An application of bi-directional evolutionary structural optimisation for optimising energy absorbing structures using a material damage model

The Bi-directional Evolutionary Structural Optimisation (BESO) method is a numerical topology optimisation method developed for use in finite element analysis. This paper presents a particular application of the BESO method to optimise the energy absorbing capability of metallic structures. The optimisation objective is to evolve a structural geometry of minimum mass while ensuring that the kinetic energy of an impacting projectile is reduced to a level which prevents perforation. Individual elements in a finite element mesh are deleted when a prescribed damage criterion is exceeded. An energy absorbing structure subjected to projectile impact will fail once the level of damage results in a critical perforation size. It is therefore necessary to constrain an optimisation algorithm from producing such candidate solutions. An algorithm to detect perforation was implemented within a BESO framework which incorporated a ductile material damage model.

Modelling Static and Dynamic FRP-Concrete Bond Behaviour Using a Local Concrete Damage Model

This paper presents a study on the bond behaviour of FRP-concrete bonded joints under static and dynamic loadings, by developing a meso-scale finite element model using the K&C concrete damage model in LS-DYNA. A significant number of single shear experiments under static pull-off loading were modelled with an extensive parametric study covering key factors in the K&C model, including the crack band width, the compressive fracture energy and the shear dilatation factor. It is demonstrated that the developed model can satisfactorily simulate the static debonding behaviour, in terms of mesh objectivity, the load-carrying capacity and the local bond-slip behaviour, provided that proper consideration is given to the selection of crack band width and shear dilatation factor. A preliminary study of the effect of the dynamic loading rate on the debonding behaviour was also conducted by considering a dynamic increase factor (DIF) for the concrete strength as a function of strain rate. It is shown that a higher loading rate leads to a higher load-carrying capacity, a longer effective bond length, and a larger damaged area of concrete in the single shear loading scenario.

Numerical considerations for the implementation of a comprehensive composite damage model

A comprehensive continuum damage mechanics model [1] had been developed to capture the detailed
behaviour of a composite structure under a crushing load. This paper explores some of the difficulties
encountered in the implementation of this model and their mitigation. The use of reduced integration
element and a strain softening model both negatively affect the accuracy and stability of the
simulation. Damage localisation effects demanded an accurate measure of characteristic length. A
robust algorithm for determining the characteristic length was implemented. Testing showed that this
algorithm produced marked improvements over the use of the default characteristic length provided
by Abaqus. Zero-energy or hourglass modes, in reduced integration elements, led to reduced
resistance to bending. This was compounded by the strain softening model, which led to the formation
of elements with little resistance to deformation that could invert if left unchecked. It was shown,
through benchmark testing, that by deleting elements with excess distortions and controlling the mesh
using inbuilt distortion/hourglass controls, these issues can be alleviated. These techniques
contributed significantly to the viability and usability of the damage model.

Validation of a 3D damage model for predicting the response of composite structures under crushing loads

A 3D intralaminar continuum damage mechanics based material model, combining damage mode interaction and material nonlinearity, was developed to predict the damage response of composite structures undergoing crush loading. This model captures the structural response without the need for calibration of experimentally determined material parameters. When used in the design of energy absorbing composite structures, it can reduce the dependence on physical testing. This paper validates this model against experimental data obtained from the literature and in-house testing. Results show that the model can predict the force response of the crushed composite structures with good accuracy. The simulated energy absorption in each test case was within 12% of the experimental value. Post-crush deformation and the damage morphologies, such as ply splitting, splaying and breakage, were also accurately reproduced. This study establishes the capability of this damage model for predicting the responses of composite structures under crushing loads.

Verification of a novel material model to predict damage in composite structures

An intralaminar damage model (IDM), based on continuum damage mechanics, was developed for the simulation of composite structures subjected to damaging loads. This model can capture the complex intralaminar damage mechanisms, accounting for mode interactions, and delaminations. Its development is driven by a requirement for reliable crush simulations to design composite structures with a high specific energy absorption. This IDM was implemented as a user subroutine within the commercial finite element package, Abaqus/Explicit[1]. In this paper, the validation of the IDM is presented using two test cases. Firstly, the IDM is benchmarked against published data for a blunt notched specimen under uniaxial tensile loading, comparing the failure strength as well as showing the damage. Secondly, the crush response of a set of tulip-triggered composite cylinders was obtained experimentally. The crush loading and the associated energy of the specimen is compared with the FE model prediction. These test cases show that the developed IDM is able to capture the structural response with satisfactory accuracy

Fatigue Damage of Composite Structures Applying a Micromechanical Approach

Fatigue damage calculations of unidirectional polymer composites is presented applying micromechanics theory. An orthotropic micromechanical damage model is integrated with an isotropic fatigue evolution model to predict the micromechanical fatigue damage of the composite structure. The orthotropic micromechanical damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. The advantage of using this approach is the cheap determination of model parameters since the orthotropic damage model parameters can be determined using available data from quasi-static loading tests. Decomposition of the state variables down to the constituent scale is accomplished by micromechanics theory. Phenomenological damage evolution models are then postulated for each constituent and for interphase among them. Comparison between model predictions and experimental data is presented.

