Journal of Engineering Mechanics

A mathematical model for the corrosion of steel in concrete when exposed to seawater was developed to enable the evaluation of the corrosion rate. The analysis was made for the case of concrete placed in the splash zone and for concrete fully immersed in the seawater. Mathematical models of transport processes significant for the steel corrosion in concrete exposed to seawater include transport of capillary water, oxygen, chloride ions, and hydroxyl ions through the concrete cover. These physical processes are described using the system of partial differential equations, which were then solved using the finite element method in the spatial domain and using the finite difference method in the time domain, for an axi-symmetric problem.

This paper is concerned with modeling, identification, and experimental determination of thermo-chemo-mechanical couplings in early age concrete for the prediction of deformation and cracking on account of strength growth as chemo-plastic coupling within the theory of elastoplasticity. By applying the thermodynamic framework of reactive porous media to concrete at early ages, the coupling terms result from Maxwell symmetries. They lead to account for autogeneous shrinkage; hydration heat; and strength growth due to chemo-mechanical, thermo-chemical, and chemo-plastic coupling with a minimum of material parameters of clear physical significance and accessible by standard material tests. Furthermore, the diffusion of water through the layers of hydrates already formed is considered as the dominant mechanism governing the kinetics of hydration. To integrate this micromechanism in the macroscopic modeling, the “normalized affinity” is identified as an intrinsic kinetic function that characterizes the macroscopic hydration kinetics of concretes. Finally, by way of example, a Drucker-Prager criterion with isotropic chemical hardening is worked out that takes into account the evolution of the plastic properties (crack threshold and hardening/softening properties) with the hydration advancing.

The main purpose of the present study is to investigate the possibility to predetermine the strength of concrete at different strain rates and cyclic loading. Particular emphasis is placed on describing the method of estimating the dynamic strength of concrete from results of monotonic tests. One approach to solving this problem is based on making allowance for the kinetic nature of fracture, i.e., taking into account that the failure of building materials (metals, glasses, polymers, composites, etc.) under loading is not a critical event but rather is the result of a process of nucleation, accumulation, and the development of damage elements. At the atomic-molecular level, this process is controlled by events of breaking of interatomic bonds by thermal fluctuations. Comparing the given physically justified method with experiments shows that developed methods of diagnostics of dynamic characteristics are sufficiently accurate to make it possible to decrease the labor input of measurements, and do not require special and expensive equipment that is used for dynamic tests.

This paper describes a new discrete algorithm for analyzing the behavior of two-dimensional (2D) assemblies of disjoint particles. The algorithm treats each particle as a 2D polygon, and generates contact normal and shear forces between two contacting particles when inference (overlap) occurs. The key new feature of the algorithm is a very efficient and effective multilevel contact detection scheme that makes it possible to track the behavior of much larger assemblies of polygonal particles than has been possible in the past. Examples involving large assemblies of particles are presented to show the capabilities of the method for (1) analyzing quasi static assemblies of particles subjected to stress (such as soil or rock masses), and (2) investigating dynamic particulate flows (such as flows through hoppers and gates). The algorithm may be used to conduct analyses of slip and failure processes in geologic materials and for investigating fracture and fatigue of metals.

This paper analyzes dynamic localization of damage in structures with softening inelastic hinges and studies implications for the seismic response of reinforced concrete or steel frames of buildings or bridges. First, the theory of limit points and bifurcation of the symmetric equilibrium path due to localization of softening damage is reviewed. It is proven that, near the state of static bifurcation or near the static limit point, the primary (symmetric) path of dynamic response or periodic response temporarily develops Liapunov-type dynamic instability such that imperfections representing deviations from the primary path grow exponentially or linearly while damage in the frame localizes into fewer softening hinges. The implication for seismic loading is that the kinetic energy of the structure must be absorbed by fewer hinges, which means faster collapse. The dynamic localizations are demonstrated by exact analytical solutions of torsional rotation of the floor of a symmetric and symmetrically excited frame, and of horizontal shear excitation of a building column. Static bifurcations with localization are also demonstrated for a portal frame, a multibay frame, and a multibay-multistory frame. The widely used simplification of a structure as a single-degree-of-freedom oscillator becomes invalid after the static bifurcation state is passed.

Representative volume (RV) of a composite material is important not only for experimental determination of materials properties, but also for theoretical analysis of various properties of the materials. RV is a random variable; this is especially true for the composites with heterogeneous microstructures. In the present study, RV is redefined as a relationship among three parameters: the volume under consideration, the measured or predicted value of a property corresponding to the volume, and the scattering of the property from the real effective property. There are two steps involved to determine RV. The first is to determine the relationship among the effective property, the properties of each constituents, and volume fractions, which is the topic in composite mechanics. The second is determination of the local variation of the heterogeneity of the composite because, with increasing size of the local volume, the statistics from the local volume asymptotically approaches the value from the global average. The main purpose of this study is to develop a theoretical model to determine local variation of heterogeneity, which is obviously related to the morphological features of the composites. The model accounts for coarseness of grain sizes, volume fractions, spatial arrangement of the constituents, and properties of each constituents. By combining the model with available composite models for effective properties of composites, RV for various materials properties can be developed. As an example, RV for elastic moduli of cementitious materials is demonstrated.

Two mathematical models are developed to analyze the transient flow of a single solid capsule in a horizontal hydraulic capsule pipeline (HCP). The method of characteristics is used to numerically solve these models. The first model assumes that the capsule is elastic and the second model assumes that it is rigid. A numerical comparison between these two models and a third point mass model published by Tomita is presented. The first two models give results that are in good agreement with each other but differ greatly from the results of the point mass model.

The nonlinear behavior of concrete is complex and is governed by a variety of parameters. As a result, there exist a number of constitutive models that try to predict concrete behavior beyond the linear elastic limit. A mature concrete model must not only remain operational under proportional and nonproportional loadings, but it should be capable of capturing the response behavior in the prepeak and postpeak regimes. Based on such a model, which resorts to an isotropic-hardening description of the prepeak behavior and to a fracture energy-based isotropic-softening description of the postpeak regime, the present paper develops a finite element reliability formulation of nonlinear stochastic concrete under both proportional and nonproportional loadings. The formulation accounts for randomness in loading and spatial variability of concrete properties. The proposed reliability formulation with focus on the prepeak regime uses analytical expressions to compute response gradients. In this manner, efficiency and accuracy concerns associated with perturbation methods are avoided. A computer code is developed for the application of the proposed method to concrete structures. Numerical results are also presented to demonstrate the capability of the computer code to evaluate the reliability of a nondeterministic concrete panel with respect to excessive plastic deformation under both proportional and nonproportional loadings.