Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2007. / Committee Chair: Itzhak Green; Committee Member; Jeffrey Streator; Committee Member: Richard Neu. Part of the SMARTech Electronic Thesis and Dissertation Collection.

A three-dimensional finite element code to analyze coupled thermomechanical deformations of composites has been developed. It incorporates geometric nonlinearities, delamination between adjoining layers, and damage due to fiber breakage, fiber/matrix debonding, and matrix cracking. The three damage modes are modeled using the theory of internal variables and the delamination by postulating a failure envelope in terms of the transverse stresses; the damage degrades elastic moduli. The delamination of adjoining layers is simulated by the nodal release technique. Coupled nonlinear partial differential equations governing deformations of a composite, and the pertinent initial and boundary conditions are first reduced to coupled ordinary differential equations (ODEs) by the Galerkin method. These are integrated with respect to time with the Livermore solver for ODEs. After each time step, the damage in an element is computed, and material properties modified. The code has been used to analyze several static and transient problems; computed results have been found to compare well with the corresponding test results. The effect of various factors such as the fiber orientation, ply stacking sequence, and laminate thickness on composite's resistance to shock loads induced by underwater explosions has been delineated. / Ph. D.

This work discusses the use of Positive Position Feedback (PPF) for Active Vibration Control as part of an Active Damage Control System (ADCS). Vibration control increases the fatigue life of a structure and decreases the in-plane stresses that can cause delamination in a composite. PPF is a collocated direct-output feedback control method that increases the effective damping in a structure. A simply-supported beam was used as the testbed which used strain gages as the sensing element and piezoelectric ceramics as the actuator. Initial investigations into sampled-data systems using PPF are presented. The issues addressed are: stability of the sampled system, the effects of the sampling rate on the system, and degradation from predicted analog performance. A digital design procedure for the tuning filters in the Z-plane is suggested if the sampling rate to be used is known. If the sampling rate varies significantly, to avoid redesigning the filters for each new sampling rate, they should be designed in the continuous-time and transformed to the Z-plane. The Tustin transformation was found to adequately map the poles and zeros of the compensator to the Z-plane for digital control. Experimental implementation of PPF on a simply-supported beam resulted in vibration suppression of three modes with a S180 controller. The beam was subjected to both a single-frequency harmonic disturbance and a broadband harmonic disturbance. One, two, and three-mode controllers were designed with disturbance suppression up to 15dB achieved. / Master of Science

A Mecânica do Dano Contínuo é atualmente uma poderosa ferramenta para se modelar o comportamento não-linear de vários materiais decorrente da evolução de um processo de microfissuração. A perda de rigidez causada pelo processo físico tem sido considerada em modelos constitutivos através de variáveis de dano escalar, vetorial ou tensorial. Quando o carregamento é proporcionalmente crescente as deformações residuais podem ser ignoradas e relações constitutivas simples podem ser obtidas, onde os efeitos do dano aparecem por uma penalização direta das propriedades elásticas. Por outro lado, efeitos de dano podem ser acoplados com deformações residuais levando a relações constitutivas mais gerais. Esse trabalho está relacionado a esses tipos de modelos assumindo que o meio ideal apresenta um comportamento elástico linear com danificação ou elastoplástico com danificação. Um dos principais aspectos discutido relaciona-se à formulação variacional, a qual está baseada em conceitos de Análise Convexa e Não-Convexa. Explorando o fato que a evolução do dano tem correspondência com a idealização de regime de encruamento negativo, a teoria de localização de deformação é abordada e um estudo da condição necessária de singularidade ou perda da condição de elipticidade é realizado. Na sequência, uma proposta preliminar para uma análise de pós-singularidade, baseada na Teoria de Bifurcação, é feita no sentido de caracterizar pontos limite ou pontos de bifurcação de solução, em sistemas conservativos. / Continuum Damage Mechanics is nowadays a powerful tool to model the non-linear behaviour of several materials due to evolution of a microcracking process. The lost of rigidity caused by such physical process has been accounted in the constitutive models through a scalar, vectorial or tensorial damage variables. When proportional loading is considered the residuals strains can be ignored and simple constitutive relations can be obtained in which damage effects appear by direct penalization of the elastic properties. On the other hand, damage effects can be coupled with residual strains leading to more general constitutive relations. This work is related to such kind of models assuming that the ideal medium presents a linear elastic-damage or an elastoplastic-damage behaviour. One of the main topics discussed is related to the variational formulation which is based on Convex and Non-Convex Analysis concepts. Exploring the fact that damage evolution has correspondence with a softening idealised regime, the strain localization theory is treated and a study of a necessary condition for singularity or ellipticity tose condition is developed. In the sequence, a introductory poscritical analysis is proposed, based in the bifurcation theory and aiming to detect if the singularity corresponds to a limit or a bifurcation point solution, in conservative systems.

