A finite element approach for predicting the ultimate rotation capacity of RC beams

This paper presents a numerical approach to model the complex failure mechanisms that define the ultimate rotational capacity of reinforced concrete beams. The behavior in tension and compression is described by a constitutive damage model derived from a combination of two specific damage models [1]. The nonlinear behavior of the compressed region is treated by the compressive damage model based on the Drucker-Prager criterion written in terms of the effective stresses. The tensile damage model employs a failure criterion based on the strain energy associated with the positive part the effective stress tensor. This model is used to describe the behavior of very thin bands of strain localization, which are embedded in finite elements to represent multiple cracks that occur in the tensioned region [2]. The softening law establishes dissipation energy compatible with the fracture energy of the concrete. The reinforcing steel bars are modeled by truss elements with elastic-perfect plastic behavior. It is shown that the resulting approach is able to predict the different stages of the collapse mechanism of beams with distinct sizes and reinforcement ratios. The tensile damage model and the finite element embedded crack approach are able to describe the stiffness reduction due to concrete cracking in the tensile zone. The truss elements are able to reproduce the effects of steel yielding and, finally, the compressive damage model is able to describe the non-linear behavior of the compressive zone until the complete collapse of the beam due to crushing of concrete. The proposed approach is able to predict well the plastic rotation capacity of tested beams [3], including size-scale effects.

Um modelo constitutivo de dano composto para simular o comportamento de materiais quase-frágeis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Processing and Composition Effects on the Fracture Behavior of Spray-Formed 7XXX Series Al Alloys

The fracture properties of high-strength spray-formed Al alloys were investigated, with consideration of the effects of elemental additions such as zinc,manganese, and chromium and the influence of the addition of SiC particulate. Fracture resistance values between 13.6 and 25.6 MPa (m)1/2 were obtained for the monolithic alloys in the T6 and T7 conditions, respectively. The alloys with SiC particulate compared well and achieved fracture resistance values between 18.7 and 25.6 MPa (m)1/2. The spray-formed materials exhibited a loss in fracture resistance (KI) compared to ingot metallurgy 7075 alloys but had an improvedperformance compared to high-solute powder metallurgy alloys of similar composition. Characterization of the fracture surfaces indicated a predominantly intergranular decohesion, possibly facilitated by the presence of incoherent particles at the grain boundary regions and by the large strength differentialbetween the matrix and precipitate zone. It is believed that at the slip band-grain boundary intersection, particularly in the presence of large dispersoids and/or inclusions, microvoid nucleation would be significantly enhanced. Differences in fracture surfaces between the alloys in the T6 and T7 condition were observed and are attributed to inhomogeneous slip distribution, which results in strain localization at grain boundaries. The best overall combination of fracture resistance properties were obtained for alloys with minimum amounts of chromium and manganese additions.

From transient to steady state deformation and grain size: A thermodynamic approach using elasto-visco-plastic numerical modeling

Numerical simulation experiments give insight into the evolving energy partitioning during high-strain torsion experiments of calcite. Our numerical experiments are designed to derive a generic macroscopic grain size sensitive flow law capable of describing the full evolution from the transient regime to steady state. The transient regime is crucial for understanding the importance of micro structural processes that may lead to strain localization phenomena in deforming materials. This is particularly important in geological and geodynamic applications where the phenomenon of strain localization happens outside the time frame that can be observed under controlled laboratory conditions. Ourmethod is based on an extension of the paleowattmeter approach to the transient regime. We add an empirical hardening law using the Ramberg-Osgood approximation and assess the experiments by an evolution test function of stored over dissipated energy (lambda factor). Parameter studies of, strain hardening, dislocation creep parameter, strain rates, temperature, and lambda factor as well asmesh sensitivity are presented to explore the sensitivity of the newly derived transient/steady state flow law. Our analysis can be seen as one of the first steps in a hybrid computational-laboratory-field modeling workflow. The analysis could be improved through independent verifications by thermographic analysis in physical laboratory experiments to independently assess lambda factor evolution under laboratory conditions.

Experimental Validation of Finite Element Analysis of Human Vertebral Collapse Under Large Compressive Strains

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towardsthe prediction of extended vertebral collapse may help in assessing fracture stability in future work.

Chemistry of minerals from amphibole-chlorite veins of ODP Site 209-1270

We examined small-scale shear zones in drillcore samples of abyssal peridotites from the Mid-Atlantic Ridge. These shear zones are associated with veins consisting of chlorite + actinolite/tremolite assemblages, with accessory phases zircon and apatite, and they are interpreted as altered plagiogranite melt impregnations, which originate from hydrous partial melting of gabbroic intrusion in an oceanic detachment fault. Ti-in-zircon thermometry yields temperatures around 820°C for the crystallization of the evolved melt. Reaction path modeling indicates that the alteration assemblage includes serpentine of the adjacent altered peridotites. Based on the model results, we propose that formation of chlorite occurred at higher temperatures than serpentinization, thus leading to strain localization around former plagiogranites during alteration. The detachment fault represents a major pathway for fluids through the oceanic crust, as evidenced by extremely low d18O of altered plagiogranite veins (+3.0-4.2 per mil) and adjacent serpentinites (+ 2.6-3.7 per mil). The uniform oxygen isotope data indicate that fluid flow in the detachment fault system affected veins and adjacent host serpentinites likewise.

