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.

A progressive failure model for composite laminates subjected to low velocity impact damage

This paper presents a 3-D failure model for predicting the dynamic material response of composite laminates under impact loading. The formulation is based on the Continuum Damage Mechanics (CDM) approach and enables the control of the energy dissipation associated with each failure mode regardless of mesh refinement and fracture plane orientation. Internal thermodynamically irreversible damage variables were defined in order to quantify damage concentration associated with each possible failure mode and predict the gradual stiffness reduction during the impact damage process. The material model has been implemented into LS-DYNA explicit finite element code within solid elements and it has proven to be capable of reproducing experimental results with good accuracy in terms of static/dynamic responses, absorbed energy and extent of damage.

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

Improving composite damage modelling through automatic placement of cohesive elements

Numerous experimental studies of damage in composite laminates have shown that intralaminar (in-plane) matrix cracks lead to interlaminar delamination (out-of-plane) at ply interfaces. The smearing of in-plane cracks over a volume, as a consequence of the use of continuum damage mechanics, does not always effectively capture the full extent of the interaction between the two failure mechanisms. A more accurate representation is obtained by adopting a discrete crack approach via the use of cohesive elements, for both in-plane and out-of-plane damage. The difficulty with cohesive elements is that their location must be determined a priori in order to generate the model; while ideally the position of the crack migration, and more generally the propagation path, should be obtained as part of the problem’s solution. With the aim of enhancing current modelling capabilities with truly predictive capabilities, a concept of automatic insertion of interface elements is utilized. The consideration of a simple traction criterion in relation to material strength, evaluated at each node of the model (or of the regions of the model where it is estimated cracks might form), allows for the determination of initial crack location and subsequent propagation by the insertion of cohesive elements during the course of the analysis. Several experimental results are modelled using the commercial package ABAQUS/Standard with an automatic insertion subroutine developed in this work, and the results are presented to demonstrate the capabilities of this technique.

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.

An Anisotropic Model of Damage and Unilateral Effect for Brittle Materials

This work deals with the initial applications and formulation of an aniscitropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

On a regular convex solver potential for an elastic-damage constitutive model: a theoretical analysis

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects involved are based on convex analysis, which is employed aiming a consistent variational formulation of the potential and its conjugate one. It is shown that the constitutive relations for the class of damage models here considered can be derived from the solver potentials by means of sub-differentials sets. The optimality conditions of the resulting minimisation problem represent in particular a linear complementarity problem. Finally, a simple example is present in order to illustrate the possible integration errors that can be generated when finite step analysis is performed. (C) 2003 Elsevier Ltd. All rights reserved.

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.

A repairability index for reinforced concrete members based on fracture mechanics

This paper proposes a repairability index for damage assessment in reinforced concrete structural members. The procedure discussed in this paper differs from the standard methods in two aspects: the structural and damage analyses are coupled and it is based on the concepts of fracture and continuum damage mechanics. The relationship between the repairability index and the well-known Park and Ang index is shown in some particular cases.

Modelization of low cycle fatigue damage in frames

Damage models based on the Continuum Damage Mechanics (CDM) include explicitly the coupling between damage and mechanical behavior and, therefore, are consistent with the definition of damage as a phenomenon with mechanical consequences. However, this kind of models is characterized by their complexity. Using the concept of lumped models, possible simplifications of the coupled models have been proposed in the literature to adapt them to the study of beams and frames. On the other hand, in most of these coupled models damage is associated only with the damage energy release rate which is shown to be the elastic strain energy. According to this, damage is a function of the maximum amplitude of cyclic deformation but does not depend on the number of cycles. Therefore, low cycle effects are not taking into account. From the simplified model proposed by Flórez-López, it is the purpose of this paper to present a formulation that allows to take into account the degradation produced not only by the peak values but also by the cumulative effects such as the low cycle fatigue. For it, the classical damage dissipative potential based on the concept of damage energy release rate is modified using a fatigue function in order to include cumulative effects. The fatigue function is determined through parameters such as the cumulative rotation and the total rotation and the number of cycles to failure. Those parameters can be measured or identified physically through the haracteristics of the RC. So the main advantage of the proposed model is the possibility of simulating the low cycle fatigue behavior without introducing parameters with no suitable physical meaning. The good performance of the proposed model is shown through a comparison between numerical and test results under cycling loading.

A Damage Model for Masonry Infilled Frames

The effect of infill walls on the behaviour of frames is widely recognized, and, for several decades now, has been the subject of numerous experimental investigations. However, the analytical modeling of infilled panels and frames under in-plane loading is difficult and generally unreliable. From the point of view of the simulation technique the models may be divided into micromodels and simplified (or macro-) models. Based on the equivalent strut approach (simplified model), in this paper a damage model is proposed for the characterization of masonry walls submitted to lateral cyclic loads. The model, developed along the lines of the Continuum Damage Mechanics, have the advantages of including explicitly the coupling between damage and mechanical behaviour and so is consistent with the definition of damage as a phenomenon with mechanical consequences.

A damage model for seismic retrofitting of structures

Numerous damage models have been developed in order to analyse the seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of Continuum Damage Mechanics are more consistent with the definition of damage like a phenomenon with mechanical consequences as they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, many of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Flórez is made in order to include the low cycle fatigue. Such model employs in its formulation irreversible thermodynamics and internal state variable theory.