The problem of damage accumulation in laminated composite materials hasreceived much attention due to their widespread application in the aerospace, automotive,civil, and sports industries. In the aerospace industry, composites are usedto make light weight and efficient structural components. In the Boeing 787, forexample, more than 50% of the structure is made of composite materials. Althoughthere have been significant developments in analyzing cross-ply laminates, none ofthe present approaches provides reasonable predictions for multidirectional laminatesin which intralaminar cracks may form in multiple orientations. Nevertheless, theprediction of damage accumulation and its effect on structural performance is a verydifficult problem due to complexity of the cracking processes.This study presents a synergistic damage mechanics (SDM) methodology to analyzedamage behavior in multidirectional composite laminates with intralaminarcracks in plies of multiple orientations. SDM combines the strengths of micro-damagemechanics (MDM) and continuum damage mechanics (CDM) in predicting the stiffness degradation due to these cracks. The micromechanics is performed on a representativeunit cell using a three-dimensional finite element analysis to calculate thecrack opening displacement accounting for the influence of the surrounding plies, theso-called constraint effect. This information is then incorporated in the CDM formulationdealing with laminates containing cracks in different ply orientations through a `constraint parameter'. Following CDM, a separate damage mode is defined for eachtype of crack and the expressions for engineering moduli of the damaged laminateare then derived in terms of crack density and the constraint parameter. The SDMmethodology is implemented for [0m/±θn/0m/2]s laminates containing cracks in ±θplies. It is then extended to [0m/±θn/90r]s and [0m/90r/±θn]s laminates with cracksadditionally in the 90°-plies. The predictions agree well with published experimentaldata as well as independent FE computations. Limited parametric studies areperformed to show usability of SDM for more general laminates.To predict the initiation and growth of intralaminar cracks, an energy basedmodel is proposed in which these cracks initiate and multiply when the work requiredto form new set of cracks exceeds a laminate dependent critical energy release rate.The approach requires determination of average crack opening and sliding displacementsat varying crack spacing. This task is performed through a suitable 3-D FEanalysis. In case of off-axis ply cracking, a mixed mode fracture criterion is utilized,where the critical energy release rates in normal and shear modes are determinedby fitting the damage model with the experimental data for a reference laminate.The predictions from the model for [0/± θ4/01/2]s and [0/90/ ± 45]s laminates showremarkable agreement with the experimental results.The methodology and the results covered in this dissertation will be of interest tomechanics of materials researchers as well as to engineers in industry where compositematerials for structural applications are of interest.

In-service inspections of high temperature pressureequipment show that weldments are prone to creep and fatiguedamage. It is not uncommon that severely damaged weldments arefound even before the design life of the component has beenreached. In order to improve this situation action has beentaken during the last decades, both from industry, universitiesand research institutes, aiming at an enhanced understanding ofthe weldment response. The work presented in this thesis focuses on numericalsimulation of weldment creep response. For a more profoundunderstanding of the evolution of creep damage in mismatchedlow alloy weldments, simulations are performed using thecontinuum damage mechanics, CDM, concept. Both design and lifeassessment aspects are addressed. The possibility to assessseam welded pipes using results from tests of cross-weldspecimens taken out from the seam is investigated. It is foundthat the larger the cross-weld specimen the better thecorrelation. The advantage to use the CDM concept prior to aregular creep analysis is also pointed out. In order to developthe CDM analysis, a modified Kachanov-Rabotnov constitutivemodel is implemented into ABAQUS. Using this model, a secondredistribution of stresses is revealed as the tertiary creepstage is reached in the mismatched weldment. Creep crack growth, CCG, in cross-weld compact tension, CT,specimens is investigated numerically where a fracturemechanics concept is developed in two steps. In the first one,the C*value and an averaged constraint parameter areused for characterising the fields in the process zone, whilein the second step, the creep deformation rate perpendicular tothe crack plane and a constraint parameter ahead of the cracktip, are used as characterising parameters. The influence oftype and degree of mismatch, location of starter notch as wellas size of CT specimen, is investigated. Results show that notonly the material properties of the weldment constituentcontaining the crack, but also the deformation properties ofthe adjacent constituents, influence the CCG behaviour.Furthermore, the effect of size is influenced by the mismatchof the weldment constituents. A circumferentially cracked girth weld with differentmismatch is assessed numerically by use of the fracturemechanics concept developed. The results show that type anddegree of mismatch have a great influence on the CCG behaviourand that C*alone cannot characterise crack tip fields.Corresponding R5 assessments are also performed. Comparisonwith the numerical investigation shows that the assumption ofplane stress or plane strain conditions in the R5 analysis isessential for the agreement of the results. Assuming the formerresults in a relatively good agreement for the axial stressdominated cases while for the hoop stress dominated cases, R5predicts higher CCG rates by an order of magnitude. <b>Keywords:</b>ABAQUS, constraint effect, continuum damagemechanics, creep, creep crack growth, design, design code,finite element method, fracture mechanics, life assessment,mismatch, numerical simulation, weldment