A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.

Predicting low-velocity impact damage on a stiffened composite panel

An intralaminar damage model, based on a continuum damage mechanics approach, is presented to model the damage mechanisms occurring in carbon fibre composite structures incorporating fibre tensile and compressive breakage, matrix tensile and compressive fracture, and shear failure. The damage model, together with interface elements for capturing interlaminar failure, is implemented in a finite element package and used in a detailed finite element model to simulate the response of a stiffened composite panel to low-velocity impact. Contact algorithms and friction between delaminated plies were included, to better simulate the impact event. Analyses were executed on a high performance computer (HPC) cluster to reduce the actual time required for this detailed numerical analysis. Numerical results relating to the various observed interlaminar damage mechanisms, delamination initiation and propagation, as well as the model’s ability to capture post-impact permanent indentation in the panel are discussed. Very good agreement was achieved with experimentally obtained data of energy absorbed and impactor force versus time. The extent of damage predicted around the impact site also corresponded well with the damage detected by non destructive evaluation of the tested panel.

Numerical prediction of the low-velocity impact damage and compression after impact strength of composite laminates

Low-velocity impact damage can drastically reduce the residual mechanical properties of the composite structure even when there is barely visible impact damage. The ability to computationally predict the extent of damage and compression after impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant development time and cost penalties. A three-dimensional damage model, to predict both low-velocity impact damage and compression after impact CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The virtual tests were executed in two steps, one to capture the impact damage and the other to predict the CAI strength. The observed intra-laminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing.

Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates

Low-velocity impact damage can drastically reduce the residual strength of a composite structure even when the damage is barely visible. The ability to computationally predict the extent of damage and compression-after-impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant time and cost penalties. A high-fidelity three-dimensional composite damage model, to predict both low-velocity impact damage and CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The intralaminar damage model component accounts for physically-based tensile and compressive failure mechanisms, of the fibres and matrix, when subjected to a three-dimensional stress state. Cohesive behaviour was employed to model the interlaminar failure between plies with a bi-linear traction–separation law for capturing damage onset and subsequent damage evolution. The virtual tests, set up in ABAQUS/Explicit, were executed in three steps, one to capture the impact damage, the second to stabilize the specimen by imposing new boundary conditions required for compression testing, and the third to predict the CAI strength. The observed intralaminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing without the need of model calibration which is often required with other damage models.

Modelling Damage in Thin-Walled Structures [Keynote speaker]

A high-fidelity composite damage model is presented and applied to predict low-velocity impact damage, compression after impact (CAI) strength and crushing of thin-walled composite structures. The simulated results correlated well with experimental testing in terms of overall force-displacement response, damage morphologies and energy dissipation. The predictive power of this model makes it suitable for use as part of a virtual testing methodology, reducing the reliance on physical testing.  

Numerical prediction of the low-velocity impact damage and compression after impact strength of composite laminates

Low-velocity impact damage can drastically reduce the residual mechanical properties of the composite structure even when there is barely visible impact damage. The ability to computationally predict the extent of damage and compression after impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant development time and cost penalties. A three-dimensional damage model, to predict both low-velocity impact damage and compression after impact CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The virtual tests were executed in two steps, one to capture the impact damage and the other to predict the CAI strength. The observed intra-laminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing.

Numerical analysis of intralaminar failure mechanisms in composite structures, Part I: FE implementation

This paper presents a three-dimensional continuum damage mechanics-based material model which was implemented in an implicit finite element code to simulate the progressive intralaminar degradation of fibre reinforced laminates. The damage model is based on ply failure mechanisms and uses seven damage variables assigned to tensile, compressive and shear damage at a ply level. Non-linear behaviour and irreversibility were taken into account and modelled. Some issues on the numerical implementation of the damage model are discussed and solutions proposed. Applications of the methodology are presented in Part II

Numerical analysis of intralaminar failure mechanisms in composite structures, Part II: Applications

A three-dimensional continuum damage mechanics-based material model was implemented in an implicit Finite Element code to simulate the progressive intralaminar degradation of fibre reinforced laminates based on ply failure mechanisms. This paper presents some structural applications of the progressive failure model implemented. The focus is on the non-linear response of the shear failure mode and its interaction with other failure modes. Structural applications of the damage model show that the proposed model is able to reproduce failure loads and patterns observed experimentally.