► The post-peak compressive fracture energy was shown to vary with the confinement pressure. ► A new model for the stress strain response of uniaxial and confined concrete is presented. ► The new ...model provides good predictions for normal and high strength concretes and for low to high levels of confinement. ► The new model also takes account of size effects due to varying specimen height and aspect ratio.
Analytical models for the full stress–strain relationship of confined and unconfined concrete in compression are required for the numerical simulation of the structural behavior of reinforced concrete structural elements. There are many analytical models presented in the literature, which are generally empirical and are based on tests either on plain concrete specimens or reinforced concrete columns. This paper reviews some widely used analytical models calibrated using triaxial test results on plain concrete and compares their predictions with available test data on uniaxial and triaxial compression on specimens with different specimen height, width or diameter and concrete strength. The model prediction’s for the peak stress and corresponding strain due to confinement are also compared. The residual stress level and the post-peak fracture energy under confinement are discussed. Estimates of the post-peak fracture energy per unit area are obtained from available experimental data showing that the post-peak fracture energy varies with confinement. The size effect on the softening behavior of uniaxial and triaxially loaded plain concrete specimens with different aspect ratios, heights and level of confinement, are also discussed. A new analytical model for unconfined and confined concrete is introduced which tries to address the limitations in previous models. The proposed model is capable of predicting the behavior of normal strength concrete, as well as high strength concrete and incorporates allowances for size effects dependent on specimen height and aspect ratio. Comparisons are made between the proposed new model, the models of others in the literature, and available compression triaxial and uniaxial test results.
This work presents an orthotropic hyperelastic strain energy function (SEF) and associated nonlinear constitutive theory that describes the response of transversely isotropic and orthotropic ...neo-Hookean materials under a range of physical deformations in which the strains are large. The proposed SEF is categorised as invariant-free and is presented as an expression involving quadruple contractions between fourth-order tensors. This form of the SEF retains directional information which can sometimes become lost in typical functions involving scalar invariants. To describe stress-strain relations, the well-known Hookean stiffness tensor for small deformations is decomposed into fourth-order Orthotropic Lamé material tensors separating coupled and non-coupled behaviours. By equating the material parameters in each direction, the model collapses to isotropic Lamé hyperelasticity. The proposed hyperelastic model remains consistent with the linear analysis of anisotropic bodies, when subject to infinitesimal deformations. The proposed SEF compares favourably to large tensile strain and simple shear experimental tests of both isotropic and transversely isotropic materials. Employing an Ogden-type formulation to include additional material terms, the proposed SEF is extended to model highly nonlinear responses such as material stiffening of biological tissues.
•A finite element and plasticity formulation to predict cover spalling behavior is presented.•The effects of restrained shrinkage caused by the presence of reinforcing bars are included.•The ...plasticity dilation rate is extended to handle tensile pressure;•Comparisons are made between experimental results and the numerical simulations using the package 3D-NLFEA.•Comparisons for the softening behavior and the first peak associated with cover spalling are excellent.
The cover spalling behavior in reinforced concrete (RC) columns can greatly affect the axial peak load carrying capacity. For RC columns with normal-strength concrete, the concrete cover still carries some load in the post-peak regime. However, for high-strength concrete, the concrete cover can spall prematurely, eliminating the cover capacity from the peak axial capacity of the column. The strength reduction due to premature cover spalling in high strength concrete columns may be recovered once confinement of the core increases and results in a second peak axial load. Hence, in nonlinear analysis a proper strategy is required to quantify any premature cover spalling for high- or very high-strength reinforced concrete columns. This paper discusses the strategies in modeling the concrete cover region spalling at the constitutive level. These strategies involve: (1) Adjusting the material properties for the concrete cover elements because of restrained shrinkage caused by the steel reinforcement; (2) Extending the plastic dilation rate into the tensile pressure region and adjusting the concrete dilatancy in presence of the tensile pressure; (3) Adding a tension cut-off failure surface to distinguish cracks caused by pure tensile stresses and concrete crushing (tensile splitting cracks) and (4) Assigning the cover spalling material properties only for cover elements outside the reinforcement cage or weak planes. To verify the proposed strategies, numerical validations against experimental published results are undertaken using a 3D-NLFEA finite element package. From the comparisons, it is shown that the proposed model is in good agreement with the experimental results and can accurately predict the location of the cover spalling in the load-deflection behavior.
Two robust methods, a Generalized Target Configuration Under Dead Loads (GTCUD) method and a simplified analytical method are developed for 3D analysis of suspension bridges. These methods provide an ...optimized initial state for 3D suspension bridges under dead loads. The current study makes application to 3D self-anchored suspension bridges with spatially curved main cables and initial cambers of the main girder. Furthermore, the unstrained length method (ULM) based on the unstrained lengths is applied to the bridge structure using two procedures. Finally, it is demonstrated through a bridge example having vertical cambers that the proposed analysis methods can indeed provide an optimized initial solution by showing that both schemes lead to practically identical initial configuration with localized small bending moment distributions.
