Two-scale approach for the nonlinear dynamic analysis of RC structures with local non-prismatic parts

There is general agreement in the fact that fully three-dimensional (3D) numerical techniques provide the most precise tools for simulating the behavior of RC buildings even when their computational costs for real structures became them unpractical. Moreover, one-dimensional formulations (1D) are rather limited for predicting the mechanical behavior of framed structures which present local weakness that can determine their global responses, such as it is the case of poor detailed joints of RC buildings in seismic zones or precast concrete structures. An alternative approach, combining both simplicity and computational efficiency, is given by coupling reduced models for prismatic elements with full 3D models for the zones corresponding to connecting joints. In this work, a two-scale approach is developed for obtaining the nonlinear dynamic response of RC buildings with local non-prismatic parts. At global scale level all the elements are rods; however, if local parts with complex geometry appear, the corresponding elements are analyzed considering fully 3D models which constitute the local scale level. The dimensional-coupling between scales is performed imposing the kinematics hypothesis of the beam model on surface-interfaces of the 3D model. An iterative Newton-Raphson scheme which considers the interaction between scales is developed to obtain the response at global level. The tangential stiffness of the local models are obtained numerically. Computationally, the problem is managed by means of a master-slave approach, where the global scale problem acts as the master and the local models are the slaves; iterative communication between scales considers internal forces and moments as well as tangential tensors. The process stops when global convergence is achieved. From the computational point of view, the developed method is implemented in a parallelized scheme, where the master and slave problems are solved independently by different programs thus minimizing the intervention on existing codes specific for beams and solids. Finally, numerical examples are included

A continuum theory of through–the–thickness jacketed shells for the elasto-plastic analysis of confined composite structures: Theory and numerical assessment

The paper proposes a generalized shell formulation devised for the triaxial stress analysis of Through-the-Thickness (TT) confining mechanisms induced by TT Jacketing (TTJ) devices in laminated composite structures, such as masonry walls retrofitted by stirrups-tied FRP sheets and TT jacketed concrete sandwich panels. Assuming a smeared description of TT reinforcements, the proposed shell formulation is constructed as an enhancement of the classical laminated shell formulation based on the Equivalent Single Layer Mindlin First-order Shear Deformation Theory (ESL-FSDT). This enhancement captures TT stretching by adding the TT displacement field among the kinematic variables and permits to describe the smeared TTJ interaction between transverse uniaxial reinforcements and confined layers in terms of continuum equilibrium and compatibility equations. Statics and kinematics of the shell are developed by following standard work-association arguments and encompassing both TT-laminated and TT-functionally graded structures. A nonlinear elasto-plastic constitutive behavior of the core material and of the TT reinforcements is considered and explicit representations of the elasto-plastic tangent operator are derived. The TTJ formulation is combined with a MITC finite element formulation and implemented in the research FE code Opensees. Results of nonlinear structural analyses of walls subject to in-plane and out-of-plane bending show that the proposed TTJ approach provides physically meaningful predictions of the structural response and is capable to efficiently track a complex triaxial confining interaction which ultimately results into marked global structural effects of increased stiffness, strength and ductility. © 2017 Elsevier Lt

Non-linear seismic analysis of RC structures with energy-dissipating devices

The poor performance of some reinforced concrete (RC) structures during strong earthquakes has alerted about the need of improving their seismic behavior, especially when they are designed according to obsolete codes and show low structural damping, important second-order effects and low ductility, among other defects. These characteristics allow proposing the use of energy-dissipating devices for improving their seismic behavior. In this work, the non-linear dynamic response of RC buildings with energy dissipators is studied using advanced computational techniques. A fully geometric and constitutive non-linear model for the description of the dynamic behavior of framed structures is developed. The model is based on the geometrically exact formulation for beams in finite deformation. Points on the cross section are composed of several simple materials. The mixing theory is used to treat the resulting composite. A specific type of element is proposed for modeling the dissipators including the corresponding constitutive relations. Special attention is paid to the development of local and global damage indices for describing the performance of the buildings. Finally, numerical tests are presented for validating the ability of the model for reproducing the non-linear seismic response of buildings with dissipators

Shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework

Impact loadings such as vehicle collisions or falling rocks on a structure could lead it to collapse and, eventually, to fatal victims. Among possible alternatives to analyse this issue, Lumped Damage Mechanics is an interesting option due to its formulation and easiness for practical application. Therefore, this paper presents a simplified lumped damage model to evaluate reinforced concrete structures under impact loads with shear failure mode. In the proposed approach, the damage variable is considered as an output parameter. Such damage variable takes values between zero and one that quantifies the concrete cracking due to impact loading. The proposed formulation was applied in experiments of reinforced concrete beams under impact loads that presents shear collapse. The obtained results showed good accuracy between the proposed model and the actual structural behaviour. Moreover, a possible flowchart for practical applications is also presented. Since the model parameters are easily associated to inelastic phenomena, the proposed formulation might become accessible to engineers in practice

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

We introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain

Cellular automaton development for the study of the neighborhood effect within polycrystals stress-fields

