Journal of Engineering Mechanics

A high-resolution 3D scanning technique called X-ray microtomography was applied to measure internal damage and crack growth in small mortar cylinders loaded in compression. Synchrotron-based microtomography allows us to resolve internal features that are only a few microns in size. Multiple tomographic scans were made of the same specimen at different levels of deformation using a custom-built loading frame. 3D image analysis was used to measure internal crack growth during each deformation increment. Measured load-deformation curves were used to calculate the nonrecoverable work of the external load on the specimen. Nonrecoverable work of load was related to measured incremental change in crack surface area to estimate work-of-fracture in three dimensions. Initial results indicate a nearly constant work-of-fracture for the early stages of crack growth. These results show that basic fracture mechanics principles may be applied to concrete in compression; however, we must think in terms of 3D multiple crack systems rather than traditional 2D single crack systems.

This paper presents a discrete formulation of the nonlinear minimum weight design of welded connections, in which global throat stresses along every fillet are approximated by piecewise linear shape functions. With this formulation it is possible to find the set of throat thicknesses of a welded connection that gives the minimum amount of weld metal necessary to support an arbitrary set of external actions and a stress field in equilibrium with these actions and satisfying a strength criterion. The formulation adopted involves a linear form of objective function and equilibrium equations, which, together with the convex character of the nonlinear constraints, gives a full convex set of constraints and consequently a global optimum of the objective function. Moreover, the structure of the set of constraints makes it possible to demonstrate that stress and throat thickness values are unique at the optimum, which allows the optimum stress distributions to be simplified, to establish practical design recommendations. Realistic conditions can be imposed on the stress field. The problem is solved with a very accessible and well-known scientific library, which allows this method to be implemented by anyone involved in welding practice. The method proposed is developed for the case of a planar connection. Two practical applications using the strength criterion of Eurocode 3 are included, discussing the results obtained for two types of common arrangements and showing that numerical results are consistent and CPU times reasonably low.

A 2D higher-order shell theory that can take into account the complete effects of higher-order deformations is applied to the buckling problems of a thick circular cylindrical shell subjected to axial compression. The effects of higher-order deformations such as shear deformations and thickness changes on buckling stresses of homogeneous isotropic circular cylindrical shells are studied. Based on the power series expansion of displacement components, a set of fundamental equations of a 2D higher-order shell theory is derived through the principle of virtual displacements. Several sets of truncated approximate theories are applied to solve the buckling problems of a simply supported thick circular cylindrical shell. To assure the accuracy of the present theory, the convergence of the buckling stresses is examined in detail, and the results are compared with those obtained in existing theories.

Concrete cracks on the tension face of beams in uniaxial bending are interpreted as a non-Fickian diffusive phenomenon resulting from a self-affine random fractal process. It is shown how a complete spatial description of the cracking geometry can be found from experimental data using both a (Hurst) scaling exponent and a diffusion-type coefficient. Once determined experimentally, these parameters are used to synthesize cracking patterns using fractional Brownian motion functions. In addition, it is shown how an effective Fokker-Planck diffusion equation can be used to describe the spatial geometry of the cracking.

A parametric study is performed to investigate influences of the opening angles, the slenderness ratios, the material types, the boundary conditions, and the thickness-to-width ratios of the cross section on the in-plane natural frequencies of symmetric cross-ply laminated circular composite beams. Governing equations are obtained based on the classical beam theory. The transfer matrix method is successfully applied to calculate exact natural frequencies with the help of an effective numerical algorithm, which was previously used for isotropic materials. The effects of the shear deformation, the axial deformation, and the rotary inertia are included in the formulation based on the first-order shear deformation theory. The physical system is considered as a continuous system. To verify the present theory, two examples are worked out for straight beams. A quite good agreement is observed with the reported results.

