11 research outputs found
Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches
A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed
Plastic buckling and collapse of thin shell structures, using layered plastic modeling and co-rotational ANDES finite elements
This study reveals an analysis of plastic buckling and collapse of thin shell structures. For this purpose, the co-rotational and layered plastic model as well as ANDES (Assumed Natural Deviatoric Strain) finite element formulations are used. The co-rotational kinematics formulation splits the translational and rotational deformations in a small deformation analysis. The ANDES finite element is modified to elastoplastic ANDES finite element by the introduction of the von Mises yield criterion elastoplastic formulation on its original deformation model. In order to accommodate the plasticity formulation, the Gauss point layered integration is inserted through of thickness of the element to produce the internal force vector and material stiffness matrix. Special effort is devoted to maintain the consistency of the internal forces and tangent stiffness as well as to enhance the robustness of element level computations. The arc-length method is used to follow the postbuckling equilibrium path. Results are presented for several benchmark elastoplastic shell problems available in the present literature, which are generally in agreement with the present wor
Analysis of Large Quasistatic Deformations of Inelastic Solids by a New Stress Based Finite Element Method
A new hybrid stress finite element algorithm suitable for analyses of large quasistatic deformation of inelastic solids is presented. Principal variables in the formulation are the nominal stress rate and spin. The finite element equations which result are discrete versions of the equations of compatibility and angular momentum balance. Consistent reformulation of the constitutive equation and accurate and stable time integration of the stress are discussed at length. Examples which bring out the feasibility and performance of the algorithm conclude the work
Material length scales in gradient-dependent plasticity/damage and size effects: theory and computation
Structural materials display a strong size-dependence when deformed non-uniformly into the inelastic range: smaller is stronger. This effect has important implications for an increasing number of applications in structural failure, electronics, functional coatings, composites, micro-electro-mechanical systems (MEMS), nanostructured materials, micro/nanometer fabrication technologies, etc. The mechanical behavior of these applications cannot be characterized by classical (local) continuum theories because they incorporate no ‘material length scales’ and consequently predict no size effects. On the other hand, it is still not possible to perform quantum and atomistic simulations on realistic time and structures. It is therefore necessary to develop a scale-dependent continuum theory bridging the gap between the classical continuum theories and the atomistic simulations in order to be able to design the size-dependent structures of modern technology. Nonlocal rate-dependent and gradient-dependent theories of plasticity and damage are developed in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the scale-dependent plasticity/damage behavior. Material length scales are implicitly and explicitly introduced into the governing equations through material rate-dependency (viscosity) and coefficients of spatial higher-order gradients of one or more material state variables, respectively. The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh, since the width of the fracture process zone (shear band) is determined by the intrinsic material length scale; while the classical continuum theories fail to address this problem. It is also shown that the proposed theory is successful for the interpretation of indentation size effects in micro/nano-hardness when using pyramidal and spherical indenters and gives sound interpretations of the size effects in micro-torsion of thin wires and micro-bending of thin beams. Future studies should be directed toward incorporation of the size effects into design procedures and code recommendations of modern engineering structures (e.g. for MEMS, NEMS, coatings, thin films), fiber composites (e.g. for aircrafts and ships), etc
Desenvolvimento de modelos computacionais anisotrópicos baseados em hipoelasticidade e hiperelasticidade incluindo endurecimento cinemático não-linear
Doutoramento em Engenharia MecânicaIn the present work, finite strain elastoplastic constitutive formulations suitable
for advanced metallic materials are developed. The main goals are the correct
description of the elastoplastic behaviour, including strong plastic anisotropy and
cyclic hardening phenomena, in the large strain regime, as well as the development
of numerically efficient algorithmic procedures for numerical implementation
of the constitutive models into codes of numerical simulation by the Finite Element
Method. Two different approaches are used in the derivation of the finite strain
constitutive formulations, namely, hypoelasticity and hyperelasticity.
On the one hand, regarding the hypoelastic-based model, particular attention is
given to the development of computationally effcient forward- and backward-Euler
algorithms considering distinct techniques. On the other hand, concerning the
hyperelastic-based model, the focus is on the possibility of using any (quadratic or
nonquadratic) yield criteria and on a new procedure that ensures that the anisotropy
is correctly described in the finite strain regime. Moreover, the constitutive relations
are solely expressed in the reference configuration, hence yielding symmetric
tensor-valued quantities only. This symmetry, allied to an algorithm that preserves
it, is crucial for the computational efficiency of the model's implementation since
it reduces the storage effort and the required solver capacities when compared to
the model's standard counterparts.