The present work focuses on the formulation of a Continuum Damage Mechanics model for nonlinear analysis of masonry structural elements. The material is studied at the macro-level, i.e. it is modelled as a homogeneous orthotropic continuum. The orthotropic behaviour is simulated by means of an original methodology, which is based on nonlinear damage constitutive laws and on the concept of mapped tensors from the anisotropic real space to the isotropic fictitious one. It is based on establishing a one-to-one mapping relationship between the behaviour of an anisotropic real material and that of an isotropic fictitious one. Therefore, the problem is solved in the isotropic fictitious space and the results are transported to the real field. The application of this idea to strain-based Continuum Damage Models is rather innovative. The proposed theory is a generalization of classical theories and allows us to use the models and algorithms developed for isotropic materials. A first version of the model makes use of an isotropic scalar damage model. The adoption of such a simple constitutive model in the fictitious space, together with an appropriate definition of the mathematical transformation between the two spaces, provides a damage model for orthotropic materials able to reproduce the overall nonlinear behaviour, including stiffness degradation and strain-hardening/softening response. The relationship between the two spaces is expressed in terms of a transformation tensor which contains all the information concerning the real orthotropy of the material. A major advantage of this working strategy lies in the possibility of adjusting an arbitrary isotropic criterion to the particular behaviour of the orthotropic material. Moreover, orthotropic elastic and inelastic behaviours can be modelled in such a way that totally different mechanical responses can be predicted along the material axes. The aforementioned approach is then refined in order to account for different behaviours of masonry in tension and compression. The aim of studying a real material via an equivalent fictitious solid is achieved by means of the appropriate definitions of two transformation tensors related to tensile or compressive states, respectively. These important assumptions permit to consider two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the fictitious space makes use of two scalar variables, which monitor the local damage under tension and compression, respectively. Such a model, which is based on a stress tensor split into tensile and compressive contributions that allows the model to contemplate orthotropic induced damage, permits also to account for masonry unilateral effects. The orthotropic nature of the Tension-Compression Damage Model adopted in the fictitious space is demonstrated. This feature, both with the assumption of two distinct damage criteria for tension and compression, does not permit to term the fictitious space as “isotropic”. Therefore, the proposed formulation turns the original concept of “mapping the real space into an isotropic fictitious one” into the innovative and more general one of “mapping the real space into a favourable (or convenient) fictitious one”. Validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry. The model is fully formulated for the 2-dimensional case. However, it can be easily extended to the 3-dimensional case. It provides high algorithmic efficiency, a feature of primary importance when analyses of even large scale masonry structures are carried out. To account for this requisite it adopts a strain-driven formalism consistent with standard displacement-based finite element codes. The implementation in finite element programs is straightforward. Finally, a localized damage model for orthotropic materials is formulated. This is achieved by means of the implementation of a crack tracking algorithm, which forces the crack to develop along a single row of finite elements. Compared with the smeared cracking approach, such an approach shows a better capacity to predict realistic collapsing mechanisms. The resulting damage in the ultimate condition appears localized in individual cracks. Moreover, the results do not suffer from spurious mesh-size or mesh-bias dependence. The numerical tool is finally validated via a finite element analysis of an in-plane loaded masonry shear wall.

