1,721,135 research outputs found
Some observations on the regularizing field for gradient damage models
No full textGradient enhanced material models can potentially preserve well-posedness of incremental boundary value problems also after the onset of strain softening. Gradient dependent constitutive relations are rooted in the assumption that some scalar or tensor field, which appears in the yield function, has to be enriched by adding a term involving its second-order gradient field. For gradient-dependent plasticity this term is universally accepted to be the equivalent plastic strain. For gradient-dependent damage models different choices have been presented in the literature. They all possess the desired regularization of the solution, but they are not identical as regards the structural response. In this paper the implications of the choice of the regularization field are discussed. As an example a plasticity-like damage material model is formulated. Finally, a well-known one-dimensional problem is solved analytically, and the results are compared with results obtained via other gradient approaches
Discontinuous modelling of strain localisation and failure
Full text linkThe computational simulation of failure in solids poses many challenges. A proper understanding of how structures respond under loading, both before and past the peak load, is important for safe and economical constructions. This requires numerical models for failure which are both faithful to the physical reality and mathematically well founded. A serious computational issue is that of objectivity with respect to the spatial discretisation of a problem. This requires that upon refinement of the spatial discretisation of a problem, a unique, physically meaningful result is approached. One approach to ensure objectivity with respect to spatial discretisation when simulating failure in solids is to allow displacement discontinuities in the solution. In this work, different techniques, of varying complexity, are developed to simulate displacement discontinuities which are independent of the spatial discretisation using finite elements. The different techniques are then critically evaluated. The first model examined involves adding only the effect of a displacement discontinuity to a finite element as an incompatible strain mode. This allows a traction–separation relationship to be applied at an interface and can be implemented simply in a standard finite element code. It is however shown that this type of model can be cast in an equivalent continuum format, a form which is known to be sensitive to the spatial discretisation. The second approach developed involves the addition of the Heaviside function to the underlying finite element interpolation basis. This method is based on the partition of unity concept, and allows the Heaviside function to be added locally to a finite element mesh to simulate a propagating displacement discontinuity. The approach is formulated for geometrically linear, geometrically nonlinear, quasi-static and dynamic problems. It is shown to be completely independent of the spatial discretisation. The partition of unity-based model is used also to simulate failure using a regularised strain softening model. When a critical level of inelastic deformation is reached, a displacement discontinuity is inserted. This model is better suited to modelling the entire failure process than a continuum or discontinuous model alone. Through numerical examples, it is shown that the inclusion of a displacement discontinuity during the failure process can lead to a different failure mode than for a continuum-only model
Stationary and Propagative Instabilities in Metals - A Computational Point of View
No full textCivil Engineering and Geoscience
Gradient-dependent plasticity in numerical simulation of localization phenomena
No full textArchitectur
Advanced Spatial Discretisation Strategies for Localised Failure - Mesh Adaptivity and Meshless Methods
No full textAerospace Engineerin
Wave Propagation, Localisation and Dispersion in Softening Solids
No full textCivil Engineering and Geoscience
Characterisation of fibre metal laminates under thermomechanical loadings
No full textFibre metal laminates, such as Arall or Glare, can offer improved properties compared to monolithic materials. Glare for example shows improved fatigue, residual strength, burn-through, impact and corrosion properties with respect to aluminium 2024, together with a considerable weight reduction and competitive costs. A large research program has proven the technological readiness of Glare and the fibre metal laminate has seen its application today in the primary structure of the Airbus A380 super jumbo. However, the effect of temperature on the performance of the fibre metal laminates has not been fully characterised. Differences in thermal expansion coefficients cause residual stresses after curing of the laminate. In service the temperature of the aircraft skin can vary between -55 up to 70 C due to solar radiation and convection, which will affect the thermal and mechanical properties of Glare. A detailed understanding of the behaviour of these laminates is necessary for further improvement of their performance and durability. With the increase in complexity of structures and material systems, the need for powerful design tools becomes evident. In this thesis, the thermo-mechanical behaviour of fibre metal laminates has been characterised via experimental testing and numerical modelling. Experimental tests have been performed to determine the temperature-dependent thermal and mechanical behaviour of unidirectional (UD) glass-fibre epoxy. Calculations based on these test results at room temperature and 80 C for the tension and shear stiffness of three different composite laminate lay-ups showed a good agreement with experimental test results. The UD glass-fibre epoxy data is used as input for the finite element