For a better description of cyclic hardening phenomena, the developed models
and corresponding algorithms, are extended to include several back stresses. This
extension is carried out by considering a modified rheological model of nonlinear
kinematic hardening and using additional state variables.
The capabilities of the developed models for accurate reproduction of the plastic
anisotropy and cyclic hardening phenomena are assessed by means of their implementation
into material user subroutines of the commercial code Abaqus. The
accuracy and computational efficiency of the models and numerical algorithms are
compared by means of simulations of benchmarks. These benchmarks allow the
models' assessment in the description of, e.g., metal forming defects such as earing
and springback, as well as the comparison of the stability and precision of the
numerical algorithms.No presente trabalho, são desenvolvidas formulações constitutivas elastoplásticas
para grandes deformações, adequadas a materiais metálicos avançados. Os principais
objectivos deste estudo consistem na correcta descrição do comportamento
elastoplástico, incluindo anisotropia plástica acentuada e fenómenos de endurecimento
cíclico, no regime de grandes deformações, bem como o desenvolvimento
de procedimentos algorítmicos eficientes para a implementação numérica dos modelos
constitutivos em códigos de simulação numérica pelo Método dos Elementos
Finitos. São usadas duas metodologias diferentes na derivação das formulações
constitutivas de grandes deformações, nomeadamente, hipoelasticidade e hiperelasticidade.
Por um lado, relativamente ao modelo baseado em hipoelasticidade, é dada particular
atenção ao desenvolvimento de algoritmos eficientes do ponto de vista computacional,
considerando técnicas particulares. Por outro lado, em relação ao modelo
baseado em hiperelasticidade, a possibilidade de usar qualquer critério de cedência
(quadrático ou não-quadrático) e a apresentação de um procedimento inovador, que
garante a correcta descrição da anisotropia na presença de grandes deformaçães,
são destacadas. Além disso, as relações constitutivas são expressas unicamente
na configuração de referência, resultando no uso de apenas variáveis simétricas de
segunda ordem. Esta simetria e o uso de um algoritmo que a preserva são cruciais
no que diz respeito à eficiência numérica da implementação do modelo, uma vez
que reduz significativamente o espaço de armazenamento e o custo computacional
de cálculo, relativamente aos modelos hiperelásticos convencionais.
Os modelos, e respectivos algoritmos de integração, são posteriormente alargados
ao uso de múltiplos tensores das tensões inversas de modo a permitir uma melhor
descrição dos fenómenos de endurecimento cíclico. Para tal, foi considerado um
modelo reológico modificado de endurecimento cinemático e usadas variáveis de
estado adicionais.
O desempenho dos modelos desenvolvidos na reprodução precisa de anisotropia
plástica e fenómenos de endurecimento cíclico é avaliado através da sua implementação no código comercial Abaqus usando subrotinas de utilizador. A precisão
e eficiência computacional dos modelos e algoritmos desenvolvidos são comparados
entre si através de simulações de benchmarks. Estes benchmarks permitem a
avaliação dos modelos na descrição de, por exemplo, defeitos na conformação de
chapas metálicas, tais como a formação de orelhas e o retorno elástico, bem como
a comparação da estabilidade e precisão dos algoritmos numéricos
Robuste Berechnungsverfahren zur nichtlinearen dynamischen Analyse von Balken- und Schalenstrukturen
Gegenwärtige und zukünftige dynamisch beanspruchte, schlanke Strukturen aus mehrschichtig verbundenen, hyperelastischen Werkstoffen, z. B. Windenergieanlagen und Hubschrauber usw., sind sehr komplex. Eine genaue Untersuchung im Zeitbereich erfordert den Einsatz von Methoden, die kinematische, geometrische sowie, bis zu einem gewissen Grad, materielle Nichtlinearitäten berücksichtigen sollten. Daher könnten Simulationen mit Beachtung von großen Verschiebungen, Drehungen und Verzerrungen nötig sein, um das mechanische Verhalten akkurat zu vorhersagen zu vermögen. Zunächst werden die Bewegungsgleichungen räumlich diskretisiert. Dann werden die zum Teil diskretisierten Gleichungen mittels eines Integrationsverfahrens zeitlich diskretisiert. Solche diskreten Gleichungen sind sehr steif, sodass sich die Berechnung der langzeitigen Lösung erschwert. Darüber hinaus ist die Einführung von Nebenbedingungen oft nötig, um komplexere Strukturen aufstellen zu können, wodurch sich die Komplexität erhöht wird und unerwünschte Eigenschaften noch verschärft werden. Um Robustheit zu gewinnen, sollen Berechnungsverfahren hergeleitet werden, die die zugrunde legende Physik in gewissem Maße erhalten können und gleichzeitig den hochfrequenten Anteil der Lösung unterdrücken
können. Die Erfüllung dieser Anforderungen stellt sich als sehr herausfordernd dar.
