Journal of Engineering Mechanics

The grain rotational field is significantly associated with the shear banding process and can be derived easily on the basis of individual grains, which could be an appropriate and convenient quantity in shear band analysis. In this paper, a novel method is proposed for directly analyzing the shear banding process in the granular assembly based on its grain rotational field. Numerical plain strain tests on a dense (S1) and an intermediate dense specimen (S2) are performed using the coupled discrete-element method (DEM) and finite-difference method (FDM). The grain rotational field is statistically characterized by the rotational distribution ${\beta }_v(\omega )$, a new index defined as the volumetric percentage of grains rotating to a greater degree than the rotation $\omega$, in which the high rotation (HR) section basically indicates the grains inside the shear band. A measurement of ${\beta }_v(\omega )$’s uniformity quantifies the degree of strain localization, and S2 is found to perform a more uniform rotational distribution than does S1. Taking the value of $\omega$ at which ${\beta }_v(\omega )$’s curvature is higher than a threshold as the boundary of the HR section, HR grains are filtered out of the sample, based on which the inclination and thickness of the shear band, as well as two local quantities (average void ratio and coordination number) inside the shear band, are analyzed.

Prediction of the elastic properties of cementitious materials has been the aim of many researchers. This study developed a new multiscale and multiphase model based on the Mori-Tanaka method for predicting effective elastic properties of hardened cement paste, such as modulus of elasticity. The model considered the microstructural variation in and nonspherical morphology of the hydration products in hardened cement paste. In order to improve prediction accuracy, the model included the effect of ettringite on the elastic properties in addition to the other major hydration products. Instead of considering cement clinker as an isotropic and homogeneous material, this study simulated the clinker as a four-phase composite. In addition, the model used a matrix-inclusion configuration that can include the clinker and ultra-high-density calcium silicate hydrate. Another improvement is that a weakened matrix-inclusion interface was introduced using the modified Eshelby tensor. The prediction results of the model were compared with the experimental data, and good agreement was obtained.

A bulk damage formulation is presented for failure analysis of brittle materials under dynamic loading. A time-delay ordinary differential equation (ODE) is used to model damage evolution. The evolution is driven by the difference between a target static damage value and the instantaneous damage value. A damage length scale is introduced from the model’s intrinsic relaxation time and elastic wave speeds. This length scale addresses the mesh sensitivity problem of some existing damage formulations for dynamic fracture, with less computational effort than some other existing remedies. The authors use the asynchronous spacetime discontinuous Galerkin (aSDG) method for the solution of the resulting hyperbolic system of equations. Local and asynchronous solution process, linear complexity of the solution versus the number of elements, local recovery of balance properties, and high spatial and temporal orders of accuracy are some of the main advantages of the aSDG method. Several numerical examples are presented to demonstrate mesh insensitivity of the method and the effect of boundary conditions on dynamic fracture patterns.

The relationship between dilatancy and anisotropy is a fundamental aspect of anisotropic behavior of granular materials. Existing test data directly investigating this relationship are scarce and conflicting. Discrete element biaxial and triaxial numerical tests on idealized granular materials in both two-dimensional (2D) and three-dimensional (3D) are conducted in this study to acquire high quality stress, strain, dilatancy, and fabric data for various anisotropic samples, which are utilized to analyze the dependency of dilatancy ratio on fabric anisotropy. The test results indicate that the dilatancy ratio is not only dependent on the initial fabric anisotropy, but is also influenced by the evolution of fabric, especially the contact normal fabric. At low deviatoric stress ratio under biaxial and triaxial loading, difference in initial fabric anisotropy of granular materials can lead to distinctly different dilatancy ratios. As loading continues, the deviatoric stress ratio, void ratio, and fabric of granular materials evolve toward the unique critical state, causing the dilatancy ratio to converge irrespective of its initial value. The anisotropic critical state theory (ACST) is shown to be capable of providing a framework for quantitative mathematical depiction of the dependency of dilatancy ratio on fabric anisotropy.

