Journal of Engineering Mechanics

In civil engineering, the behavior of a cracked concrete is a major challenge with regard to the management of a structure’s durability. The purpose of this experimental work is to better understand the behavior of a quasi-brittle cracked material at macro-scale, and to provide new data for numerical models. Cyclic compression/tension tests were performed on a notched concrete specimen. The effects of cracks’ closure opening were investigated by classical measurements (displacement sensors) and digital image correlation. Damage and inelastic strains were exhibited when cracks propagate during the tensile phase. When the load is reversed to induce compressive stress, the effect of damage on the concrete stiffness was progressively reduced. A relation between the inelastic strains and the damage variable emerges, and it is proved that these two variables are not thermodynamically independent. The study on the crack lips’ displacement shows that at least a part of the inelastic strain is due to the friction between the crack lips. The evolution of the damage and the dissipated energy during a loading cycle were also calculated, and results showed that the dissipated energy grows hyperbolically with the crack propagation.

Recognizing that the most serious structural stresses often occur at holes or notches, the ability to determine such stresses by combining recorded load-induced temperature information with simple stress functions is demonstrated. Purely theoretical/analytical or numerical stress analyses typically require knowing the external boundary conditions, something which is frequently unknown. Moreover, theoretical stress analyses tend to be restricted to simple, infinite structures. Stresses evaluated at the edge of geometric discontinuities by traditional experimental approaches can be very unreliable. On the other hand, the present technique provides accurate stresses at and in the neighborhood of a hole in an edge-loaded finite plate by processing the recorded temperature data with a simple, general stress function.

Using the Laplace integral transform technique (LITT), an analytical solution to the advection–dispersion–reaction (ADR) equation for a semi-infinite homogeneous geological formation is derived, considering the effect of a retardation factor, zero-order production, and a first-order decay constant. The initial pollutant concentration is considered space dependent in the direction of longitudinal flow in the formation (i.e., aquifer and aquitard). At one end of the aquifer, i.e., the origin, pollutant through time-dependent source concentration is taken into account; but at the other end of the aquifer, the concentration gradient is assumed to be zero due to the uniform flow of the contaminant with respect to the spatial variable. The analytical solution may help evaluate the pattern of concentration for exponentially decreasing or sinusoidally varying unsteady flow in different types of geological formations with average porosity values. The analytical solution is compared with a numerical solution, and they are found to be in very good agreement. The accuracy of the solution is verified with root-mean-square-error (RMSE or RMS-error) analysis.

New integral representations for thermal stresses in Beltrami–Michel equations are proposed in this paper. Using these representations, the author derived thermoelastic volume dilatation (TVD) on the boundary and inside a generalized octant. Then, applying the integral representations for the main thermoelastic Green’s functions (MTGFs) for Lame’s equations, there have been derived new structural formulas for MTGFs. These results are formulated in two theorems. According to structural formulas, many MTGFs for 22 boundary value problems (BVPs) of thermoelasticity may be obtained in terms of elementary functions by changing the respective well-known Green’s functions for Poisson’s equation (GFPE), its regular parts, and calculating some simple integrals. As an example of the application of structural formulas, new MTGFs for a particular BVP for an octant are derived in elementary functions that are very important for their numerical implementation, especially for the elaboration of new boundary elements. Validation of the obtained MTGFs is confirmed on the known MTGFs for a half-space. Graphical and numerical computer evaluation of the derived MTGFs using Maple 15 software is also included. Using the proposed integral representation and technique, it is possible to extend all the obtained results onto any domain of a Cartesian system of coordinates.

This paper presents a hybrid numerical method for the evaluation of dynamic impedance of rigid foundation embedded in anisotropic multilayered soil. The proposed approach includes two main parts: (a) the solution of wave propagation in anisotropic multilayered soil in the frequency wave-number domain; (b) the evaluation of Green’s functions for a buried source lying in the anisotropic multilayered soil in the frequency spatial domain. The derivation of part (a) is based on the precise integration method (PIM) and the mixed variable formulation (MVF) of wave motion equations, which ensure accuracy of the solution and make it convenient to deal with the assembly of layers for multilayered soil. Part (b) can be preceded by applying the inverse Fourier transformation directly. Finally, the flexible volume method is used to obtain the impedance of foundation embedded in anisotropic multilayered soil. A comparison of the numerical results with those available in the literature validates the effectiveness of the proposed approach.

The energy dissipated in a vehicle suspension system due to road roughness affects rolling resistance and the resulting fuel consumption and greenhouse gas emission. The key parameters driving this dissipation mechanism are identified via dimensional analysis. A mechanistic model is proposed that relates vehicle dynamic properties and road roughness statistics to vehicle dissipated energy and thus fuel consumption. A scaling relationship between the dissipated energy and the most commonly used road roughness index, the International Roughness Index (IRI), is also established. It is shown that the dissipated energy scales with IRI squared and scaling of dissipation with vehicle speed $V$ depends on road waviness number $w$ in the form of $V^{w-2}$. The effect of marginal probability distribution of the road roughness profile on dissipated energy is examined. It is shown that although the marginal distribution of the road profile does not affect the identified scaling relationships, the multiplicative factor in these relationships does change from one distribution to another. As an example of practical application, the model is calibrated with the empirical HDM-4 model for different vehicle classes.