Journal of Engineering Mechanics

The objective of this study is to create explicit prediction models for the complex shear modulus (${\mathrm{G}}^{*}$) and phase angle ($\delta$) of bitumen mastic fabricated using an evolutionary machine learning approach. The dynamic shear rheometer (DSR) test in frequency sweep mode at seven test temperatures was performed to measure ${\mathrm{G}}^{*}$ and $\delta$. In order to create specific prediction models for each modifier, multigene genetic programming (MGGP) was employed. These models took into account various factors including the dosage of the additive, filler volume filling rate, loading frequency, temperature, as well as the ${\mathrm{G}}^{*}$ and $\delta$ values of the neat bitumen. In general, six explicit prediction models are presented for different additives with R-squared values of more than 0.9. The results showed that the hybrid machine learning approach can effectively develop precise, meaningful, and yet simple formulas for calculating ${\mathrm{G}}^{*}$ and $\delta$ of the bitumen mastic. To gain a deeper understanding of the developed models, a comprehensive parametric study and sensitivity analysis were carried out.

Although imperceptible at the macroscale, fluctuations of physical properties are ubiquitous at the nanoscale because of thermal agitation. While fluctuations are detrimental to the accuracy of molecular simulations, their magnitude is actually a great source of information since it quantifies the elasticity of the system with respect to any evolution of the control variables. Fluctuation formulas are well known for fluids or solids but have not yet been derived for porous media. In this article, we derive fluctuation formulas for all the moduli involved in thermoporoelasticity. These fluctuation formulas are applicable even for adsorbing media and can be used for poroelasticity extended to adsorption, whereas usual poroelasticity assumes a bulk fluid in the pores. Moreover, the practical application of the fluctuation formulas in molecular simulation is straightforward, as one only needs to collect extensive quantities readily accessible and at almost no additional computational cost. The application of these fluctuation formulas is illustrated by considering a typical example of mechanosorption coupling, namely, amorphous cellulose submitted to moisture at various relative humidities. The thermoporoelastic behavior is fully characterized from the fluctuations computed during molecular simulation of amorphous cellulose. Some peculiarities of moisture-induced behavior of cellulose are discussed, such as the high Biot coefficient, the negative Biot modulus, the negative thermal expansion, and the high heat capacity. This work investigates only the case of a pure fluid in the pores with volumetric deformations but can be easily extended to fluid mixture and shearing effects.

Accurate and efficient parameter identification along with uncertainty quantification in nonlinear systems is crucial for enabling practical and reliable structural health monitoring and digital twinning. This paper presents a novel procedure for estimating parameters that combines Bayesian filters and truncated probability density functions (PDFs). To simplify the state-space equations, only model parameters are incorporated in the state equations, whereas the measurement equations are implicitly considered in the state vector of displacement and velocity. This simplification enables the unified implementation of three different types of Bayesian filters: the unscented Kalman filter, third-degree cubature Kalman filter, and fifth-degree cubature Kalman filter. Consequently, it facilitates the seamless integration of complex numerical models into the parameter identification procedure. To improve the robustness of the proposed method, the truncated PDF is employed to enforce constraints that prevent the covariance matrix from becoming singular. The applicability and accuracy of the proposed method were evaluated using a 10-story numerical example and a 12-story shake-table model. Based on the selected parameters for tuning, the estimated results are consistent with both the simulated and experimental data, demonstrating that the Bayesian filters can estimate parameters and quantify their uncertainties. Comparison of the estimation accuracy, computational cost, and efficiency index among the three types of Bayesian filters reveals that the fifth-degree cubature Kalman filter has the highest accuracy. When dealing with less complex structural models, the unscented Kalman filter demonstrates superior efficiency. These findings are useful for finite-element model updating and assessment of structural performance.

Cementitious materials contain multiple phases, from the nanoscale to the macroscale. Although different mechanical properties are observed at each scale length, similarities can still be found in their spatial structural features and in the geometry of the stress–strain curves over various scales. This study aims to provide a quantitative description of the scaling effect based on the concept of self-similarity. Multiscale models are proposed for the tensile strength, peak strain, and elastic modulus of cementitious materials. The results obtained from these models exhibit a change of five orders of magnitude in tensile strength as the scale length increases from ${10}^{-9}\mathrm{m}$ to ${10}^0\mathrm{m}$, whereas a slight decrease in the elastic modulus is observed. Combined with the models above and the Morse function, a continuous constitutive model is proposed to describe the tensile stress–strain behavior at each scale length. This paper studied the scale effect of cementitious materials from the viewpoint of self-similarity and investigated this phenomenon over a very broad length range, including the nano-, micro-, meso-, and macro-scale. The tensile stress–strain relationship was unified and characterized across scales, which not only reflected the atomic interaction on the nanoscale via the Morse potential energy function, but also depicted the macroscopic tensile tests results. These findings provide new insights in revealing the mechanism of quasi-brittle materials’ size effect.

On the basis of elastic–plastic theory and generalized Hooke’s law, and with the rate effect and random damage characteristics of cement-stabilized steel slag taken into consideration, an elastic–plastic dynamic damage constitutive model of cement-stabilized steel slag under a complex stress state was established in this paper. In the aspect of damage deterioration, the damage evolution equation of cement-stabilized steel slag was established by using statistical theory and introducing the concepts of damage threshold and equivalent plastic strain. With the influence of pore water pressure on materials taken into consideration, Terzaghi’s effective stress principle was introduced and the effective stress expression was modified based on the characteristics of cement-stabilized steel slag. With the existence of the ultimate dynamic strength of brittle materials, the $S$-type dynamic strength criterion of cement-stabilized steel slag was established based on this property. The explicit integral stress return algorithm of the elastic–plastic dynamic damage constitutive model of cement-stabilized steel slag was derived through elastic–plastic theory, and the solving program of the elastic–plastic dynamic damage constitutive model of cement-stabilized steel slag was developed by using the subroutine interface vectorized user defined material (VUMAT) provided by ABAQUS.