Support is one of the most important aspects that contribute to long-term stability and tunnel safety. Lining cracking and even failure often occur during tunneling construction, especially for soft rock tunnels. To address such a problem, a supporting scheme that a flexible layer is adopted and placed between the first lining and second lining is proposed in this study. An exact closed form solution is derived for the mechanical behavior of a circular tunnel supported by such a supporting scheme. Analytical formulas are provided for displacements and pressures of linings, taking into account the installation delay of the second lining. Numerical results of the finite element method validate the results calculated from these formulas. Further, a parametric study is performed to investigate the effects of thickness, Young’s modulus and Poisson’s ratio for the flexible layer on supporting effect. It is concluded that the flexible layer plays a good role in absorbing deformations due to rock rheology. The displacement and pressure can achieve a good improvement, and this improvement is dramatically affected by the thickness and deformability of the reserved flexible layer.

Moisture warping of concrete slab occurs as a long process due to the slow transportation nature of moisture in concrete materials. Creep, as a time-dependent property of concrete, will inevitably affect the mechanical responses of slabs on ground during this process. This study considered the effect of concrete creep in pavement slab for analyzing moisture warping, warping stress, and the total stress under traffic loads. A method is proposed to calculate the time-dependent warping deformation and stress in concrete slab on ground. This method uses the sequential coupled hygromechanical finite-element analysis and incorporates a concrete creep model which is capable of considering the relative humidity effect. The effect of environmental relative humidity; the design parameters, including concrete type, slab size, thickness, and bonding condition with the base; and the age of concrete exposed to drying on the warping and stress of slabs were investigated considering the creep effect. It was found that concrete creep has a significant effect on the warping and stress of slabs. It is important to consider creep effect in designing and analyzing deformation and stress generated in concrete pavement slabs, particularly when a moisture gradient exists in slabs.

A Hilbert transform based definition of the response amplitude of randomly excited nonlinear oscillators has been proposed recently to address certain limitations associated with the standard stochastic averaging solution treatment. In comparison to standard stochastic averaging, the requirement of a priori determination of an equivalent natural frequency is bypassed, yielding flexibility in the ensuing analysis and potentially higher accuracy. In this paper, relying on the Hilbert transform based stochastic averaging, a semianalytical technique is developed for determining the time-dependent survival probability and first-passage time probability density function of stochastically excited nonlinear oscillators, even endowed with fractional derivative terms. To this aim, a Galerkin scheme based on the orthogonality of the confluent hypergeometric functions is utilized to solve approximately the backward Kolmogorov partial differential equation governing the survival probability of the oscillator response. Further, two distinct approximations for the equivalent instantaneous natural frequency are introduced, while their accuracy with respect to oscillator first-passage time statistics is also assessed. The hardening Duffing and the bilinear stiffness nonlinear oscillators, both with and without fractional derivative elements, are considered in the numerical examples for ascertaining the reliability of the technique. For comparison, the analytical results are examined in relation to pertinent Monte Carlo simulation data.

The transportation sector contributes up to 27% of the total greenhouse gas (GHG) emissions in the United States; on-road transportation is responsible for 84% of the entire sector, implying that vehicles are a major cause of global warming. To understand the fuel energy dissipated through a vehicle’s suspension and tires, researchers have recently examined stochastic pavement models combined with mechanics-based vehicle models. These approaches assume the pavement is nondeformable with a certain random roughness level. In this paper, a pavement–vehicle interaction model is developed that can accommodate both road roughness and the deflection of rigid pavement. A quarter-car model is considered to represent the vehicle, a filtered white noise model is used to characterize the road roughness, and a two-elastic layered foundation (Euler–Bernoulli beam for the top pavement and Winkler foundation for the subgrade) is employed to simulate the rigid pavement. Subsequently, an augmented state-space representation is formulated for the entire pavement–vehicle system. The Lyapunov equation governing the covariance of the response is solved to obtain the energy dissipation of the vehicle’s suspension and tires. Finally, examples are presented and compared with the nondeformable pavement model to understand the impact of rigid pavement deformation on vehicle fuel energy dissipation.

A nonnodal extended finite-element method (NXFEM) was developed to predict two-dimensional dynamic failure with four-node quadrilateral elements. A new nonnodal enrichment scheme is presented such that the enriched quadrilateral finite elements satisfy the linear completeness and represent a strong discontinuity, i.e., crack. The enrichment bases for both solutions and the gradient fields are included in the finite-element approximation through the nonnodal enrichment scheme. The partition of unity is also naturally satisfied without adopting additional neighbor blending elements. To facilitate an implementation of the NXFEM into pre-existing finite-element analysis software, a generalized notation is proposed which is universally applicable to both quadrilateral and triangular finite elements. The developed method was initially verified with a convergence study on benchmark near-crack-tip field problems. The effectiveness of the method was further demonstrated with mixed-mode dynamic failure problems.

