Dimensionless Stress Research Articles

Prediction of fracture toughness of concrete using the machine learning approach

In the process of structural design, it is useful to estimate the fracture toughness of concrete samples. This research showcases the effectiveness of utilizing machine learning methods to determine the fracture toughness of concrete. Taking into account variables such as mix design, machine learning techniques can accurately predict the mode I fracture toughness of concrete. Dimensionless stress intensity factor of concrete prediction using twelve different machine learning techniques namely, Linear regression (LR), Extreme Gradient-Boosting (XGboost), K-Nearest Neighbors (KNN), Random Forest (RF), Category Boosting (CB), Decision Tree (DT), Extra Trees (ET), Light Gradient-Boosting (LightGB), Adaptive boosting (AdaBoost), Bagging (BA), Gaussian Process (GP), Artificial Neural Network (ANN) and Support Vector Machine (SVM). The result of utilizing the training adaptive moment estimation algorithm has been developed to create an outstanding machine learning-based system. After carefully analyzing comparisons between the predictions produced by different models and experimental findings, it has been discovered that the models demonstrate an impressive accuracy rate of about 90 percent when it comes to forecasting concrete fracture toughness. The research findings emphasize that the ANN model exhibited superior accuracy in its predictions (R2 value of 0.90, RMSE of 0.1517, and MAE of 0.1238). Upon conducting a thorough examination of the ANN method’s sensitivity, the cement parameter holds utmost significance in accurately estimating concrete’s fracture toughness using the available dataset. So, the ANN model can be used as a valuable method to provide practical assistance in predicting the fracture toughness of concrete. When evaluating the effective parameters, the cement and metakaolin dosage and the notch height to specimen height ratio have the greatest effect on the fracture resistance, while the coarse aggregate content is minimal. This result is consistent with the experimental data.

Investigating the influence of geometric configurations and loading modes on mixed mode I/II fracture characteristics of rocks: Part I-Numerical simulation

The influence of geometric configurations and loading modes is a bottleneck that restricts the accurate determination of rock fracture parameters and the precise understanding of fracture mechanisms. Therefore, the phase field method is employed to analyze the influences of specimen geometry and loading modes on the dimensionless stress intensity factors, peak load, fracture toughness, and crack initiation angle during the rock mixed mode I/II fracture process. Three new configurations of specimens are proposed to test rock mixed mode I/II fracture. The research results indicate that as the prefabricated crack inclination angle increases, the peak load of three-point bending type specimen increases, while the peak load of diametric-compression type specimen decreases. Moreover, the influence of geometric configurations on the fracture parameters of three-point bending specimens is greater than that of diametric-compression disk specimens. The research findings of this work can provide basic supporting data for the establishment of mixed mode I/II fracture testing standards.

Numerical calibration for fracture parameters of three-point bending semi-circular specimens

This study aims to refine the fracture characterization of three-point bending semi-circular specimens used in rock fracture toughness assessments. The primary objective is to improve the accuracy of such evaluations by developing numerical simulations of specimens with pre-engineered cracks of varying geometries. Numerical simulations were conducted using the finite element method. The interaction integral method was employed to quantify the stress intensity factors (SIFs) and T-stress at crack tips. Initially, the model’s accuracy was validated by replicating stress singularities at crack tips in a benchmark circular disk with a central straight crack. Following validation, dimensionless fracture parameters specific to the three-point bending semi-circular specimens were calibrated. The numerical results demonstrate that the dimensionless stress intensity factor (YI) increases with both the relative crack length (a/R) and the spacing between support points. Notably, for relative crack lengths a/R ≤ 0.5, the dimensionless T-stress assumes negative values, initially decreasing and then increasing as the relative crack length increases. The findings of this study provide valuable insights into the fracture behavior of three-point bending semi-circular specimens with pre-engineered cracks. Based on the observed trends in the dimensionless fracture parameters, it is recommended that relative crack lengths within the range of 0.2–0.6 be used to maintain the accuracy of rock fracture toughness tests. The finite element method used in this study serves as a robust tool for calibrating fracture parameters, thereby laying a strong foundation for the application of these specimens in rock fracture toughness evaluations.