Overall and local mechanical behaviour of dissimilar laser welded joints

The present investigation addresses the overall and local mechanical performance of dissimilar joints of low carbon steel (CS) and stainless steel (SS) thin sheets achieved by laser welding in case of heat source displacement from the weld gap centreline towards CS. Microstructure characterization and residua! strain scanning, carried out by neutron diffraction, were used to assess the joints features. It was found that the heat source position influences the base metals dilution and the residua! stress field associated to the welding process; the transverse residual stress is smaller than for the longitudinal component, of magnitudes close to the parent CS yield strength. Furthermore, compressive transverse residual stresses were encountered at the SS-weld interface. The tensile behavior of the joint different zones assessed by using a video-image based system (VIC-2D) reveals that the residual stress field, together with the positive difference in yield between the weld metal and the base materials protects the joint from being piastically deformed. The tensile loadings of flat transverse specimens generate the strain localization and failure in CS, far away from the weld.En este trabajo se exponen los resultados de una investigacion sobre el comportamiento mecanico de soldaduras disimiles acero inoxidable-acero al carbono, realizadas para unir chapas delgadas, desplazando la fuente de calor del eje longitudinal de la union soldada por laser sobre el acero al carbono. Se han determinado las caracteristicas microestructurales de la union soldada, las tensiones residuales generadas (mediante difraccion de neutrones) y las curvas tension-deformacion locales y globales, mediante medidas locales de deformacion empleando el sistema VIC-2D "video image correlation". El desplazamiento de la fuente de calor infiuye en la dilution de los metales base y el campo de tensiones residuales asociado al proceso de soldeo; las tensiones residuales medidas en direction longitudinal se aproximan al limite elastico del acero al carbono, mientras que las tensiones residuales transversales son menores, e incluso de compresion. El ensayo a traccion de la union soldada revela que las tensiones residuales y la diferencia de limite elastico entre los metales base y la soldadura propician que la rotura se produzca por inestabilidad plastica del acero al carbono, lejos de la soldadura, sin que la union plastifique.

Overall vs. local mechanical behaviour of ferritic austenitic steel joints made by laser welding

The present investigation addresses the overall and local mechanical performance of dissimilar joints of low carbon steel (CS) and stainless Steel (SS) thin sheets achieved by laser welding in case of heat source displacement from the weld gap centreline towards CS. Welding was performed on a Nd:YAG laser DY033 (3300 W) in a continuos wave (CW), keyhole mode. The tensile behavior of the joint different zones assessed by using a video-image based system (VIC-2D) reveals that the residual stress field, together with the positive difference in yield between the weld metal and the base materials protects the joint from being plastically deformed. The tensile loadings of flat transverse specimens generate the strain localization and failure in CS, far away from the weld.

Um modelo multiescala concorrente para representar o processo de fissuração do concreto.

Este trabalho propõe uma técnica de modelagem multiescala concorrente do concreto considerando duas escalas distintas: a mesoescala, onde o concreto é modelado como um material heterogêneo, e a macroescala, na qual o concreto é tratado como um material homogêneo. A heterogeneidade da estrutura mesoscópica do concreto é idealizada considerando três fases distintas, compostas pelos agregados graúdos e argamassa (matriz), estes considerados materiais homogêneos, e zona de transição interfacial (ZTI), tratada como a parte mais fraca entre as três fases. O agregado graúdo é gerado a partir de uma curva granulométrica e posicionado na matriz de forma aleatória. Seu comportamento mecânico é descrito por um modelo constitutivo elástico-linear, devido a sua maior resistência quando comparado com as outras duas fases do concreto. Elementos finitos contínuos com alta relação de aspecto em conjunto com um modelo constitutivo de dano são usados para representar o comportamento não linear do concreto, decorrente da iniciação de fissuras na ZTI e posterior propagação para a matriz, dando lugar à formação de macrofissuras. Os elementos finitos de interface com alta relação de aspecto são inseridos entre todos os elementos regulares da matriz e entre os da matriz e agregados, representando a ZTI, tornando-se potenciais caminhos de propagação de fissuras. No estado limite, quando a espessura do elemento de interface tende a zero (h ?0) e, consequentemente, a relação de aspecto tende a infinito, estes elementos apresentam a mesma cinemática da aproximação contínua de descontinuidades fortes (ACDF), sendo apropriados para representar a formação de descontinuidades associados a fissuras, similar aos modelos coesivos. Um modelo de dano à tração é proposto para representar o comportamento mecânico não linear das interfaces, associado à formação de fissuras, ou até mesmo ao eventual fechamento destas. A fim de contornar os problemas causados pela malha de elementos finitos de transição entre as malhas da macro e da mesoescala, que, em geral, apresentam diferenças expressivas 5 de refinamento, utiliza-se uma técnica recente de acoplamento de malhas não conformes. Esta técnica é baseada na definição de elementos finitos de acoplamento (EFAs), os quais são capazes de estabelecer a continuidade de deslocamento entre malhas geradas de forma completamente independentes, sem aumentar a quantidade total de graus de liberdade do problema, podendo ser utilizados tanto para acoplar malhas não sobrepostas quanto sobrepostas. Para tornar possível a análise em multiescala em casos nos quais a região de localização de deformações não pode ser definida a priori, propõe-se uma técnica multiescala adaptativa. Nesta abordagem, usa-se a distribuição de tensões da escala macroscópica como um indicador para alterar a modelagem das regiões críticas, substituindo-se a macroescala pela mesoescala durante a análise. Consequentemente, a malha macroscópica é automaticamente substituída por uma malha mesoscópica, onde o comportamento não linear está na iminência de ocorrer. Testes numéricos são desenvolvidos para mostrar a capacidade do modelo proposto de representar o processo de iniciação e propagação de fissuras na região tracionada do concreto. Os resultados numéricos são comparados com os resultados experimentais ou com aqueles obtidos através da simulação direta em mesoescala (SDM).

