Archive of Applied Mechanics最新文献

Necking plays a central role in the challenge of accurately describing the mechanical behavior, particularly hardening, of ductile materials at large strains. However, the evolution of the necked zone remains poorly understood. This study elucidates the nucleation, onset, and shape evolution of the necked zone in a 6061 aluminum alloy sheet under uniaxial stretching via a deep learning approach. A DeepLabv3 + image segmentation model is developed to accurately define the real-time shape of the necked zone. Fundamental parameters characterizing the necked zone are calculated through geometric analysis of segmented images. The evolution of these parameters is examined and compared to delineate the changing properties of the necked zone and its relationship with evolving stress. The study reveals that strain concentration zones emerging along the specimen boundary prior to yielding are prone to evolve into the final necking and fracture sites. This finding suggests the potential for early prediction of necking location. After a long phase of necking nucleation, the bifurcation point of stress appears earlier than the peak load point predicted by the famous Considère’s criterion. These results introduce a novel approach for identifying necking events and present new insights into the necking phenomenon and its description. Additionally, these findings propose a new way to identify the representative constitutive relationship of ductile materials at large strains.

In the present work, stationary points of the Poisson’s ratio for six-constant tetragonal crystals are investigated. For simple cases, analytical expressions for the points and stationary values are provided. The work expands on earlier study: analyzes general case when no strict restrictions applied on loading direction and evaluates crystallographic directions corresponding to stationary points. Using data on elasticity constants, stationary points and values for 94 crystals are determined. Behavior of auxetic crystals investigated for specific crystallographic planes and directions.

In this study, the fundamental mechanical properties of silt in Yellow River flooded area were analyzed, and the effects of various influencing factors on its mechanical behavior were considered. A fractional-order elasto-plastic constitutive model was established to reflect the state-dependent behavior and non-associated flow of the soil. Shear-dilation relationships based on the Riemann–Liouville (R–L) and Caputo fractional derivatives were derived. The gradient non-orthogonality of fractional differentials was utilized to describe the non-orthogonal relationship between the plastic flow direction and the yield surface, thereby avoiding the limitations of traditional elasto-plastic models that require separate definitions for loading and plastic potential surfaces. The proposed model contains ten parameters, each with a clear physical meaning and ease of determination. A parameter calibration method was introduced, and a sensitivity analysis was carried out to evaluate the influence of individual parameters on the model’s predictive accuracy. Finally, the predictive performances of the R–L and Caputo derivative forms were compared and analyzed. The results have demonstrated that the fractional-order elasto-plastic model is capable of accurately reproducing the key mechanical characteristics of silt in Yellow River flooded area, including compressibility, shear dilation, and state dependence. The R–L model and Caputo model have similar accuracy in simulating the strain-hardening law, but the R–L fractional constitutive model will underestimate the dilatancy of silt in Yellow River flooded area when predicting the development of volumetric strain.

Orthotropic materials feature high specific strength and specific stiffness, and are therefore widely used in ribbed cantilever structures in aerospace engineering and other fields. Since shear deformation has a greater effect on orthotropic plates, the analytical solutions for solving vibration and buckling of ribbed orthotropic cantilever plates are presented in this paper based on the theories of Mindlin thick plate and Timoshenko thick beam using finite integral transform method. The analytical solutions for vibrations and buckling of ribbed orthotropic cantilever plates are verified by finite element analysis method. The buckling characteristics of (ribbed) orthotropic and isotropic cantilever plates under various in-plane loadings are analyzed. Additionally, the dynamic model is further verified by free and forced vibration experiments. The vibration behavior of orthotropic cantilever plates is analyzed, and the effect of rib on plate vibration is also investigated. The analytical model developed in this paper can provide theoretical guidance and judgment basis for vibration analysis and stability prediction in large-scale engineering projects involving ribbed orthotropic cantilever plates.

The increasing prevalence of additive manufacturing with material extrusion necessitates a rigorous understanding of the process-property-performance relationship in 3D-printed polymers, particularly the consistency of mechanical properties despite manufacturing anomalies. This study experimentally and analytically investigates the variability in stiffness and tensile strength of polylactic acid (PLA) samples fabricated as flat layers and isogrids. Experimental tensile testing revealed comparable stiffness and strength across most configurations, irrespective of manufacturing-induced anomalies. Analytical models that were statistically penalized to account for manufacturing variability, considering randomized cross-sectional areas, demonstrated excellent agreement with the experimentally determined stiffness variability. Furthermore, the tensile strength of the flat layer was accurately predicted using the Tresca criterion, while Cohesive Zone Modelling effectively captured the failure behavior of the isogrid. Despite its linear assumptions, this integrated experimental-statistical framework offers a viable approach for predicting the mechanical response and assessing the reliability of additively manufactured components.