Laminar planar jets of elastoviscoplastic fluids

We perform numerical simulations of planar jets of elastoviscoplastic (EVP) fluid (Saramito (2007) model) at low Reynolds number. Three different configurations are considered: (i) EVP jet in EVP ambient fluid, (ii) EVP jet in Newtonian ambient fluid (miscible), and (iii) EVP jet in Newtonian ambient fluid (immiscible). We investigate the effect of the Bingham number, i.e. of the dimensionless yield stress of the EVP fluid, on the jet dynamics, and find a good agreement with the scaling for laminar, Newtonian jets for the centerline velocity uc/u0∝(x/h)−1/3 and for the jet thickness δmom/h∝(x/h)2/3 at small Bingham number. This is lost once substantial regions of the fluid become unyielded, where we find that the spreading rate of the jet and the decay rate of the centerline velocity increase with the Bingham number, due to the regions of unyielded fluid inducing a blockage effect on the jet. The most striking difference among the three configurations we considered is the extent and position of the regions of unyielded fluid: large portions of ambient and jet fluids (in particular, away from the inlet) are unyielded for the EVP jet in EVP ambient fluid, whereas for the other two configurations, the regions of unyielded fluid are limited to the jet, as expected. We derive a power law scaling for the centerline yield variable and confirm it with the results from our numerical simulations. The yield variable determines the transition from the viscoelastic Oldroyd-B fluid (yielded) to the viscoelastic Kelvin–Voigt material (unyielded).

Structural strength and fatigue analyses of large-scale underwater compressed hydrogen energy storage accumulator

Underwater compressed hydrogen energy storage (UWCHES) is a potential solution for offshore energy storage. By taking advantage of the hydrostatic pressure of deep seawater, the compressed hydrogen can be isobarically stored in underwater artificial energy storage accumulators. The accumulator should withstand high pressure and large buoyancy and possess reliable anchoring to the seabed. In this study, the structural strength analysis and fatigue life of the large-scale accumulator is conducted employing the finite element method (FEM). The dimensionless stress prediction model and dimensionless fatigue life prediction model are developed through dimensional analysis and multivariate regression analysis. The performance of the accumulator with operating water depth of 100∼300 m, gas storage volume of 1081∼10128 m³, and concrete wall thickness of 0.1∼0.63 m is investigated. The results show that with an operating water depth of 100 m, gas storage capacity of 10,128 m3, and concrete wall thickness of 0.63 m, the maximum compressive stress is 1.43 MPa (yield strength is 60 MPa) and the maximum tensile stress of the accumulator is 2.55 MPa (yield strength is 6 MPa). The design fatigue life is 106 cycles which is larger than the expected service life of 104 cycles. Therefore, the accumulator structure meets the static strength and fatigue life. As the operating water depth increases with a consistent gas storage capacity, a transition in the stress state shifts from primarily tensile stress to predominantly compressive stress. The accuracy of the dimensionless stress prediction model and the dimensionless fatigue life prediction model were verified, with maximum deviations of 10.3 % and 13.7 %, respectively. Furthermore, the anchoring factor of safety of 1.12 is achieved.

Analysis of Elastic Buckling and Static Bending Properties of Smart Functionally Graded Porous Beam

Background: A Smart Functionally Graded (SFG) porous beam is a Functionally Graded (FG) Porous beam consisting of a piezo-electric layer integrated on the top layer. Aim: This research work addresses the lack of information by examining the bending as well as elastic buckling performance of SFG beams having two distinct Porosity Distributions (PDs). The main purpose of this research work is to study and analyze the bending deflections as well as CBLs of SFG beams with two different PDs, considering various boundary conditions, voltage levels (20V and 100V), and changes in slenderness ratio. Objective: The objectives of this work are as follows: to analyze the impact of variations in voltage levels and slenderness ratios on the critical buckling and bending properties of the SFG beam and to showcase the effect of variation in the slenderness ratio on the dimensionless normal stress through the thickness of the Hinge-Hinge beam. Method: The research work analyzes the elastic buckling as well as static bending of Smart Functionally Graded (SFG) porous beams, considering the equations derived from the Timoshenko beam theory. To simulate the results and analyze the various effects, the ANSYS software has been utilized in this paper. Results: This research work examines how the slenderness ratio impacts the maximum deflection, CBL, along with stress distribution. Experimental data demonstrates that as the slenderness ratio increases, CBL reduces, and maximum deflections in SFG porous beams increase. Also, it has been observed that normal stress distribution shifts from linear to non-linear and changes significantly. Further, the PDs significantly affect the static bending as well as the buckling performance of the beam. The symmetric distribution pattern provides superior buckling capability and enhanced bending resistance compared to the unsymmetric distribution pattern. Additionally, it has been found that as the voltage across the SFG increases, the buckling load increases and the deflection of the beam decreases. Conclusion: This research work has analyzed the effects of slenderness ratio and voltage level on the Critical Buckling Load (CBL) and bending properties of SFG porous beams, considering four different boundary conditions and a fixed set of parameters. The key findings of this paper are that as the slenderness ratio increases, the CBL decreases, and distribution shifts from linear to nonlinear region. Changes are significant, whereas maximum deflection increases. A significant effect is observed in the performance of static bending and buckling of SFG beams. It has been investigated that with an increase in voltage across the SFG beam, the buckling load increases, whereas the maximum deflection of the beam decreases.

