Modeling of Early-Age Creep of Shotcrete. I: Model and Model Parameters

In this paper, creep and viscous flow are revisited from the standpoint of constitutive modeling of thermo-chemo-mechanical couplings in early-age concrete. Within the framework of closed reactive porous media, creep is modeled by means of two mechanisms: a stress-induced water movement within the macropores and a relaxation mechanism in the micropores of cement gel, both of which lead to aging effects on creep and viscous flow of concrete. Regarding the first creep mechanism, aging results from chemomechanical couplings. Concerning the second mechanism, long-term aging is attributed to the relaxation of microprestresses in the micropores. Following the formulation of the model, it is shown how the material parameters can be identified from creep tests performed at different ages of loading. Finally, the model is applied to shotcrete, for which proper experimental data are missing.     

The “Chunnel” Fire. I: Chemoplastic Softening in Rapidly Heated Concrete

This paper and its companion paper present the main results of an assessment of the fire in the Channel Tunnel (the “Chunnel”), which destroyed a part of the concrete tunnel rings by thermal spalling. The study seeks (1) to evaluate the effect of thermal damage (loss of elastic stiffness) and thermal decohesion (loss of material strength) upon the stress state and cracking at a structural level; and (2) to check whether restrained thermal dilatation can explain the thermal spalling observed during the fire. In the present paper, a macroscopic material model for rapidly heated concrete is developed. It accounts explicitly for the dehydration of concrete and its cross-effects with deformation (chemomechanical couplings) and temperature (chemothermal couplings). The thermal decohesion is considered as chemoplastic softening within the theoretical framework of chemoplasticity. Furthermore, kinetics of dehydration, dimensional analysis, and thermodynamic equilibrium considerations show that a unique thermal dehydration function exists that relates the hydration degree to the temperature rise, provided that the characteristic time of dehydration is much inferior to the characteristic time of structural heat conduction. The experimental determination of the thermal dehydration function from in-situ measurements of the elastic modulus versus furnace temperature rise is shown from experimental data available from the chunnel concrete. Finally, by way of an example, the proposed constitutive model for rapidly heated concrete is combined with the three-parameter William-Warnke criterion extended to isotropic chemoplastic softening.     

The “Chunnel” Fire.?II: Analysis of Concrete Damage

In Part I of this study, a material model for the in-situ behavior of rapidly heated concrete was developed that accounts explicitly for the dehydration of concrete and its cross-effects with deformation (chemomechanical couplings) and temperature (chemothermal couplings). In this part of the study, the model is used in finite-element analysis of the tunnel rings of the Channel Tunnel (the “Chunnel”) exposed to fire. An analysis of the finite-element results—i.e., the profiles of temperature, dehydration, stresses, and plastic strains—clearly shows that the thermal spalling that occured during the Chunnel fire is initiated by an in-plane biaxial compressive stress clog closed to the heated surface. The compressive stresses are caused by restrained thermal dilatation and are bounded by chemoplastic softening due to dehydration. They provoke permanent radial deformation, which can be attributed to spalling. The role of thermal damage and thermal decohesion is discussed by comparing elastic, chemoelastic, and chemoplastic stress developments during the 10 h fire exposure. It is found that the salient feature to capture the initiation of thermal spalling at a structural level is the chemoplastic softening behavior at a constitutive material level. It is also shown that a reinforcement on the cold-side, as well as steel fiber reinforcement of concrete, in tunnel rings may significantly increase the risk of thermal spalling.     