This study proposes a novel cell-based smoothed 3-node triangular flat shell element, including real drilling degrees of freedom for the analysis of porous plates and shells, based on higher-order shear deformation theory (HSDT). This theory eliminates the transverse shear strains at both the top and bottom surfaces of the structures without the need for shear correction factors. The true drilling degrees of freedom of the proposed flat shell element are achieved using Allman-type in-plane displacement approximations. To smooth the membrane and bending strains, enhance strain gradients, and explicitly compute stiffness matrices for both plates and shells, we combine a cell-based smoothed technique with cubic shape functions at a bubble node, which is located at the centroid of the element. The proposed HSDT-type CS-MITC3 + flat shell element is applicable for both thick and thin plates and shells, utilizing the MITC3 + shear removal technique to re-interpolate transverse shear strains. The proposed flat shell element demonstrates excellent precision and convergence in analyses of porous plate and shell structures with different geometries, thicknesses, porosity distributions, porosity coefficients, and boundary conditions.

The standard Bayesian updating method consists in calculating the joint posterior probability distribution of some parameters of a computational model using the Bayes rule and experimental data. When the model output has large dimension and its probability distribution is not assumed to belong to a prescribed family, the estimation of the likelihood function and the storage of the posterior joint probability density function for point estimation of the parameters or for subsequent stochastic analysis of the quantity of interests become very challenging, requiring the use of MCMC sampling methods with a large number of samples. In addition, when the number of parameters to be updated is large, the computational cost associated with the estimation of their posterior marginal distributions becomes significantly high. In this paper, a one-parameter-at-a-time Bayesian updating method is formulated. This novel approach consists in calculating the posterior marginal distribution of each parameter separately by constructing for each parameter a one-dimensional output that is sensitive to this parameter only, enabling the corresponding (1) likelihood function to be estimated easily and (2) the marginal posteriors to be build and stored directly and independently of the other parameters. This approach is illustrated through a numerical example consisting of the Bayesian updating of a three-storey structure with model-form uncertainties and for which the mass and stiffness parameters are calibrated.

Constitutive models for engineering materials exhibit significant differences under varying strain rate conditions, necessitating improved quantitative descriptions of strain rate effects. This study examines experimental data for three categories of engineering materials—metals, brittle materials, and plastics—across low, medium, and high strain rates. The results reveal that material strength or yield stress is insensitive to strain rate in both the low and high strain rate conditions (corresponding to the weakly sensitive and saturation zones, respectively), while showing high sensitivity at medium strain rates (strongly sensitive zone). The classical Johnson–Cook constitutive model fails to accurately capture this phenomenon due to limitations in its strain rate effect term formulation. Building upon the Johnson–Cook constitutive model, this study proposes a unified phenomenological constitutive model applicable across different engineering materials, effectively characterizing the weakly sensitive, strongly sensitive, and saturation zones of strain rate effects on material strength or yield stress. The fitted curves using this model align well with experimental data.

This study investigates the propagation of Rayleigh- and Love-type surface acoustic waves in one-dimensional layered half-space structures composed of hexagonal piezoelectric quasicrystals with imperfect interfacial bonding. A comprehensive mathematical framework is developed by combining wave mechanics, interfacial spring–membrane models, and dispersion relations to capture the effects of structural inhomogeneity and coupling parameters. The methodology integrates analytical modeling with numerical dispersion analysis, supported by comparative case studies between perfect and imperfect interfaces. Results reveal that interfacial imperfections significantly reduce phase velocity, alter cutoff frequencies, and enhance attenuation, thereby highlighting their critical influence on surface acoustic wave behavior. The findings provide valuable insight into optimizing sensor sensitivity, improving SAW filter performance, and designing advanced MEMS and ultrasonic devices. The novelty of this work lies in addressing both piezoelectric quasicrystal anisotropy and interfacial bonding simultaneously, which has been scarcely reported in the literature. Limitations include the absence of experimental validation and higher-dimensional modeling, which are recommended for future studies. Overall, this research offers a new theoretical basis for developing next-generation acoustic wave devices.

In this paper, the fracture mechanics of one-dimensional hexagonal quasicrystals (1D-HQCs) with arbitrary location periodic mode-III cracks emanating from a nanoscale hole is investigated theoretically. According to the Gurtin–Murdoch surface elasticity theory, the surface effects of nano-defects (holes and cracks) are considered. A new deformation mapping function was obtained by using the conformal transformation technology. Combined with the analytical function boundary value problem theory, the generalized stress field of the problem is obtained, and the analytical expressions of the stress intensity factors of the phonon field and the phason field of the arbitrary location crack tip are derived. The effects of crack position angle, crack number, crack length/aperture ratio, phonon field–phason field coupling coefficient and applied loads on the dimensionless stress intensity factors are discussed. The crack position angle significantly affects the generalized stress intensity factors, both with and without surface effects. The stress intensity factors have obvious size effects under considering surface effect. The influence of other factors on the generalized stress intensity factors is different.