughening material to trigger multiple delaminations toughening laminated composite structures against delamination is presented. The studies use an adaptive refinement formulation that uses cohesive elements to model delamination initiation and propagation. A DCB specimen is loaded under displacement control with two cohesive interfaces and a single pre-crack is introduced in one of them. The studies show that multiple delaminations can be initiated in the secondary originally uncracked interface by placing interface toughening patches at the main pre-cracked interface or interface weakening patches at the secondary one. The energy dissipation significantly increases compared to a standard DCB specimen featuring a single delamination. @en

In this work, Floating Node Method (FNM), first developed for fracture modelling of laminate composites, is coupled with cell-wise strain Smoothed Finite Element Method (SFEM) for modelling 2D linear elastic fracture mechanics problems. The proposed method is termed as Smoothed Floating Node Method (SFNM). In this framework, FNM is used to represent the kinematics of crack and the crack front inside the domain without the requirement of remeshing and discontinuous enrichment functions during crack growth. For smoothing, a constant smoothing function is considered over the smoothing domains through which classical domain integration changes to line integration along each boundary of the smoothing cell, hence derivative of shape functions are not required in the computation of the field gradients. The values of stress intensity factor are obtained from the SFNM solution using domain based interaction integral approach. Few standard fracture mechanics problems are considered to check the accuracy and effectiveness of the proposed method. The predictions obtained with the proposed framework improves the convergence and accuracy of the results in terms of the stress intensity factors and energy norms.

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A novel efficient numerical formulation for the analysis of multiple fatigue-driven delamination cracks is presented. A cohesive zone model is used in combination with an Adaptive Refinement Scheme (ARS) and an Adaptive Floating Node Method (A-FNM) element that refine the model effectively during the analysis. Novel techniques are proposed to track the positions of multiple crack tips and calculate the mode decomposed energy release rates for the individual crack tips using the J-integral. The method has been implemented in a Matlab finite element code and validated with single and multiple delamination cases with varying mode mixities. Comparisons with theoretically based predictions and available experimental data showcase the high accuracy of the method. The presented method lowers the computational time compared to standard, fully refined finite element models by a factor of 4–5.

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A numerical study on toughening laminated composite materials against delamination by initiating multiple interlaminar cracks is presented. Different configurations of interface toughening and weakening patches, that modify the interface properties at selected locations, are investigated as a way to trigger multiple delaminations. Both interface toughening and weakening patches can be configured to toughen the laminated material by initiating multiple delaminations. The initiation of multiple delaminations and the increase in toughness depend on the interface strengths and toughness of the patches. The main mechanisms behind the initiation of multiple delaminations for both cases are presented. An adaptive refinement method implemented within a Matlab Finite Element Analysis code that models the interfaces of the laminate with cohesive elements is used for the analyses. The adaptive refinement framework allows efficient analysis of multiple delaminations with very fine meshes at the wake of the crack tips. A discussion on the overall performance of the toughening concept, and the main parameters affecting the results, i.e. the length of the interface toughening or weakening patches, the distance of the substrate between the affected interfaces, and the material's mechanical properties, is carried out. The results presented in the paper show that a toughening effect against delamination can be achieved using interface toughening or weakening patches to onset multiple delaminations.

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Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on classical, that is, silicon-based computer hardware, becomes prohibitive. Quantum computing, though still in its infancy, holds the promise of enabling a new generation of algorithms that can execute the most cost-demanding parts of PDE solvers up to exponentially faster than classical methods, at least theoretically. Also, increasing research and availability of quantum computing hardware spurs the hope of scientists and engineers to start using quantum computers for solving PDE problems much faster than classically possible. This work reviews the contributions that deal with the application of quantum algorithms to solve PDEs in structural mechanics. The aim is not only to discuss the theoretical possibility and extent of advantage for a given PDE, boundary conditions and input/output to the solver, but also to examine the hardware requirements of the methods proposed in literature.@en

A novel and efficient numerical formulation for the modelling of multiple delaminations growth in laminated composite materials subjected to quasi-static loading is presented. The proposed formulation alleviates the high computational cost associated with models featuring cohesive elements by using a novel Adaptive Refinement Scheme and an Adaptive Floating Node Method Element to refine the model effectively during the analysis without modifying the global finite element connectivity. The formulation has been implemented in a MATLAB finite element code and validated with single and multiple delamination numerical models with varying mode mixities. The new formulation provides accurate results comparable to standard fully refined finite element models while drastically lowering the computational time of the analysis.

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With the rising number of Unmanned Aerial Systems (UAS) flying in the sky, an increase in collisions with manned aircraft seems inevitable. Since these devices are permitted to operate in airspace which they share with rotorcraft, a helicopter is certainly not retained from the risk of colliding with a UAS. The only prevailing impact related certification requirement for rotorcraft is the §29.631, which is only applicable to all larger (Part 29) rotorcraft. This requirement states that the rotorcraft must be capable of safe continuation of the flight and/or safe landing after an impact with a 1 kg bird up to the rotorcraft’s maximum horizontal velocity. In this paper, simulations have been performed in explicit Finite Element software to assess how much damage a Part 29 compliant helicopter would sustain after colliding with a UAS. For this purpose, an Agusta A-109 helicopter windshield was impacted by a DJI Phantom III quadcopter UAS under various conditions. The results of the simulations showed that the windshield would sustain severe damage after the impact. Not only would the windshield break into dangerous fragments that could enter the cockpit, parts of the UAS would also penetrate the windshield. These items could strike the crew and a safe continuation of the flight and/or safe landing following the impact cannot be guaranteed. A similar level of safety compared to the bird strike requirement in the prevailing certification requirement is therefore not assured.@en