Chemoporoplasticity of Calcium Leaching in Concrete

This paper presents a macroscopic material model for calcium leaching in concrete, for the quantitative assessment, in time and space, of the aging kinetics and load bearing capacity of concrete structures subjected to severe chemical degradation (such as radioactive waste disposal applications). Set within the framework of chemically reactive porous continua, the model accounts explicitly for the leaching of calcium of portlandite crystals and C-S-H, and its cross-effects with the elastic deformation (chemical damage) and irreversible skeleton deformations (chemical softening) treated within the theory of chemoplasticity. In the first part of this paper the governing equations are derived focusing on the chemomechanical couplings between calcium dissolution, increase in porosity, and deformation and (micro-) cracking of concrete. Without any a priori assumption concerning local equilibrium between the solid calcium concentration s and the interstitial calcium concentration c the well-known calcium leaching state function s = s(c) is then derived using combined thermodynamic equilibrium and dimensional arguments relating to the structural dimension of containment structures. In the second part, this paper addresses the experimental determination of chemical damage and chemical softening of the calcium leaching. For chemical damage, a simple mixture rule involving different skeleton constituents suffices to capture the main chemoelastic features of leaching; in turn, microhardness measurements allow access to the chemical softening state function capturing chemoplastic cross-effects. The intrinsic nature of these functions, and of the proposed procedure, is validated by means of finite-element analysis of experimental compression tests of a degraded specimen with nonhomogeneous chemical degradation states.     

Two-Phase Composite Model for High Performance Cementitious Composites

This paper presents a new constitutive model for fiber reinforced cementitious composite materials (FRCC), which is particularly suitable for High Performance Cementitious Composites (HP2C). The model is a two-phase composite model, one phase presenting the matrix, the other the composite fibers. In addition, the matrix–fiber interaction is taken into account as internal cross effects (i.e., thermodynamic couplings) between the irreversible deformations of the composite constituents. From one-dimensional thermodynamics, the partial stresses in the matrix and fibers are derived as thermodynamic forces associated with the irreversible deformations of matrix and fibers, respectively. Next, the identification of the model parameters from tensile data is detailed. In particular, it is shown that the model allows quantification of the ductility enhancement of HP2C in comparison with ordinary FRCC, through two material parameters derived from the constitutive model: a matrix–fiber coupling modulus and a friction-to-fracture strength ratio, to which we refer as ductility ratio. The physical significance of these model parameters is discussed in the context of micromechanical theory. The coupling modulus is found to depend mainly on the fiber volume fraction and the matrix quality. The ductility ratio depends on four material design parameters, which are intrinsic to the matter, and which are not affected by structural size effects. We conclude that any ductility gain, which can be obtained through the use of HP2C, is only related to the mix design, and not to structural dimensions.     

Three-Dimensional Finite-Element Analysis of High Damping Rubber Bearings

A three-dimensional finite element modeling of high damping rubber bearings is studied. At first, the constitutive model of high damping rubber materials proposed by the writers is formulated in order to derive the constitutive tensor, which is required in the application of the finite element method. Second, a mixed finite-element method consistent with the proposed constitutive model is described. In this method, slightly compressible materials with rate form constitutive models are applied. Then, using the constitutive model and the finite-element method, a three-dimensional finite element model of high damping rubber bearings is constructed. The simulations by the model are found to be in good agreement with the experimental results of the bearing. Finally, complex deformation such as torsional or rotational deformation of the bearing are simulated by the finite-element model, and the design equations for these deformation are proposed on the basis of the simulations or experimental results.     

Creep of Polymer Matrix Composites. I: Norton/Bailey Creep Law for Transverse Isotropy

This research concerns polymer matrix composite (PMC) materials having long or continuous reinforcement fibers embedded in a polymer matrix. The objective is to develop comparatively simple, designer friendly constitutive equations intended to serve as the basis of a structural design methodology for this class of PMC. Here (Part I), the focus is on extending the deformation model of an anisotropic deformation/damage theory presented earlier. The resulting model is a generalization of the simple Norton/Bailey creep law to transverse isotropy. A companion paper (Part II) by the writers deals with damage and failure of the same class of PMC. An important feature of the proposed deformation model is its dependence on hydrostatic stress. Characterization tests on thin-walled tubular specimens are defined and conducted on a model PMC material. Additional exploratory tests are identified and carried out for assessing the fundamental forms of the multiaxial creep law.     