Simulating Granite Emplacement and Deformation with Centrifuge Analogue Modelling

The Greater Himalayan leucogranites are a discontinuous suite of intrusions emplaced in a thickened crust during the Miocene southward ductile extrusion of the Himalayan metamorphic core. Melt-induced weakening is thought to have played a critical role in strain localization that facilitated the extrusion. Recent advancements in centrifuge analogue modelling techniques allow for the replication of a broader range of crustal deformation behaviors, enhancing our understanding of large hot orogens. Polydimethylsiloxane (PDMS) is commonly used in centrifuge experiments to model weak melt zones. Difficulties in handling PDMS had, until now, limited its emplacement in models prior to any deformation. A new modelling technique has been developed where PDMS is emplaced into models that have been subjected to some shortening. This technique aims to better understand the effects of melt on strain localization and potential decoupling between structural levels within an evolving orogenic system. Models are subjected to an early stage of shortening, followed by the introduction of PDMS, and then a final stage of shortening. Theoretical percentages of partial melt and their effect on rock strength are considered when adding a specific percentage of PDMS in each model. Due to the limited size of the models, only PDMS sheets of 3 mm thickness were used, which varied in length and width. Within undeformed packages, minimal surface and internal deformation occurred when PDMS is emplaced in the lower layer of the model, showing a vertical volume increase of ~20% within the package; whereas the emplacement of PDMS into the middle layer showed internal dragging of the middle laminations into the lower layer and a vertical volume increase ~30%. Emplacement of PDMS results in ~7% shortening for undeformed and deformed models. Deformed models undergo ~20% additional shortening after two rounds of deformation. Strain localization and decoupling between units occur in deformed models where the degree of deformation changes based on the amount of partial melt present. Surface deformation visible by the formation of a bulge, mode 1 extension cracks and varying surface strain ellipses varies depending if PDMS is present. Better control during emplacement is exhibited when PDMS is added into cooler models, resulting in reduced internal deformation within the middle layer.

On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

Mean grain size and structure of ODP Hole 140-504B samples

Microstructural investigations of ocean crust samples provide a complementary approach to both marine surveys and laboratory experiments. The recovery of relatively undeformed diabases from Deep Sea Drilling Project (DSDP)/Ocean Drilling Program (ODP) Hole 504B provides a first opportunity to examine a reference section of microstructural features that influence strain localization at depths of 2 km in the ocean crust. Syn- and post-crystallization features in plagioclase and augite crystals have been examined by optical microscopy and secondary and backscattered electron imaging. These features show a strong influence of modal composition and primary textures on early sites of strain localization. Thermal cracking and subsequent alteration intensities and distribution are strongly phase dependent. A consistently higher intragranular fracture density is observed in augite crystals relative to plagioclase. The impact of alteration on the mechanical response of diabases is likely to depend on the primary textural characteristics. Even where extensive augite alteration occurs, the rock remains supported by a framework of weakly altered plagioclase crystals. The Hole 504B diabases from Leg 140 provide a valuable comparison for future studies of more deformed sections likely to be encountered at depth. Advances in constraining the detailed rheology of the ocean crust at spreading centers would benefit from experimental deformation of texturally diverse diabase and gabbro samples.

The effect of energy feedbacks on continental strength

The classical strength profile of continents(1,2) is derived from a quasi-static view of their rheological response to stress-one that does not consider dynamic interactions between brittle and ductile layers. Such interactions result in complexities of failure in the brittle-ductile transition and the need to couple energy to understand strain localization. Here we investigate continental deformation by solving the fully coupled energy, momentum and continuum equations. We show that this approach produces unexpected feedback processes, leading to a significantly weaker dynamic strength evolution. In our model, stress localization focused on the brittle-ductile transition leads to the spontaneous development of mid-crustal detachment faults immediately above the strongest crustal layer. We also find that an additional decoupling layer forms between the lower crust and mantle. Our results explain the development of decoupling layers that are observed to accommodate hundreds of kilometres of horizontal motions during continental deformation.