Journal of Engineering Mechanics

The stochastic response of a rigid platform is quasi-static and can be represented as a linear combination of nonlinear random wave loadings. In this study two efficient probabilistic approaches are respectively presented to estimate the higher-order statistics of mildly and highly non-Gaussian structural responses. The eigenvalue analysis of structural quasi-static response in the first approach is based on the expansion of the response in terms of independent Gaussian random variables. The second approach extends the earlier quasi-static analysis procedures to obtain the higher moments of response by including current effects and inundation effects. The interested prediction of extreme responses during a short-term storm, by mean upcrossing rates and mean extremes, can then be achieved by applying Winterstein’s functional transformation. These quantities are found in good agreement with not only Monte Carlo simulation results but also the extreme values obtained using a recently proposed method by Naess et al. in 2007.

Basin-scale internal waves are inherently nonhydrostatic; however, they are frequently resolved features in three-dimensional hydrostatic lake and coastal ocean models. Comparison of hydrostatic and nonhydrostatic formulations of the Centre for Water Research Estuary and Lake Computer Model provides insight into the similarities and differences between these representations of internal waves. Comparisons to prior laboratory experiments are used to demonstrate the expected wave evolution. The hydrostatic model cannot replicate basin-scale wave degeneration into a solitary wave train, whereas a nonhydrostatic model does represent the downscaling of energy. However, the hydrostatic model produces a nonlinear traveling borelike feature that has similarities to the mean evolution of the nonhydrostatic wave.

In this paper a consistent method including damage criteria in the seismic response of single-degree-of-freedom systems is proposed. The method allows the determination of suitably modified strength or displacement inelastic spectra through the introduction of an equivalent damage factor $p_{\text{dam}}$ that accounts for earthquake damage potential; analogously capacity spectra could be obtained. Three types of damage indices are considered (Park and Ang index $D_{\text{P}\&\text{A}}$ , energy index $D_E$ , and low-cycle fatigue index $D_F$ ) and derivation of $p_{\text{dam}}$ is pursued for all these cases. Moreover approximate simplified expressions in the function of Cosenza and Manfredi seismological $I_D$ index, which accounts for cyclic damage potential of an earthquake, are also proposed. In this way damage capacity spectra are obtained to improve the seismic assessment of existing structures including damage effect.

A generic framework for stochastic modeling of deterioration processes is proposed, based on dynamic Bayesian networks. The framework facilitates computationally efficient and robust reliability analysis and, in particular, Bayesian updating of the model with measurements, monitoring, and inspection results. These properties make it ideally suited for near-real time applications in asset integrity management and deterioration control. The framework is demonstrated and investigated through two applications to probabilistic modeling of fatigue crack growth.

An efficient method is presented to characterize the damage state for two-dimensional multicracked elastic solids. This method is based on the concept of a path-independent $M_c$ -integral, through which the surface energy associated with creation of all the cracks is evaluated. On one hand, when the cracked media are homogeneously stressed, the correspondence relation between the effective material moduli and $M_c$ is established. On the other hand, when the cracked solids are nonhomogeneously stressed, the effective structural stiffness is determined by using the result of $M_c$ . Through proper use of $M_c$ , the damage state of the cracked structure can be assessed both qualitatively and quantitatively.

A three-dimensional (3D) micromechanics-based evolutionary damage model is proposed to predict the effective elastic behavior of continuous fiber-reinforced brittle matrix composites with microcracks and imperfect interfaces. Eshelby’s tensor for a circular cylindrical inclusion with slightly weakened interface is adopted to model continuous fibers with imperfect interfaces. The nucleation of microcracks is simulated by employing the continuum damage model. A multilevel damage modeling process in accordance with Weibull’s probabilistic function is incorporated into the micromechanical framework to describe the sequential evolution of imperfect interfaces in the composites. Numerical examples corresponding to uniaxial loadings in the longitudinal and transverse directions are solved to illustrate the potential of the proposed damage model. Furthermore, the present prediction is compared with available experimental data in the literature to highlight the applicability of the proposed model.