This study intends to answer how nonlinear beam theories could be rigorously derived when based on three hypotheses: Haringx/Reissner, Engesser, and Ziegler. For this purpose, Reissner formulation is ...first summarized for an elastic beam segment undergoing large displacements and strains, and the nonlinear equations obtained are compactly converted into a non-dimensional form using two parameters of shear-flexibility and extensibility. After that, conjugate strain measures corresponding to axial and shear forces based on Engesser and Ziegler's assumptions are consistently derived, and the resulting governing equations are presented in a dimensionless form. Finally, nonlinear problems of extensible and shearable cantilever beams are solved using the 4th order Runge-Kutta method combined with a shooting method. Shear-deformation and extensibility effects are addressed through two examples showing large deflections and post-buckling behaviors of cantilever beams.
The conventional representation of isotropic hyperelastic strain energy densities as functions of scalar invariants of finite deformation tensors does not naturally extend to the field of anisotropic ...mechanics. Formulating an invariant-free representation of the strain energy function, fourth-order Orthotropic Lamé tensors define the constitutive law whilst naturally collapsing to the transversely isotropic and fully isotropic case where necessary simply as a by-product of known material symmetries. In this study, a simple linear isoparametric hexahedral finite element capable of describing anisotropic invariant-free hyperelasticity is presented. Careful conversion of the fourth-order tensor operations present in the strain energy function to computational arrays then applying to the principle of virtual work generates a weak formulation for finite element analyses. The finite element is then applicable to materials of any degree of anisotropy or compressibility and is particularly useful for predicting highly nonlinear responses such as the stiffening of fibrous biological tissues. A discussion of simple shear experimentation and modelling follows, as well as remarks on modelling nearly-incompressible materials.
This paper presents a plasticity constitutive formulation for actively and passively confined concrete. The loading surface is based on Menetrey and Willam’s model with an additional frictional ...driver parameter. The frictional driver parameter controls the prediction of the peak stress and the residual stress level. The proposed flow rule has a plastic dilation rate control parameter which is a function of the restraining device or the local lateral modulus. A non-constant plastic dilation rate formulation is proposed to improve the prediction of the lateral strain behaviour of concrete. The proposed plastic dilation rate formulation is able to model plastic volumetric compaction caused by the use of very stiff confining devices, as well as the initial plastic compaction after the onset of localized cracking. Furthermore, the formulation is able to distinguish between active and passive confinement by monitoring the local lateral modulus. The accuracy of the proposed plastic dilation rate formulation is verified by comparison with experimental results for specimens subjected to either active or passive confinement from a variety of concrete strengths. The comparison between the proposed plasticity model and the experimental results for concrete under passive confinement (specimens with FRP confining material) was excellent.
Developments in microscopic imaging techniques for soft biological tissues have greatly improved understanding of their underlying microstructures, notably the three-dimensional orientation and ...dispersion of fibrous constituents. In structural constitutive modelling, assuming that the collagenous and muscle fibres in soft tissues are perfectly aligned along a prescribed orientation can limit the ability to accurately predict the experimentally detected stress–strain response of biological samples. The objective of this paper is to extend the representation of hyperelasticity for anisotropic bodies using fourth-order structural tensors (FOSTs) to incorporate the effects of fibre dispersion according to the generalised structural tensor (GST) approach. Dispersion within a family of reinforcing collagen fibres is a common phenomenon in soft tissues which alters their overall mechanical behaviour. The FOST-based representation of the strain energy density function (SEF) separates the constitutive properties of the continuum from the nonlinear descriptions of geometric deformations; with each of these being described by different fourth-order tensors. The constant-valued material and structural properties of the continuum reside within fourth-order material tensors referred to as the anisotropic Lamé tensors. Nonlinearity in the model is then solely applied to the components of the displacement gradient tensor in fourth-order strain measures. The framework provided leads to a unique set of fourteen generalised FOSTs for two-direction preferred hyperelasticity including fibre families which are dispersed according to normalised distributions. In the absence of dispersion, the model collapses to the conventional FOST-based model. Models for the hyperelastic response of arterial wall and passive ventricular myocardium tissues are postulated and show good agreement with experimental data using minimal ground-state material constants.
The relationship between the lateral and axial strain is important when predicting the confinement stresses within reinforced concrete or fiber-reinforced polymer confined columns. Difficulties in ...measuring reliable lateral strains in triaxial compressive experiments mean that, there is a scarcity of lateral strain experimental results. Two recent lateral strain models will be compared with available experimental results. Discussed in this article is the transition point in the lateral and axial strain relationship at which the volumetric strain changes sign, and how this transition point is related to the peak stress. A lateral strain-versus-axial strain model is proposed based on the supposition that the concrete behaves linear elastically in the early stages of loading. Once microcracks form, nonlinear hardening occurs up to the peak stress. After the peak stress, the inelastic lateral strain varies linearly with the inelastic axial strain. The lateral-to-axial inelastic strain ratio is shown to be a function of the lateral confinement level and the failure mechanism.
The authors provided a novel explicit expression for the dot derivative of an isotropic tensor function in the work by Kellermann et al. An alternate proof is provided in this addendum without the ...power series assumption.
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