The problem of damage accumulation in laminated composite materials hasreceived much attention due to their widespread application in the aerospace, automotive,civil, and sports industries. In the aerospace industry, composites are usedto make light weight and efficient structural components. In the Boeing 787, forexample, more than 50% of the structure is made of composite materials. Althoughthere have been significant developments in analyzing cross-ply laminates, none ofthe present approaches provides reasonable predictions for multidirectional laminatesin which intralaminar cracks may form in multiple orientations. Nevertheless, theprediction of damage accumulation and its effect on structural performance is a verydifficult problem due to complexity of the cracking processes.This study presents a synergistic damage mechanics (SDM) methodology to analyzedamage behavior in multidirectional composite laminates with intralaminarcracks in plies of multiple orientations. SDM combines the strengths of micro-damagemechanics (MDM) and continuum damage mechanics (CDM) in predicting the stiffness degradation due to these cracks. The micromechanics is performed on a representativeunit cell using a three-dimensional finite element analysis to calculate thecrack opening displacement accounting for the influence of the surrounding plies, theso-called constraint effect. This information is then incorporated in the CDM formulationdealing with laminates containing cracks in different ply orientations through a `constraint parameter'. Following CDM, a separate damage mode is defined for eachtype of crack and the expressions for engineering moduli of the damaged laminateare then derived in terms of crack density and the constraint parameter. The SDMmethodology is implemented for [0m/±θn/0m/2]s laminates containing cracks in ±θplies. It is then extended to [0m/±θn/90r]s and [0m/90r/±θn]s laminates with cracksadditionally in the 90°-plies. The predictions agree well with published experimentaldata as well as independent FE computations. Limited parametric studies areperformed to show usability of SDM for more general laminates.To predict the initiation and growth of intralaminar cracks, an energy basedmodel is proposed in which these cracks initiate and multiply when the work requiredto form new set of cracks exceeds a laminate dependent critical energy release rate.The approach requires determination of average crack opening and sliding displacementsat varying crack spacing. This task is performed through a suitable 3-D FEanalysis. In case of off-axis ply cracking, a mixed mode fracture criterion is utilized,where the critical energy release rates in normal and shear modes are determinedby fitting the damage model with the experimental data for a reference laminate.The predictions from the model for [0/± θ4/01/2]s and [0/90/ ± 45]s laminates showremarkable agreement with the experimental results.The methodology and the results covered in this dissertation will be of interest tomechanics of materials researchers as well as to engineers in industry where compositematerials for structural applications are of interest.

This thesis presents a continuum model for asphalt concrete incorporating non- linear viscoelasticity, viscoplasticity, mechanically-induced damage and moisture- induced damage. The Schapery single-integral viscoelastic model describes the nonlinear viscoelastic response. The viscoplastic model of Perzyna models the time- dependent permanent deformations, using a Drucker-Prager yield surface which is modified to depend on the third deviatoric stress invariant to include more complex dependence on state of stress. Mechanically-induced damage is modeled using continuum damage mechanics, using the same modified Drucker-Prager law to determine damage onset and growth. A novel moisture damage model is proposed, modeling moisture-induced damage using continuum damage mechanics; adhesive moisture- induced damage to the asphalt mastic-aggregate bond and moisture-induced cohesive damage to the asphalt mastic itself are treated separately. The analytical model is implemented numerically for three-dimensional and plane strain finite element analyses, and a series of simulations is presented to show the performance of the model and its implementation. Sensitivity studies are conducted for all model parameters and results due to various simulations corresponding to laboratory tests are presented. In addition to the continuum model, results are presented for a micromechanical model using the nonlinear-viscoelastic-viscoplastic-damage model for asphalt mastic and a linear elastic model for aggregates. Initial results are encouraging, showing the strength and stiffness of the mix as well as the failure mode varying with moisture loading. These initial results are provided as a an example of the model's robustness and suitability for modeling asphalt concrete at the mix scale.

A local isotropic damage coupled hyperelastic-plastic framework is formulated in principal axes where thermo-mechanical extensions are also addressed. It is shown that, in a functional setting, treatment of many damage growth models, including ones originated from phenomenological models (with formal thermodynamical derivations), micro-mechanical models or fracture criteria, proposed in the literature, is possible. Quasi-unilateral damage evolutionary forms are given with special emphasis on the feasibility of formulations in principal axes. Local integration procedures are summarized starting from a full set of seven equations which are simplified step by step initially to two and finally to one where different operator split methodologies such as elastic predictor-plastic/damage corrector (simultaneous plastic-damage solution scheme) and elastic predictor-plastic corrector-damage deteriorator (staggered plasticdamage solution scheme) are given. For regularization of the post peak response with softening due to damage and temperature, Perzyna type viscosity is devised. Analytical forms accompanied with algorithmic expressions including the consistent material tangents are derived and the models are implemented as UMAT and UMATHT subroutines for ABAQUS/Standard, VUMAT subroutines for ABAQUS/Explicit and UFINITE subroutines for MSC.Marc. The subroutines are used in certain application problems including numerical modeling of discrete internal cracks, namely chevron cracks, in direct forward extrusion process where comparison with the experimental facts show the predicting capability of the model, isoerror map production for accuracy assessment of the local integration methods, and development two novel necking triggering methods in the context of a damage coupled environment.