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

This paper presents a fully developed nonlinear analytical (exact) model for analyzing composite beams under transverse bending load. The model reproduces the elements responsible for the relative slip between the layers (shear connectors and interface) with an elastoplastic strain-softening interlayer. Further than the slip, the model predicts stresses due to a given load and ultimate load for debonding of bilayered composite beams. All the details on the mathematical development are presented. This paper advances the state of the art, since the last development available in literature is an analytical (nonexact) linear model. A number of parametric studies are conducted to evaluate the influence of various geometrical and material parameters, the main results of which are presented together with the interpretation, e.g., the dependence of load-carrying capacity, stresses, and deflection on the local nonlinear load-slip relationship. The research proves as well that the shear connection lower and upper bounds (respectively, totally flexible and infinite rigid shear connectors) do not imply any lower and upper bound for the response.

This paper presents a fast treatment of essential boundary conditions in three-dimensional (3D) meshfree computation for computational efficiency. Due to the loss of Kronecker delta properties in the meshfree shape functions, the imposition of essential boundary conditions is tedious, especially in 3D applications. The proposed boundary singular kernel (BSK) method introduces singularities to the kernel functions associated with the essential and kinematically constrained boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values, and consequently constraints can be imposed directly. In this work, the recovery of nodal value properties on essential boundary nodes is proved for general $n$ -dimensional geometries. The extension of previously proposed two-dimensional BSK method to 3D formulation thus becomes straightforward, and essential boundary treatment consumes almost no additional cost to meshfree computation and makes the method affordable for industrial applications. The effectiveness of the proposed method is demonstrated in 3D metal forming examples.

The response of a saturated fine sand (Nevada sand No. 120) with relative density $D_r\approx 70\%$ in drained and undrained conventional triaxial compression and extension tests and undrained cyclic shear tests in a hollow cylinder apparatus with rotation of the stress directions was studied. It was observed that the peak mobilized friction angle for this dilatant material was different in undrained and drained tests; the difference is attributed to the fact that the rate of dilation is smaller in an undrained test than it is in a drained test. Consistent with the findings of others, the material is more resistant to undrained cyclic loading for triaxial compression than for triaxial extension. In rotational shear tests in which the second invariant of the deviatoric stress tensor is held constant, the shear stress path (after being normalized by the mean normal effective stress) approached an envelope that is comparable but not identical in shape to a Mohr-Coulomb failure surface. As the stress path approached the envelope, the shear end deviatoric strains continued to increase in an unsymmetrical smooth spiral path. During the rotational shear tests, the direction of the deviatoric strain-rate vector (deviatoric strain increment divided by the magnitude of change in Lode angle) was observed to be about midway between the deviatoric stress increment vector and the normal to a Mohr-Coulomb failure surface in the deviatoric plane. The stress ratio at the transition from contractive to dilative behavior (i.e., “phase transformation”) was also observed to depend on the direction of the stress path; therefore this stress ratio is not a fundamental property. Results from torsional hollow cylinder tests with rotation of stress directions are presented in new graphical formats to help understand and interpret the fundamental soil behavior.

The paper investigates the characteristics of propagating shock waves in soil, resulting from an explosion of a cylindrical line charge. The main purpose of this investigation is to study the full locking parameter’s effect on the qualitative and quantitative behavior of the peak pressure attenuation. The soil is modeled as a bulk irreversible compressible elastic plastic medium, including full bulk locking and dependence of the current deviatoric yield stress on the pressure. The Lagrange approach and the modified variational-difference methods are used to simulate the process. A study of the characteristics of the equation of the state of soil was carried out for the case of a cylindrical line charge explosion in an infinite soil medium. The computed results were compared with experimental data. It was found that the full locking model somewhat overpredicts the measured stresses. The dependence of the peak stress attenuation, during the shock wave propagation, on the full locking parameter of the equation of state was studied. When the pressure-volumetric strain relationship beyond the point of full compaction is not steep, the attenuation may be described by a power law that may be expressed as a linear relationship on a logarithmic scale. When this relationship is relatively steep however, the logarithmic dependence of the peak stress on the shock wave coordinate is close to a bilinear function. It was also shown that the shock wave peak stress parameters of this power law for the high pressure range (i.e., short distance of the wave front from the explosive charge) are linearly dependent on the full locking parameter. Also it was shown that the full compaction density affects the exponent of stress-distance power relationship only at the earlier stage of the wave propagation and only when the range of nonlinear elastic compaction is relatively narrow.