Constitutive Equation Models of Hot-Compressed T122 Heat Resistant Steel

 Based on dislocation reaction theory and Avrami equation, a constitutive equation model was developed to describe dynamic recovery and dynamic recrystallization during hot deformation of T122 heat resistant steel, which have taken the effect of dynamic strain aging into account. Uniaxial hot compression test had been carried out over a wide range of strain rate (001 to 10 s-1) and temperature (900 to 1200 ℃) with the help of Gleeble 3500. Obtained experimental data was applied to determine the material parameters in proposed constitutive equations of T122 steel, by using the non-linear least square regress optimization method. The calculated constitutive equations are quantitatively in good agreement with experimentally measured curves and microstructure observation. It shows that propose constitutive equation T122 steel is able to be used to predict flow stress of T122 steel during hot deformation in austenite temperature scope.     

Anisotropic Damage Model for Concrete

In this paper, a damage constitutive model accounting for induced anisotropy and bimodular elastic response is applied to two-dimensional analysis of reinforced concrete structures. Initially, a constitutive model for the concrete is presented, where the material is assumed as an initial elastic isotropic medium presenting anisotropy and bimodular response (distinct elastic responses, whether tension or compression stress states, prevail) induced by damage. Two damage tensors govern the stiffness under prevailing tension or compression stress states. Criteria are then proposed to characterize the dominant states. Finally, the proposed model is used in plane analysis of reinforced concrete beams to show its potential for use and to discuss its limitations.     

A general material law of plasticity and its numerical application

FE-codes for numerical simulations of metal forming processes need very general material laws. In this paper constitutive equations are proposed which include real-time and endochronic effects as well as kinematical hardening and a variable Hill-anisotropy. The law presented here is denoted in terms of strain spaces. The objective rates occurring in the evolutional rules of internal parameters include the concept of plastic spin to avoid physically meaningless oscillations of stresses in case of shear processes. Additionally an integrational scheme is presented which works very robustly and highly precisely even if very large strain differences occur within one time-step of the integration.     

钢锭与锭模三维应力场耦合分析有限元系统

介绍了由清华大学开发的耦合分析钢锭与锭模钢锭凝固过程中应力场的三维有限元软件，导出了弹塑性蠕变在各种差分格式下的有限元迭代公式，并给出拉压性能不同的材料的有限元计算法，此外，分析了各类边界条件的处理方法，并对接触边界与斜约束边界的算法作了专门的探讨。有限元计算结果对锭模突发性顺裂产生部位及时间的分析结论与现场观察结果的吻合证明了该系统的可靠性。     

A load perturbation method of examining dynamic strain ageing

Load perturbation tests carried out on a 6063 AlMgSi alloy under load rate control verify the predictions of a constitutive model proposed earlier to describe the mechanical response in the dynamic strain ageing regime. The verification is based on a comparison of the measurements with the analytical solution of linearized constitutive equations for small perturbations as well as with numerical solutions for the full nonlinear constitutive model. The possibility of using this type of perturbative testing for accurate determination of the onset of plastic instability is discussed.     

Constitutive behavior of as-cast AA1050, AA3104, and AA5182

Recent thermomechanical modeling to calculate the stress field in industrially direct-chill (DC) cast-aluminum slabs has been successful, but lack of material data limits the accuracy of these calculations. Therefore, the constitutive behavior of three aluminum alloys (AA1050, AA3104, and AA5182) was determined in the as-cast condition using tensile tests at low strain rates and from room temperature to solidus temperature. The parameters of two constitutive equations, the extended Ludwik equation and a combination of the Sellars-Tegart equation with a hardening law, were determined. In order to study the effect of recovery, the constitutive behavior after prestraining at higher temperatures was also investigated. To evaluate the quantified constitutive equations, tensile tests were performed simulating the deformation and cooling history experienced by the material during casting. It is concluded that both constitutive equations perform well, but the combined hardening-Sellars-Tegart (HST) equation has temperature-independent parameters, which makes it easier to implement in a DC casting model. Further, the deformation history of the ingot should be taken into account for accurate stress calculations.     