The authors would like to point out three writing mistakes that have been found after the publication of the original paper: Equation (13) should be written as: 1 (Formula presented.) to correctly represent the intended column vector of the element's degrees of freedom. Equation (49) and (50) should be written as: 2 (Formula presented.) to keep the vector format consistent across the terms. The derivations afterwards are not affected by this change. Equation (63) should have no minus sign on the second term of the second row, that was a typographical error. The correct Equation (63) should be written as: 4 (Formula presented.) The above mistakes appear only in the writing of the manuscript, not in the actual implementation of the method. Hence, the results and conclusions in the original paper remain unchanged. ACKNOWLEDGMENT The authors would like to thank Mr. Zhe Han from Nanjing University of Aeronautics and Astronautics for pointing out some of the above mistakes.

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Tremendous efforts have been put into the study of structural integrity and the understanding of failure mechanisms in composites. Geometric non-linearity, receiving few attention in coupon-level simulations, can play an important role in the design and analysis of larger structures. This paper aims at extending the recently-developed Floating Node Method for damage analysis of laminated composites subjected to large deformations. The kinematics of strong discontinuities including interfacial delamination and matrix cracks are explicitly described in a geometrically nonlinear framework. Interactions between these two kinds of failure patterns are enabled through enriched elements equipped with floating nodes. To verify this proposed method, buckling-induced delamination and low-velocity impact damage are modelled, the results of which show good agreement with results from literature.

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Cohesive element (CE) is a well-established finite element for fracture, widely used for the modeling of delamination in composites. However, an extremely fine mesh is usually needed to resolve the cohesive zone, making CE-based delamination analysis computationally prohibitive for applications beyond the scale of lab coupons. In this work, a new CE-based method of modeling delamination in composites is proposed to overcome this cohesive zone limit on the mesh density. The proposed method makes use of slender structural elements for the plies, a compatible formulation with adaptive higher-order integration for the CEs, and the corotational formulation for geometrically nonlinear analysis. The proposed method is verified and validated on the classical benchmark problems of Mode I, II, mixed-mode delamination, a buckling-induced delamination problem and a double-delamination problem. The results show that elements much larger than the cohesive zone length can be used while retaining accuracy.

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The interaction between matrix cracks and interface delamination is a major failure mechanism in composite laminates and has been a subject of active research in recent years. Although coupled failure behaviour of composite laminates between matrix cracks and delamination has been observed in experiments, accurate modelling of this phenomenon for application in composite structures remains challenging. In this work, a three-dimensional separable cohesive element (SCE) is proposed to enable the modelling of interaction between matrix cracking and interfacial delamination in laminated fibre-reinforced composite materials. It is demonstrated that traditional cohesive elements are incapable of modelling the coupled failure mechanisms accurately if partitioning is not allowed. The SCE may be partitioned according to the configuration and geometry of matrix cracks in adjacent plies, thus maintaining appropriate connection between plies. Physically, the original interface is split and new interfaces are formed to bond the homologous cracked solids during fracturing process. The stress concentration induced by matrix cracks and the load transfer from cracked solid elements to interface cohesive element are effectively modelled. The proposed SCE is applied to model progressive failure in composite laminates and the results are found to agree with experiments.

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Design and optimisation of large structures, including the positioning of lower-level components, typically require extensive user involvement and sequential mechanical analysis/optimisation iterations. This paper presents an original method that enables adaptive positioning of lower-level models (such as components) within higher level-models (such as large structures), and that achieves a combined mechanical/optimisation problem for the design of structures with various hierarchical levels (such as the positioning of stiffeners within a wingbox). As the position of the lower-level model evolves, our proposed method does not require re-generating of the geometry, remeshing or modifying the stiffness matrix of the elements corresponding to the various hierarchical levels. Instead, we achieve the adaptive positioning via an original concept that we propose here: Floating Connector (FC) elements. In this paper, we validate the FC elements against reference purely-mechanical solutions, show that they can be combined with gradient-descent method and genetic algorithms, and that they can be applied to optimise the positioning of a stiffener runout taking into account a debonding manufacturing defect.

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Cohesive Element (CE) is a well-established finite element for fracture, widely used for the modelling of delamination in composites. However, the computational time of CE-based method is prohibitive. This is because the steep and non-smooth stress gradient in the cohesive zone requires a very fine mesh. In this context, a new type of CE is here proposed, aiming to loosen the mesh constraint and reduce the computational time. It uses a higher-order interpolation of the displacement field with rotational degree of freedom and an adaptive integration scheme based on the status of the element. The proposed CE has been validated through comparison with benchmark solutions of delamination in Mode I, Mode II and Mixed-Mode cases, and has demonstrated superior performance than standard CE in computational efficiency while retaining a high level of accuracy.

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In practical applications, the use of computational modeling has been industry-wide adopted to speed up product development as well as reduce physical testing costs. Such models of complex or large systems are, however, often computationally expensive, hence solution times of hours or more are not uncommon. Additionally, as these models are typically evaluated using blackbox solvers, the direct study of relations between design parameters renders demanding in terms of computational time and provides poor engineering insight and understanding. To address this, a modular framework integrating computation automation with the use of surrogate-based modeling, optimization and visualization techniques is presented. The framework is built in the Python programming language. Its use is illustrated on a study of the side impact response of a car body using an artificial neural network as a surrogate together with the NSGA-III genetic algorithm for optimization.

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