Asymptotic theories of classical micromechanics are built on a fundamental assumption of large separation of scales. For random heterogeneous materials the scale-decoupling assumption however is inapplicable in many circumstances from conventional failure problems to novel small-scale engineering systems. Development of new theories for scale-coupling mechanics and uncertainty quantification is considered to have significant impacts on diverse disciplines. Scale-coupling effects become crucial when size of boundary value problems (BVPs) dynamic wavelength is comparable to the characteristic length of heterogeneity or when local heterogeneity becomes crucial due to extreme sensitivity of local instabilities. Stochasticity, vanishing in deterministic homogenization, resurfaces amid multiscale interactions. Multiscale stochastic modeling is expected to play an increasingly important role in simulation and prediction of material failure and novel multiscale systems such as microelectronic-mechanical systems and metamaterials. In computational mechanics a prevalent issue is, while a fine mesh is desired to achieve high accuracy, a certain mesh size threshold exists below which deterministic finite elements become questionable. This work starts investigation of the scale-coupling problems by first looking at uncertainty of material responses due to randomness or incomplete information of microstructures. The classical variational principles are generalized from scale-decoupling problems to scale-coupling BVPs, which provides upper and lower variational bounds for probabilistic prediction of material responses. It is expected that the developed generalized variational principles will lead to novel computational methods for uncertainty quantification of random heterogeneous materials.

A vast amount of indentation studies on coating/substrate systems focused on extracting the mechanical properties of the film, by either avoiding or subtracting off the substrate effect. However, in engineering and biomedical applications, very often the substrate properties, in particular the substrate modulus, need to be measured from an indentation test and the protective layer cannot be removed. For the model system of an elastic film deposited on an elastic substrate, we establish the general approach of spherical indentation focusing on the substrate property determination. Indentation data are taken from different indentation depths which reflect different degrees of film and substrate effects. An effective reverse analysis algorithm is established such that, from an indentation test if either the film modulus or film thickness is known, the other variable can be measured along with the substrate modulus. Error sensitivity of the proposed formulation is analyzed in a systematic way.

In this paper, a new method capable of predicting the critical deformation of composite materials with interfacial cracks is presented under mixed mode conditions using stress intensity factors $K_1$ and $K_2$ and the fracture criteria of the interface between concrete and cement-based wet finishing are evaluated. Two types of stress intensity factors are considered on the basis of the interfacial fracture mechanics. The stress distribution and singularity of the interface between dissimilar materials are obtained by two-dimensional elastostatic boundary element analyses under a plane strain state. Two types of stress intensity factors determine the mixed mode fracture criteria of the interfaces. Prediction of the first delamination and its development by these factors are compared with the empirical results of compressive tests on composite model specimens containing several types of finishing. It was confirmed that critical deformation could generally be predicted by the present method.

A novel mathematical modeling has been proposed to generate synthetic vertical force signal induced by a single person jumping. This model can replicate much of the temporal and spectral features of the real jumping loading more reliably than the existing half-sine models coupled with Fourier series analysis. This includes lack of symmetry of individual jumping pulses and near-periodic nature of consecutive pulses. The model therefore offers way forward as to the development of a new generation of synthetic narrow-band jumping loads. In these, the shape and frequency content of the jumping force can be changed easily on a jump-by-jump basis, which simulates better on what is happening in reality during human jumping. The synthetic jumping loading can be used in assessing vibration serviceability of civil engineering structures for which such dynamic excitation is relevant, such as assembly structures and concert venues.