Experimental Study on Fracture Toughness of Shale Based on Three-Point Bending Semi-Circular Disk Samples

A large number of construction practice projects have found that there are many joints and microcracks in rock, concrete, and other structures, which cause the complexity of rock mechanical properties and are the main cause of geological or engineering disasters such as earthquakes, landslides, and rock bursts. To establish a rock fracture toughness evaluation method and understand the distribution range of fracture toughness of Longmaxi Formation shale, this study prepared three-point bending semi-circular disk shale samples of Longmaxi Formation with different crack inclination angles. The dimensionless fracture parameters of the samples, including the dimensionless stress intensity factors of type I, type II, and T-stress, were calibrated using the finite element method. Then, the peak load of the samples was tested using quasi-static loading, and the load–displacement curve characteristics of Longmaxi Formation shale and the variation in fracture toughness with crack inclination angle were analyzed. The study concluded that the specimens exhibited significant brittle failure characteristics and that the stress intensity factor is not the sole parameter controlling crack propagation in rock materials. With an increase in crack inclination angle, the prefabricated crack propagation gradually transitions from being dominated by type I fracture to type II fracture, and the T-stress changes from negative to positive, gradually increasing its influence on the fracture. An excessively large relative crack length increases the error in fracture toughness test results. Therefore, this paper suggests that the relative crack length a/R should be between 0.2 and 0.6. The fracture load distribution range of shale samples with different crack angles is 3.27 kN to 10.92 kN. As the crack inclination angle increases, the maximum load that the semi-circular disk shale samples can bear gradually increases. The pure type I fracture toughness of Longmaxi Formation shale is 1.13–1.38 MPa·m1/2, the pure type II fracture toughness is 0.55–0.62 MPa·m1/2, and the T-stress variation range of shale samples with different inclination angles is −0.49–9.48 MPa.

Onset of dynamic void coalescence in porous ductile solids

This paper investigates void growth and coalescence in porous ductile solids under dynamic loading condition. A physical definition for the onset of void coalescence in porous ductile solids under dynamic loading is proposed. The onset is deemed to occur when the third invariant of the tensorial form of the Hill–Mandel condition attains a zero value. The definition allows for systematic investigations on the effects of dimensionless stress rate κ and stress state, defined by the stress triaxiality T and Lode parameter L, on the onset of void coalescence via micromechanical analyses. The analyses reveal that the critical macroscopic effective strain for the onset of void coalescence displays an increasing–decreasing transition trend as the dimensionless stress rate increases, for all levels of T and L considered. The macroscopic effective strain at the transition is identified as the “ductile–brittle” transition strain. The dimensionless stress rate at which the transition strain occurs is found to be relatively constant. A mapping in the κ−T space for L=−1, representative of a generalized uniaxial tension typical in spall fracture experiments, is established which depicts regions where coalescence and non-coalescence can take place, as well as the ductile–brittle regions demarcated by a ductile–brittle transition curve. The results also show that the critical void volume fraction and macroscopic effective strain at the onset of void coalescence are insensitive to inertia at high stress triaxialities at L=−1.

Analysis of a hollow cylinder with variable thermal conductivity and diffusivity by fractional thermoelastic diffusion theory

Based on fractional thermoelastic diffusion theory, an infinite hollow cylinder with variable thermal conductivity and diffusivity is studied. The inner surface of the hollow cylinder is free and subjected to thermal and chemical shocks, while the outer surface is fixed and adiabatic. The closed forms of dimensionless displacement, temperature, chemical potential, stress, and concentration in the Laplace transform domain are given by eigenvalue method. These physical quantities are then numerically obtained through the inverse Laplace transformation. The effects of fractional order parameters, variable thermal conductivity and diffusivity on these quantities are discussed. The present model may be helpful for better understanding the thermoelastic diffusion problems in actual engineering.

