Browsing by Author "Djordjevic, Nenad"
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Item Open Access Constitutive model for fibre reinforced composites with progressive damage based on the spectral decomposition of material stiffness tensor(Elsevier, 2022-05-11) Vignjevic, Rade; Djordjevic, Nenad; Galka, Agata; Appleby-Thomas, Gareth J.; Hughes, KevinComplex nature of the fibre reinforced composites, their non-homogeneity and anisotropy make their modelling a challenging task. Although the linear – elastic behaviour of the composites is well understood, there is still a significant uncertainty regarding prediction of damage initiation, damage evolution and material failure especially for a general loading case characterised with triaxial state of stress or strain. Consequently, simplifying assumptions are often unavoidable in development of constitutive models capable of accurately predicting damage. The approach used in this work uses decomposition of the strain energy based on spectral decomposition of the material stiffness tensor and an assumption that each strain energy component represent free energy for a characteristic deformation mode. The criteria for damage initiation are based on an assumption that the damage corresponding to a deformation mode is triggered when the strain energy for that mode exceeds a specified critical limit. In the proposed model the deformation modes are not interacting at continuum scale due to orthogonality of the eigenvectors, i.e. the stiffness tensor symmetry. Damage and its evolution are modelled by reduction of the principal material stiffness based on the effective stress concept and the hypothesis of strain energy equivalence. The constitutive model was implemented into Lawrence Livermore National Laboratory (LLNL) Dyna3d explicit hydrocode and coupled with a vector shock Equation of State. The modelling approach was verified and validated in a series of single element tests, plate impact test and high velocity impact of hard projectile impact on an aerospace grade carbon fibre reinforced plastic. The model accurately predicted material response to impact loading including the test cases characterised by presence of shock waves, e.g. the plate impact test. It was also demonstrated that the model was capable of predicting damage and delamination development in the simulation of the high velocity impact tests, where the numerical results were within 5% of the post impact experimental measurements.Item Open Access Modeling shock waves in orthotropic elastic materials(American Institute of Physics, 2008-08-01T00:00:00Z) Vignjevic, Rade; Campbell, James C.; Bourne, Neil K.; Djordjevic, NenadA constitutive relationship for modeling of shock wave propagation in orthotropic materials is proposed for nonlinear explicit transient large deformation computer codes (hydrocodes). A procedure for separation of material volumetric compression (compressibility effects equation of state) from deviatoric strain effects is formulated, which allows for the consistent calculation of stresses in the elastic regime as well as in the presence of shock waves. According to this procedure the pressure is defined as the state of stress that results in only volumetric deformation, and consequently is a diagonal second order tensor. As reported by Anderson et al. [Comput. Mech.15, 201 (1994)], the shock response of an orthotropic material cannot be accurately predicted using the conventional decomposition of the stress tensor into isotropic and deviatoric parts. This paper presents two different stress decompositions based on the assumption that the stress tensor is split into two components: one component is due to volumetric strain and the other is due to deviatoric strain. Both decompositions are rigorously derived. In order to test their ability to describe shock propagation in orthotropic materials, both algorithms were implemented in a hydrocode and their predictions were compared to experimental plate impact data. The material considered was a carbon fiber reinforced epoxy material, which was tested in both the through-thickness and longitudinal directions. The psi decomposition showed good agreement with the physical behavior of the considered material, while the zdeta decomposition significantly overestimated the longitudinal stresses.Item Open Access Modelling of Dynamic Behaviour of Orthotropic Metals Including Damage and Failure(Elsevier Science B.V., Amsterdam., 2012-11-01T00:00:00Z) Vignjevic, Rade; Djordjevic, Nenad; Panov, ViliA physically based material model for metals, with elastic plastic and damage/failure orthotropy is proposed in this paper. The model is defined within the frameworks of irreversible thermodynamics and configurational continuum mechanics and integrated in the isoclinic configuration. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Klepaczko (Klepaczko, 1990) was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model (Follansbee and Kocks, 1988; Chen and Gray, 1996; Goto et al., 2000; Gray et al., 1999; Chen et al., 1998) which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a shock equation of state which allows for modelling of shock wave propagation in the material. The new model was implemented in DYNA3D and our in-house non-linear transient SPH code, MCM (Meshless Continuum Mechanics). Parameters for the new constitutive model for AA7010 (a polycrystalline aluminium alloy, whose orthotropy is a consequence of grain morphology), were derived on the basis of the tensile tests and Taylor anvil tests. The tensile tests were performed for the range of temperatures between 343.15K and 413.15K, and strain rates between and . The new model was validated in two stages. The first stage comprised a series of single element tests design to separately validate elasticity, plasticity and damage related parts of the model. The second stage comprised a series of numerical simulations of Taylor anvil and plate impact tests for AA7010 and comparison of the numerical results with the experimental data. The numerical results illustrate the ability of the new model to predict experimentally observed behaviour.Item Open Access Modelling of dynamic damage and failure in aluminium alloys(Elsevier Science B.V., Amsterdam., 2012-11-30T00:00:00Z) Vignjevic, Rade; Djordjevic, Nenad; Campbell, James C.; Panov, ViliA physically based damage and failure model, applicable to orthotropic metals is proposed in this paper. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Klepaczko [1], has been adopted as the basis for the model. This assumption makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model [2-6], which was used within the overall constitutive model to describe material behaviour in the plastic regime. A shock equation of state [7] was coupled with the rest of the constitutive model to allow for modelling of shock wave propagation in the material. The new model was implemented in DYNA3D [8] and coupled with our in-house non-linear transient SPH code, MCM (Meshless Continuum Mechanics). Parameters for the new constitutive model, i.e. parameters for the plasticity model and the damage model, were derived on the basis of the uniaxial tensile tests and Taylor anvil tests. The subject of investigation is a polycrystalline aluminium alloy AA7010, whose orthotropy is a consequence of meso-scale phase distribution, or grain morphology. Tensile tests were performed for the range of temperatures between and , and strain rates between and . In order to validate the new damage model, a numerical simulation of Taylor anvil tests has been performed for AA7010, using a single stage gas gun at velocity of . The numerical analysis clearly demonstrates the ability of this new model to predict experimentally observed damage and failure.Item Open Access A numerical study on the influence of internal corrugated reinforcements on the biaxial bending collapse of thin-walled beams(Elsevier, 2019-07-25) Vignjevic, Rade; Liang, Ce; Hughes, Kevin; Brown, Jason C.; De Vuyst, Tom; Djordjevic, Nenad; Campbell, James C.The Heat Treatment Forming and in-die Quench (HFQ) process allows for manufacturing of more complex geometries from Aluminium sheets than ever before, which can be exploited in lightweight automotive and aerospace structures. One possible application is manufacturing thin walled beams with corrugated internal reinforcements for complex geometries. This work considers different internal reinforcements (C-section and corrugated) to improve the energy absorption properties of thin walled rectangular beams under uniaxial and biaxial deep bending collapse, for loading angles ranging from 0 to 90 deg, in 15° increments. Using LS-DYNA simulations experimentally validated through unreinforced metallic tubes under quasi-static bending collapse, the finite element results demonstrate the stabilising effect of the reinforcements and an increase in the buckling strength of the cross section. Corrugated reinforcements showed a greater potential for increasing specific energy absorption (SEA), which was supported by investigating key geometric parameters, including corrugation angle, depth and number. This favourable response is due to an increased amount of material undergoing plastic deformation, which consequently improves performance of the beam undergoing post buckling and deep collapse. This concept is applicable to vehicle and aircraft passive safety, with the requirement that the considered geometries are manufacturable from Aluminium Alloys sheet only, using the HFQ process