Das Hauptziel dieser Arbeit liegt an der Entwicklung von Berechnungsverfahren zur Vertiefung des Verständnises des dynamischen Verhaltens von Balken- und Schalenstrukturen. Um dieses Ziel zu erreichen, wird ein umfassender Ansatz vorgeschlagen. Dieser besteht aus: i) Einer auf Direktoren basierenden, Finite-Elemente-Formulierung für den geometrisch exakten Balken mit allgemeinen Querschnittseigenschaften; ii) einer auf Direktoren basierenden, Finite-Elemente-Formulierung für die Kontinuumsmechanik-basierte Schale aus mehrschichtig verbundenen, hyperelastischen Werkstoffen; iii) einer vereinheitlichten Beschreibung von Starrkörpern, Balken und Schalen und deren Kopplung mittels kinematischer
Nebenbedingungen; und, iv) einem robusten Integrationsverfahren basierend auf dem gemittelten Vektorfeld. Des Weiteren wird Folgendes ebenfalls vorgeschlagen:
v) Die Partikularisierung der Hauptgeodätenanalyse zur nichtlinearen Identifikation von Bewegungsmoden an Balkenstrukturen; und, vi) ein neues konservatives/dissipatives Integrationsverfahren für allgemeine nichtlineare mechanische Systeme basierend auf optimierten Modifizierungen höherer Ordnung, die die Defizite der Mittelpunktsregel beheben. Die sehr gute Leistung des vorgeschlagenen Ansatzes wird durch mehrere Beispiele unterschiedlicher Komplexität nachgewiesen.Existing and new slender structures made of hyperelastic multilayer composite materials subject to highly dynamic loads, e.g., wind turbines, helicopters, cars, speedboats or submarines inter alia, are very complex. Their dynamic analysis requires fully nonlinear formulations, at least from the kinematic and geometric point of view, and also to some extent from the material point of view. Thus, simulations in time-domain involving large displacements, rotations and strains could be necessary to predict their mechanical behavior accurately. Numerical procedures to carry out such simulations rely firstly on the partial discretization in space of the governing equations, for instance with finite elements. These semi discrete equations are further discretized in time with an integration scheme. The resulting discrete equations are in fact very stiff and therefore, the computation of the long-term behavior could be problematic. In many applications, the introduction of constraints is also necessary for rendering more complex structures. Besides introducing a new level of complexity, this can sharpen conditioning problems already present in the fully discrete problem. Additionally, we also require procedures able to annihilate the unwanted unresolved high-frequency content without upsetting of the underlying physics. However, the simultaneous satisfaction of all these requirements is a very challenging task. The main objective of this work is to provide means intended for helping to understand further the nonlinear dynamics of beam and shell structures made of hyperelastic multilayer
composite materials subject to highly dynamic loads. To accomplish this main goal, we propose a unifying computational approach that relies on: i) a director-based finite-element formulation for geometrically exact beams with general cross-section properties; ii) a director-based finite-element formulation for solid-degenerate shells made of hyperelastic multilayer composite materials; iii) a unifying description of rigid bodies, geometrically exact beams and solid-degenerate shells and their combination with kinematic pairs, which avoids inherently the necessity of rotational degrees of freedom; and, iv) a robust integration scheme based on the average vector field. Additionally, we propose: v) the particularization of the principal geodesic analysis to identify motion patters exhibited by beam structures in a purely nonlinear setting; and, vi) a new conservative/dissipative integration method for general nonlinear mechanical systems, which relies on high-order correction terms that optimally modify the midpoint rule. Moreover, the excellent numerical performance of the proposed unifying framework and procedures is illustrated
by means of a good number of examples with different difficulty levels
Continuum-based Multiscale Computational Damage Modeling of Cementitous Composites
Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage
model coupled with a novel plasticity model for plain concrete is proposed in this
research. Two different damage evolution laws for both tension and compression are
formulated for a more accurate prediction of the plain concrete behavior. In order to
derive the constitutive equations, the strain equivalence hypothesis is adopted. The
proposed constitutive model has been shown to satisfy the thermodynamics requirements,
and detailed numerical algorithms are developed for the Finite Element implementation
of the proposed model. Moreover, the numerical algorithm is coded using the user
subroutine UMAT and then implemented in the commercial finite element analysis
program Abaqus, and the overall performance of the proposed model is verified by
comparing the model predictions to various experimental data on macroscopic level.