This research uses laser ultrasonic techniques to quantify the frequency-dependent attenuation losses of Rayleigh waves in cement-based materials; these materials are heterogeneous in nature, and this heterogeneity is seen at multiple length scales. As a result, ultrasonic waves that propagate in cement-based materials exhibit a high degree of (material) attenuation losses. Physically, these attenuation losses are a combination of internal friction, such as the work done at material interfaces (ultrasonic absorption) and the scattering losses due to material heterogeneity. The high fidelity, large frequency bandwidth, and absolute, noncontact nature of laser ultrasonics makes this an ideal methodology to measure attenuation in these materials. This research uses a dual-probe, heterodyne interferometer to experimentally measure these attenuation losses (as a function of frequency) in three different materials: (1) aluminum; (2) mortar; and (3) granite. The aluminum results (aluminum is homogeneous at the wavelengths used here) are used to demonstrate the fidelity of the laser ultrasonic measurement technique, while the mortar and granite results (both are heterogeneous at these wavelengths) are used to quantify the attenuation losses present in each material.

In this paper, a microgranular mechanics approach is used to derive an expression for the elastic moduli of an assembly of bonded granulates, based on the response of two particles that are connected by an elastic binder. The derived modulus is a function of the particle/binder modulus, the particle size, the binder thickness, the binder width, the assembly coordination number, the binder content, and the porosity. To demonstrate its applicability, the predicted range of the modulus using the derived model is compared with that measured from experiments. The difference between this method and the traditional homogenization models will be discussed.

Negative bending moments acting in the support regions of continuous composite beams generate tensile stresses in the concrete slab and compressive stresses in the lower steel profile. As a result the mechanical behavior of these beams is strongly nonlinear even for low stress levels, due not only to the slip at the beam-slab interface, but also to cracking in the slab. Therefore, an adequate theoretical modeling should take account of the interactions between the structural steel and the concrete slab by shear connectors and also between steel rebars and concrete in tension by bond phenomenon. In this paper a model of steel and concrete composite beams subjected to negative bending is presented. It accounts for the slip occurring at both the beam-slab interface and the steel reinforcement-concrete interface. Some numerical results, obtained using a suitable numerical procedure, are discussed to show the capacity of the model.

A structure consisting of two pressurized shells in the form of arches that lean against each other and are connected at the point of contact is considered. Such leaning arch-shells have been used in the framework of fabric shelters. The finite-element method is applied to determine the deflections, stability, and vibrations of a pair of these leaning tubes. Symmetric and asymmetric snow loads are treated, along with wind loads parallel to the longitudinal direction of the structure. Results are presented for both fixed and pinned bases, and for arch-shells that are tilted at angles of 15 and 30° with respect to the vertical. Buckling is found for certain cases of snow loading. The corresponding buckling modes involve sway to the side if the bases are fixed, whereas for pinned ends the structure buckles by twisting about a vertical axis through the center. The first three vibration modes are dominated either by side sway, longitudinal sway, or twist about a vertical axis.

The 2D scattering and diffraction of plane shear horizontal waves by a surface semicircular canyon on top of an underground circular unlined tunnel (cavity) in a homogeneous elastic half-space has been analyzed. Using an exact analytic series solution of the problem for a general angle of wave incidence, the ground motions of the half-space surface on and near the canyon and that of the underground cavity were evaluated. These surface motions depend on the following parameters: (1) The angle of incidence ζ of the plane shear horizontal waves; (2) the dimensionless frequency or wave number ka; (3) a₀/a, the ratio of the radius of the surface canyon to that of the underground cavity; and (4) D/a, the ratio of the depth of the cavity to its radius.

The effect of material compressibility on the load-carrying capacity of rectangular section beams is studied in this work by using the Hencky's total strain theory of plasticity. Interaction relations between axial force, shear, and bending moment are obtained for an elastic-linear hardening material. The general form of the obtained equations yields the cases of a reduced combination of applied forces, an incompressible material, and the simpler modeling by the elastic-perfectly plastic behavior. As is well known, results obtained from this modeling coincide with those of the more accurate flow theory only for proportional straining. However, the accuracy remains quite acceptable when the applied loading increases monotonically in a quasi-proportional manner. The constructed model is a generalization of a number of previous works that all dealt with the case of incompressible materials. Demonstration of the important role of Poisson's coefficient is made in the case of short beams for which the load-carrying capacity is not determined by elastic buckling but by a condition of stability corresponding to the existence of a limit loading point in the plastic range of deformation.