This study proposed a general semianalytical solution for axisymmetric consolidation of unsaturated soil where the unified boundary is extended under electroosmotic and surcharge preloading, allowing for the diversity of permeability at the top boundary of the soil layer. In the coupled electric-flow-mechanic fields, the Laplace transform, decoupling technique, and Laplace inversion were used to derive a semianalytical solution. Then, the proposed solution was examined respectively against the two cases of considering only electroosmosis in saturated soils and only surcharge preloading in unsaturated soils to verify the validity of the solution. The analysis of the factors affecting the consolidation characteristics shows that as the permeability of the top boundary increases, the excess pore pressures dissipate faster, and then the final negative excess pore-water pressure decreases. The electroosmotic-enhanced preloading technique can significantly improve the speed of foundation consolidation and reduce the post-work settlement compared to a single method. Moreover, the excess pore pressures induced by the surcharge preloading dissipate faster as the electrical-to-radial water permeability ratio decreases. It is meritorious to note that the new solution in the present study is applicable to the axisymmetric consolidation model for unsaturated soils under arbitrary time-varying loading and different permeability topsides.

In this study, free oscillation of a cracked smart plate made of magneto-electro-elastic functionally graded materials (MEE-FGMs) lying on a Pasternak elastic foundation is investigated according to high-order shear deformation theory (HSDT). The MEE properties of the functionally graded plate are assumed to vary through the thickness direction and are estimated with the power-law rule. The cracks are in the center of the sheet with variable length and angle of inclination. Phase-field theory is used to simulate the crack state of smart plates. A detailed parametric analysis was performed to evaluate the effects of electric and magnetic fields, thickness ratio, power-law index, elastic foundation, and crack geometry on the free vibrational properties of magneto-electro-elastic functionally graded plates.

To study the dynamic properties of intermediate strain rates for filiform or filmy materials, a miniature tensile-test system with an intermediate strain rate based on magnetic resistance actuation is designed herein. The loading part of the system is formed by inertial movement and an electromagnetic launcher, and the testing part is formed by high-speed optical noncontact measurements using a microforce sensor. Constant tension and intermediate speed are realized by designing the inertial motion of a large-mass combined accelerator. Friction and vibration are offset using magnetic attraction. The electromagnetic acceleration force was eliminated by adjusting the length differences, construction, and relative motion of the structures. The stress–strain curves are obtained by synchronizing the strain signal measured using the optical extensometer method and the stress signal measured using the microforce sensor. The system is verified to be miniature, stable, easy to control, accurate for strain rate, economic, and used for small samples. The stability and reliability of the system are verified using speed testing and motion-state photography. Therefore, the designed system is miniature, easy to control, highly cost-effective, and can be used for filiform or filmy samples.

Nonlinear dynamical systems in applications such as design and control generally depend on a set of variable parameters that represent system geometry, boundary conditions, material properties, etc. Modeling of such parameterized nonlinear systems from first principles is often challenging due to insufficient knowledge of the underlying physics (e.g., damping), especially when the physics-associated parameters are considered to be variable. In this study, we present a dynamics-embedded conditional generative adversarial network (Dyn-cGAN) for data-driven modeling and identification of parameterized nonlinear dynamical systems, capturing transient dynamics conditioned on the system parameters. Specifically, a dynamics block is embedded in a modified conditional generative adversarial network, thereby identifying temporal dynamics and its dependence on the system parameters, simultaneously. The data-driven Dyn-cGAN model is learned to perform long-term prediction of the dynamical response of a parameterized nonlinear dynamical system (equivalently a family of nonlinear systems with different parameter values), given any initial conditions and system parameter values. The capability of the presented Dyn-cGAN is evaluated by numerical studies on a variety of parameterized nonlinear dynamical systems including pendulums, Duffing, and Lorenz systems, considering various combinations of initial conditions and system (physical) parameters as inputs and different ranges of nonlinear dynamical behaviors including chaotic. It is observed that the presented data-driven framework is reasonably effective for predictive modeling and identification of parameterized nonlinear dynamical systems. Further analysis also indicates that its prediction accuracy degrades gracefully as the complexity of the nonlinear system increases, such as strongly nonlinear systems and systems with multiple parameters changing. The limitations of this work and potential future work are also discussed.

This paper proposes an inverse eigenstrain analysis procedure to estimate full-field residual stress from an incompletely measured residual elastic strain or stress field. The inverse problem is solved by minimizing the linear elastic constitutive relation discrepancy that arises from different admissible stress and strain fields within an alternating minimization framework. First, a standard forward thermoelastic problem is solved to obtain a statically admissible total strain field. Then, full-field residual stress (or elastic strain) that satisfies partial measurement is obtained by minimizing a Hellinger-Reissner-type energy functional under a mixed variational framework. We have used standard two and three-dimensional hybrid finite elements to obtain a stress field. Finally, a full-field eigenstrain field is obtained by minimizing constitutive disparity due to dissimilar elastic strain and total strain fields. We show the efficacy of the proposed procedure with some numerically obtained and experimentally reported data.