Using the proposed coupled plasticity-damage constitutive model, the effect of
the micromechanical properties of concrete, such as aggregate shape, distribution, and
volume fraction, the ITZ thickness, and the strength of the ITZ and mortar matrix on the tensile behavior of concrete is investigated on 2-D and 3-D meso-scale. As a result of
simulation, the tensile strength and thickness of the ITZ is the most important factor that
control the global strength and behavior of concrete, and the aggregate shape and
volume fraction has somewhat effect on the tensile behavior of concrete while the effect
of the aggregate distribution is negligible. Furthermore, using the proposed constitutive
model, the pull-out analysis of the single straight and curved CNT embedded in cement
matrix is carried out. In consequence of the analysis, the interfacial fracture energy is the
key parameter governing the CNT pull-out strength and ductility at bonding stage, and
the Young's modulus of the CNT has also great effect on the pull-out behavior of the
straight CNT. In case of the single curved CNT, while the ultimate pull-out force of the
curved CNT at sliding stage is governed by the initial sliding force when preexisting
normal force is relatively high, the ultimate pull-out force, when the preexisting normal
force is not significant, is increased linearly proportional to the curvature and the
Young's modulus of the CNT due to the additionally induced normal force by the
bending stiffness of the curved CNT
Nonlinear Constitutive Relations for High Temperature Applications
The topics of discussion addressed were material behavior, design analysis, deformation kinetics, metallurgical characterization, mechanical subelement models, stress analysis, fracture mechanics, viscoplasticity, and thermal loading
Numerical Methods in Shape Spaces and Optimal Branching Patterns
The contribution of this thesis is twofold. The main part deals with numerical methods in the context of shape space analysis, where the shape space at hand is considered as a Riemannian manifold. In detail, we apply and extend the time-discrete geodesic calculus (established by Rumpf and Wirth [WBRS11, RW15]) to the space of discrete shells, i.e. triangular meshes with fixed connectivity. The essential building block is a variational time-discretization of geodesic curves, which is based on a local approximation of the squared Riemannian distance on the manifold. On physical shape spaces this approximation can be derived e.g. from a dissimilarity measure. The dissimilarity measure between two shell surfaces can naturally be defined as an elastic deformation energy capturing both membrane and bending distortions. Combined with a non-conforming discretization of a physically sound thin shell model the time-discrete geodesic calculus applied to the space of discrete shells is shown to be suitable to solve important problems in computer graphics and animation. To extend the existing calculus, we introduce a generalized spline functional based on the covariant derivative along a curve in shape space whose minimizers can be considered as Riemannian splines. We establish a corresponding time-discrete functional that fits perfectly into the framework of Rumpf and Wirth, and prove this discretization to be consistent. Several numerical simulations reveal that the optimization of the spline functional—subject to appropriate constraints—can be used to solve the multiple interpolation problem in shape space, e.g. to realize keyframe animation. Based on the spline functional, we further develop a simple regression model which generalizes linear regression to nonlinear shape spaces. Numerical examples based on real data from anatomy and botany show the capability of the model. Finally, we apply the statistical analysis of elastic shape spaces presented by Rumpf and Wirth [RW09, RW11] to the space of discrete shells. To this end, we compute a Fréchet mean within a class of shapes bearing highly nonlinear variations and perform a principal component analysis with respect to the metric induced by the Hessian of an elastic shell energy. The last part of this thesis deals with the optimization of microstructures arising e.g. at austenite-martensite interfaces in shape memory alloys. For a corresponding scalar problem, Kohn and Müller [KM92, KM94] proved existence of a minimizer and provided a lower and an upper bound for the optimal energy. To establish the upper bound, they studied a particular branching pattern generated by mixing two different martensite phases. We perform a finite element simulation based on subdivision surfaces that suggests a topologically different class of branching patterns to represent an optimal microstructure. Based on these observations we derive a novel, low dimensional family of patterns and show—numerically and analytically—that our new branching pattern results in a significantly better upper energy bound