The plane thermoelastic problems of a stationary heat source in an infinite plane with an elliptic rigid inclusion and an elliptic hole are analyzed under thermally adiabatic and isothermal boundary conditions. The problems of an elliptic rigid inclusion are derived for the following cases: (1) the case that there are rigid-body displacement and rotation; and (2) the case that there is no rigid-body displacement or rotation. To analyze these problems, the following three fundamental solutions are derived: Problem A, in which a point heat source exists within an infinite domain; Problem B, in which the inclusion has a small amount of rotation; and Problem C, in which the inclusion is subjected to concentrated loads. Two cases can be obtained by superimposing these fundamental solutions. For the hole problem, the fundamental solution (Green's function) is also derived. In analysis, the complex stress functions, the mapping function, and the thermal dislocation method are used. The complex stress functions are obtained as a closed form. For analytic examples, the stress distributions are shown under thermally adiabatic and isothermal boundary conditions. For the crack problem, the stress intensity factors are shown for the location of the heat source.

Employing a thermodynamic framework, chemomechanical couplings for shotcrete are treated in this paper. A new material model based on multisurface chemoplasticity is presented. It accounts for hydration kinetics and chemomechanical couplings related to the strength growth and the evolution of stiffness properties as well as for autogeneous shrinkage in early-age shotcrete. The underlying intrinsic material functions, which are independent of field and boundary conditions, are determined from standard material tests. As for the numerical treatment of the constitutive equations of the material model, an extended form of the return mapping algorithm is proposed. The constitutive equations are applied to a two-surface chemoplastic model, consisting of a Drucker-Prager loading surface and a tension cut-off. In a companion paper, the proposed material model is employed for 2D structural analyses of tunnels driven according to the New Austrian Tunneling Method.

This paper deals with application of the multisurface chemoplastic model for shotcrete, as described in a companion paper, to isothermal 2D structural analyses of tunnels driven according to the principles of the New Austrian Tunneling Method (NATM) in drained, overconsolidated, creep-active soil. The latter is modeled by means of a viscoplastic material law. The influence of each ingredient of the chemoplastic model on the structural behavior of the tunnel is studied. In this manner, it is determined under which circumstances the full chemoplastic model is advisable for the description of the structural behavior of the tunnel and where more simple models are sufficient. Moreover, the nature of the soil-shotcrete interaction problem governing the NATM is elucidated by means of a dimensionless parameter, which is derived directly from the constitutive evolution equations for both soil and shotcrete.

The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm has a truncation error of order 2. As a consequence, the global performance of the second algorithm is clearly superior. However, for the particular case of shear-free deformation paths, the first algorithm correctly predicts null shear stresses, while the second one does not. This behavior was reported in a previous paper for an extension-rotation test. In this note a general shear-free deformation path is considered in full detail.

An improved method for interpreting strain gauge data is proposed to reduce the effects of the measurement errors. The results obtained by this modified method are compared with both a traditional strain gauge solution using two data points and a theoretical solution derived from complex potentials. The comparison shows that the modified solution is in better agreement with the theoretical solution as compared with the traditional solution.

Fracture toughness for microcracking in a viscoelastic particulate composite is derived theoretically from the relationship between a continuum damage model and a micromechanical model. The continuum model presented by Park et al. and the micromechanical model presented by Schapery, which account for viscoelasticity and growing damage, are reviewed and compared in this paper. The condition for local microcrack growth is linked to the evolution law for damage growth in the homogenized continuum. Local microcrack growth is governed by an energy-based fracture criterion. Damage growth in the continuum is described by a phenomenological evolution law determined from an experiment. The resulting fracture toughness for asphalt concrete decreases rapidly with loading duration.