The objective of this Ph.D. project was to develop an analytical model able to predict the heterogeneous micromechanical fields within polycrystals for a very low computational cost in order to evaluate a material fatigue life probability. Many analytical models already exist for that matter, but they have disadvantages: either they are not efficient enough to rapidly generate a large database and perform a static analysis, or the impacts of certain heterogeneities on the stress fields, such as the neighborhood effect, are neglected. The mechanisms underlying the neighborhood effect, which is the grain stress variations due to a given close environment, are unheralded or misunderstood. A finite element analysis has been carried out on this question in the case of polycrystals oriented randomly with a single phase submitted to an elastic loading. The study revealed that a grain stress level is as much dependent on the crystallographic orientation of the grain as the neighborhood effect. Approximations were drawn from this analysis leading to the development of an analytical model, the cellular automaton. The model applies to regular polycrystalline structures with spherical grains and its development was conducted in two steps: first in elasticity then in elasto-plasticity. In elasticity, the model showed excellent predictions of micromechanical in comparison to the finite element predictions. The model was then used to evaluate the worst grain-neighborhood configurations and their probability to occur. It has been shown in the case of the iron crystal that certain neighborhood configurations can increase by 2 times a grain stress level. In elasto-plasticity, the model underestimates the grains plasticity in comparison to the finite element predictions. Nonetheless, the model proved its capacity to identify the worst grain-neighborhood configurations leading important localized plasticity. It has been shown that grains elastic behaviors determine the location and the level of plasticity within polycrystals in the context of high cycle fatigue regime. The grains undergoing the highest resolved shear stress in elasticity are the grains plastifying the most in high cycle fatigue regime. A statistical study of the neighborhood effect was conducted to evaluate the probability of the true yield stress (stress level applied to the material for which the first sign of plasticity would occur in a grain). The study revealed, in the case of the 316L steel, a significant difference between the true elastic limit at 99% and 1% probability, which could be one of the causes of the fatigue life scatter often observed experimentally in high cycle fatigue regime. Further studies on the effect of a free surface and the morphology of the grains were carried out. The study showed that a free surface have the effect to spread even more the grains stress levels distributions. The neighborhood effect approximations used in the developed model were unaffected by a free area. The grains morphology also has shown to have a significant impact on the stress fields. It has been shown that in the case of a high morphology ratio, the stress variations induced by the morphology of the grains are as important as those induced by the neighborhood effect

Microstructure-sensitive fatigue modeling of heat treated and shot peened martensitic gear steels

High strength secondary hardening lath martensitic steel is a strong candidate for high performance and reliable transmission systems in aircraft and automotives. The fatigue resistance of this material depends both on intrinsic microstructure attributes, such as fine scale (M2C) precipitates, and extrinsic attributes such as nonmetallic primary inclusions. Additionally, the aforementioned attributes are affected by processing history. The objective of this research is to develop a computational framework to quantify the influence of both extrinsic (primary inclusions and residual stresses) and intrinsic (martensite laths and carbides) microstructure attributes on fatigue crack formation and the early stage of microstructurally small crack (MSC) growth that dominate high cycle fatigue (HCF) lifetime. To model the fatigue response at various microstructure scales, a hierarchical approach is adopted. A simplified scheme is developed to simulate processing effects such as shot peening that is suitable to introduce representative residual stresses prior to conducting fatigue calculations. Novel strategies are developed to couple process route (residual stresses) and microstructure scale response for comprehensive analysis of fatigue potency at critical life-limiting primary inclusions in gear steels. Relevant microstructure-scale response descriptors that permit relative assessment of fatigue resistance are identified. Fatigue crack formation and early growth is highly heterogeneous at the grain scale. Hence, a scheme for physically-based constitutive models that is suitable to investigate crack formation and early growth in martensitic steel is introduced and implemented. An extreme value statistical/probabilistic framework to assess the influence of variability of various microstructure attributes such as size and spatial distribution of primary inclusions on minimum fatigue crack formation life is devised. Understanding is sought regarding the relative role of microstructure attributes in the HCF process, thereby providing a basis to modify process route and/or composition to enhance fatigue resistance. Parametric studies are conducted to assess the effect of hot isostatic pressing and introduction of compliant coatings at debonded inclusion-matrix interface on enhancement of fatigue resistance. A comprehensive set of 3D computational tools and algorithms for hierarchical microstructure-sensitive fatigue analysis of martensitic gear steels is developed as an outcome of this research; such tools and methodologies will lend quantitative and qualitative support to designing improved, fatigue-resistant materials and accelerating insertion of new or improved materials into service.Ph.D.Committee Chair: David L. McDowell; Committee Member: G. B. Olson; Committee Member: K. A. Gall; Committee Member: Min Zhou; Committee Member: R. W. Ne

Dynamic analysis of beam structures considering geometric and constitutive nonlinearity

A fully geometric and constitutive nonlinear model for the description of the dynamic behavior of beam structures is developed. The proposed formulation is based on the geometrically exact formulation for beams due to Simo but, in this article an intermediate curved reference configuration is considered. The resulting deformation map belongs to a nonlinear differential manifold and, therefore, an appropriated version of Newmark’s scheme is used in updating the kinematics variables. Each material point of the cross-section is assumed to be composed of several simple materials with their own constitutive laws. The mixing rule is used to describe the resulting composite. An explicit expression for the objective measure of the strain rate acting on each material point is deduced in this article. Details about its numerical implementation in the time-stepping scheme are also addressed. Viscosity is included at the constitutive level by means of a thermodynamically consistent visco damage model developed in terms of the material description of the First Piola Kirchhoff stress vector. The constitutive part of the tangent tensor is deduced including the effect of rate dependent inelasticity. Finally, several numerical examples, validating the proposed formulation, are given

Computationally-efficient multiscale models for progressive failure and damage analysis of composites

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