model, together with aluminium 2024-T3 data from the literature. Glare laminates with a special lay-up have been experimentally tested to determine the effect of temperature and mechanical loadings on the laminate characteristics. The test results show that the off-axis and temperature effect can give a reduction of 24% in ultimate strength at room temperature due to off-axis loading and a further reduction of 17% at 80 C temperature. For standard Glare from the literature, where tests at elevated temperature have only been performed in fibre direction, the strength and stiffness reductions are at most 12% compared to room temperature. Numerical simulation is a very powerful tool to investigate the behaviour of materials and structures. Therefore, a thermo-mechanical finite element model, based on a solid-like shell element and including thermal expansion and heat transfer, has been developed to capture the behaviour of Glare in a fully three-dimensional state. The through-the-thickness temperature and stress distributions can thereby be determined, which allows for a straight-forward implementation of damage and plasticity models. Moreover, the solid-like shell element is ideal for thin-walled (aerospace) structures since it can have high aspect ratios without showing Poisson thickness locking, which occurs in standard continuum elements, and can have multiple layers in one element. To account for physical nonlinearities, a strain hardening model for the aluminium 2024-T3 and an orthotropic damage model for the UD glass-fibre epoxy layers in Glare are used. The strain hardening behaviour of aluminium has been modelled with a yield function based on an isotropic Von Mises plasticity formulation. An exponentially saturating hardening law has been assumed, which gives a good agreement with the experimental aluminium 2024-T3 stress-strain curve. A return-mapping algorithm is used to project the stress back onto the yield surface when the stress state violates the loading condition. The concept of continuum damage mechanics is used, with a separate damage parameter for fibre and matrix, to describe the appearance of microcracks that lead to ultimate failure. The equivalent strain measure is obtained by rewriting the yield function of the orthotropic Hoffman plasticity model into a strain-based format. The damage parameters are directly implemented into the stiffness matrix to avoid undesirable coupling terms in the damage matrix. The simulations of the shear and tensile test in transverse direction show a good fit with the experimental curves for the UD glass-fibre epoxy. The transient behaviour is captured by taking the heat capacity, inertia forces and damping into account. Park's method is used to solve the dynamic system of equations. The good performance of the thermomechanical solid-like shell element and the transient solver have been demonstrated for a single element under thermo-mechanical loadings and the snap-through of a cylindrical panel subjected to a concentrated load. Via a number of benchmark tests for practical applications the obtained numerical model is compared with the experimental test results. Bluntnotch test simulations have been performed on Glare3-3/2-0.4 and on a special Glare laminate (tested at 0, 45, 67.5, and 90 off-axis angle), which show a good agreement with experimental results. Simulations of off-axis tensile tests on a 0/90 composite, tensile tests on standard Glare laminates, and off-axis tensile tests on special Glare laminates with additional fibre layers in -45 and 45 direction, also showed a good agreement with experimental results. The thermo-mechanical solid-like shell element and the experimentally obtained material data, presented in this thesis, together create a powerful simulation tool for the effective and accurate characterisation of fibre metal laminates under thermo-mechanical loadings.Aerospace Engineerin
Foundations of Acoustic Methods Used in Non-Destructive Inspection of Laminated Materials
No full textUltrasonic inspection has become one of the most popular nondestructive testing technique because of its versatility and easy operation. It can detect internal cracks and inclusion type defects in homogeneous or layered materials, often without much difficulty. Layered materials, which are also called laminated materials, have become widely used in the aerospace industry, naval engineering and many other industries, and thus have attracted considerable interest of researchers in the last two decades. The present work can logically be subdivided into two parts: conventional ultrasonic methods and laser driven techniques. First, the conventional ultrasonic methods applied to a planar laminated structure immersed in a fluid are considered from a general point of view. Next, the study is extended to laser ultrasonic methods. An extended physical description of phenomenon of elastic wave excitation due to laser irradiation is given. Then, the focus is shifted to the directivity of laser generated ultrasound and various methods of control. As a means to achieve a narrow directivity of radiation the moving laser sources is introduced. Special properties of the radiation due to moving sources such as directivity and spectrum are described and analyzed thoroughly. Considerable part of the work is devoted to the theoretical study of ultrasound generation in laminates by moving laser sources. The following cases have been investigated: a) rectilinear motion of the laser beam; b) oscillatory motion of the beam; c)saw-tooth motion; d) uniform circular motion of the beam. Finally, in the last chapter we introduce more realistic laminates with anisotropic elastic properties. Such laminates consist of one or many fiber-reinforced lamina that are bonded together in order to achieve better structural properties and performance over conventional materials.Applied Science
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