Materials engineering problems related to polycrystalline solids often require the prediction of grain growth and the stress analysis of polycrystalline materials. This study presents the particle difference method (PDM) as a reliable computational method applicable to this class of engineering problems. The PDM is a meshfree collocation method that directly discretizes the strong form of the governing partial differential equations based on Taylor series approximation and the moving least-squares approach. The PDM was applied to polycrystalline solids in the context of two-dimensional grain growth solidification and stress analysis of the resulting polycrystalline morphology. First, the PDM was used to predict grain growth during the solidification process of polycrystalline materials using a multiphase field model. Then the resulting morphology of the polycrystalline solids was adopted for successive stress analysis of the polycrystalline solids. Results from these analyses were compared with the results from the conventional finite-element method to verify the accuracy and efficacy of the PDM.

This manuscript provides a combined computational-experimental investigation of the interaction of damage mechanisms in carbon fiber–reinforced polymer (CFRP) laminated composites subjected to fatigue loading. The investigations particularly focus on ${[60,0,-60]}_{\mathrm{3S}}$ laminates, whose behavior demonstrates strong interactions between the relevant damage modes. Numerical investigations are performed using a spatiotemporal computational homogenization-based multiscale life prediction model. The computational approach relies on a model order reduction methodology to develop a meso model that can capture the relevant failure mechanisms in a computationally efficient manner. The model was calibrated using a suite of experimental data from the static and fatigue response of simple laminates made of the same constituents. The calibrated model along with experimental observations from acoustic emission and X-ray computed tomography were employed to understand the relative roles of delamination and splitting and their interactions in controlling fatigue failure processes in CFRPs.

This paper introduces a novel nonlocal hardening-damage model for beams and integrates it within a flexibility-based frame element formulation. The proposed formulation eliminates strain singularity phenomena, which are common in (local) beam theories in the presence of softening materials, and achieves objective response (i.e., convergence with mesh refinements). Strain singularity phenomena have prevented accurate simulation of framed structures experiencing structural softening and have introduced major uncertainty in predictions of structural damage and collapse. The proposed model extends classical nonlocal elastodamage models to account for hardening (as opposed to elastic) materials by combining a damage/softening factor that is a (decreasing) function of nonlocal strains together with a hardening constitutive model that is solely a function of local strains. This allows simulation of a variety of responses combining stiffness and strength deterioration (captured by the damage/softening factor) together with hysteretic/cyclic response (captured by the hardening model). Moreover, unlike common elastodamage models, this model is also capable of capturing residual deformations, which are of importance to structural engineering applications. Because the damage/softening factor is fully decoupled from the hardening model, any (local) hardening model, simple or complex, can be used, including the large variety of (local) material constitutive relations currently used in nonlinear dynamic analyses of buildings and bridges. On the basis of the proposed nonlocal hardening-damage beam model, a flexibility-based frame element formulation is developed, which allows exploration of integral and (implicit) gradient nonlocal formulations with various boundary conditions (BCs). Symmetry considerations are employed to select nonlocal models (and their BCs) that provide physically plausible response predictions. The performance of these formulations is explored for axial and bending problems in terms of response properties and convergence rate. The performance and accuracy of the proposed formulation is further assessed through comparison with experimental data from quasi-static cyclic testing of a reinforced concrete column.

Because of oscillatory asymptotic mechanical behavior, it is difficult to properly examine the extent of the near-front singular-dominant region for interface cracks. An approach is proposed for generating a near-front “deoscillatory displacement jump” (DDJ) field led by a pure square-root-dominant (i.e., $r^{1/2}$-dominant) term. In the DDJ approach, the real and the imaginary parts of the complex expressions for near-front displacement discontinuities are decoupled, so oscillatory asymptotic behavior does not explicitly appear in the formulation. This enables direct incorporation of finite-element solutions for proper examination of the extent of the singular-dominant region and the accuracy of near-front numerical solutions.