3D Modeling of an NATM Tunnel in High K0 Clay Using Two Different Constitutive Models

This paper studies the accuracy of the three-dimensional finite-element predictions of a displacement field induced by tunneling using new Austrian tunneling method (NATM) in stiff clays with high K0 conditions. The studies are applied to the Heathrow express trial tunnel. Two different constitutive models are used to represent London Clay, namely a hypoplastic model for clays and the modified Cam-clay (MCC) model. Good quality laboratory data are used for parameter calibration and accurate field measurements are used to initialize K0 and void ratio. The hypoplastic model gives better predictions than the MCC model with satisfactory estimate for the displacement magnitude and slightly overestimated width of the surface settlement trough. Parametric studies demonstrate the influence of variation of the predicted soil behavior in the very-small-strain to large-strain range and the influence of the time dependency of the shotcrete lining behavior.     

Hybrid Method for Analysis of Segmented Shotcrete Tunnel Linings

When driving tunnels according to the New Austrian Tunneling Method. (NATM), shotcrete is applied onto the newly excavated areas of the tunnel surface. Large deformations occurring when driving tunnels under squeezing rock conditions lead to the destruction of a conventional shotcrete lining. As a remedy, segmented shotcrete linings characterized by an increased compliance have successfully been installed. In this paper a hybrid method for the analysis of such segmented tunnel linings is presented. It combines in situ displacement measurements with a thermochemomechanical material law for shotcrete. The application of this method to the Semmering pilot tunnel provides new insights into the load-carrying behavior of segmented tunnel linings.     

Dynamic Behavior of Reinforced Concrete Beams Strengthened with Composite Materials

The dynamic behavior of reinforced concrete (RC) beams strengthened with externally bonded composite materials is analytically investigated. The analytical model is based on dynamic equilibrium, compatibility of deformations between the structural components (RC beam, adhesive, composite material) and the concept of the high order approach. The equations of motion along with the boundary and continuity conditions are derived using Hamilton’s variational principle and the kinematic relations of small deformations. The mathematical formulation also includes the constitutive laws that are based on beam and lamination theories, and the two-dimensional elasticity representation of the adhesive layer including the closed form solution of its stress and displacement fields. The Newmark time integration method, which is directly applied to the resulting set of coupled partial differential equations, is adopted. This procedure yields a set of ordinary differential equations, which are analytically or numerically solved in every time step. The response of a strengthened beam to different dynamic loads that include impulse load, harmonic load, and seismic base excitation is numerically investigated. The numerical study highlights some of the phenomena associated with the dynamic response and explores the capabilities of the proposed model. The paper closes with a summary and conclusions.     

Thermomechanical Framework for the Constitutive Modeling of Asphalt Concrete

This study is concerned with the constitutive modeling of asphalt concrete. Unlike most constitutive models for asphalt concrete that do not take into account the evolution of the microstructure of the material, this study incorporates the evolution of the microstructure by using a framework that recognizes that a body’s natural configurations can evolve as the microstructure changes. The general framework, on which this study is based, is cast within a full thermomechanical setting. In this paper, we develop models within the context of a mechanical framework that stems from the general framework for models based on the full thermodynamic framework and the resulting equations represent a nonlinear rate type viscoelastic model. The creep and stress relaxation experiments of Monismith and Secor are used for validating the efficacy of the model, and it is found that the predictions of the theory agree very well with the available experimental results. The advantages of using such a framework are many, especially when one wants to model the diverse mechanical and thermodynamic response characteristics of asphalt and asphalt concrete.     

Numerical Simulations of Upsetting Process of the Fresh Fiber-Cement Paste

In this paper, first, the technical aspects for applications of finite-element method (FEM) in modeling material forming processes are reviewed, with a final determination of employing the solid formulation explicit finite element code, ANSYS/LS-DYNA, with the arbitrary Lagrangian–Eulerian mesh to simulate upsetting process, which is the uniaxial compression of a cylindrical specimen between two flat platens, of the fresh fiber-cement paste. After combining a previously proposed elasto-viscoplastic constitutive model for the fresh fiber-cement paste into the numerical procedure, satisfactory agreement between experimental and simulated results is observed for the upsetting force-imposed displacement data. The evolution of the deformation within the material flow in the upsetting process is then interpreted based on the calculated results. The study indicates that the present finite-element procedure, as well as the material constitutive model and the boundary condition treatment, are appropriate for modeling the upsetting process of the fresh fiber-cement paste.