Using deep learning method to predict dimensionless values of stress intensity factors and T‐stress of edge notch disk bend (ENDB) specimen

AbstractA deep learning (DL) approach is implemented to determine the dimensionless stress intensity factors of mode‐I (YI) and mode‐III (YIII), as well as the normalized T‐stress (T*) of the edge notch disk bend specimen. The deep neural network (DNN) method as the DL approach is used to model the relationship between the geometry parameters of the specimen a/t, S/R, and β as inputs, and YI, YIII, and T* as output variables. To this end, three datasets consisting of 176, 176, and 123 finite element method data points from the previous studies are extracted for YI, YIII, and T*, respectively. The developed DNN models predicted the YI, YIII, and T* with correlations of 0.97003, 0.96918, and 0.97047, respectively. Then partial dependence plot is performed to determine the relationship between YI, YIII, and T* and the geometry parameters, which is useful in predicting and optimizing YI, YIII, and T*.

Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity

Abstract In this study, we investigated the effect of a rotation field and magnetic field on a homogeneous photo-thermoelastic nonlocal material and how its thermal conductivity changes as a result of a linearly distributed thermal load. The thermal conductivity of an interior particle is supposed to increase linearly with temperature under the impact of laser pulses. Microelastic (microelements distribution), non-local semiconductors are used to model the problem under optoelectronic procedures, as proposed by the thermoelasticity theory. According to the microelement transport processes, the micropolar-photo-thermoelasticity theory accounts for the medium’s microelongation properties. This mathematical model is solved in two dimensions using the harmonic wave analysis. Non-local semiconductor surfaces can generate completely dimensionless displacement, temperature, microelongation, carrier density, and stress components with the appropriate boundary conditions. The effects of thermal conductivity, thermal relaxation times, magnetic pressure effect, laser pulses, and rotation parameters on wave propagation in silicon (Si) material are investigated and graphically displayed for a range of values.

Long-term sealing performance evaluation and service life prediction of O-rings under thermal–mechanical coupling conditions

In service, thermal–mechanical coupling conditions can exacerbate stress relaxation of O-rings and lead to their thermal expansion, further complicating the sealing problem. A finite element method is developed to simulate the mechanical deformation behavior of O-rings under thermal–mechanical coupling conditions, and its validity is verified by comparison with experimental data. Based on a substantial amount of simulation data, it is found that a dimensionless contact stress SG˜=SG/SG0 can be used as an indicator of the degradation of sealing performance and can be related to temperature T and time τ in the form of an aging kinetic equation. By combining this equation with the existing interfacial leakage model, an approach of predicting the long-term leakage rate of O-rings is proposed to quantitatively evaluate the effect of various factors on the performance of O-rings, and some important conclusions are drawn. Regarding the effect of temperature on O-rings, the thermal expansion effect dominates when the service time is less than 20 d, and the stress relaxation effect prevails when it is greater than 20 d. The higher the temperature, the more significant the stress relaxation, and the faster the leakage rate of O-rings. Increasing the fluid pressure enhances the relaxation effect. Using the maximum allowable leakage rate as the failure criterion, a pressure–temperature curve is plotted representing the safety boundaries, which can be used to guide the design of the sealing structures. Furthermore, an exhaustive study on the service life evaluation shows that at high temperature (T ⩾ 120 °C), the service life curves show a plunging segment near a pressure rise to 0.42 MPa.

Stress Intensity Factors for Thermoelectric Bonded Materials Weakened by an Inclined Crack

Thermoelectric Bonded Materials (TEBM) weakened by an Inclined Crack Problems (ICP) subjected to remote stress was presented in this study. The problems are addressed by employing the Modified Complex Variable Function (MCVF) method, which incorporates the Continuity Conditions (CC) for the Resultant Electric Force (REF) and Displacement Electric Function (DEF) to formulate the Hypersingular Integral Equations (HSIEs) associated with these problems. By applying the curved length coordinate method, the unknown functions of Crack Opening Displacement (COD), Electric Current Density (ECD), and Energy Flux Load (EFL) are mapped onto the square root singularity function. The resulting equations are then numerically solved using appropriate quadrature formulas, with the traction along the crack utilized as the right-hand term. The obtained COD, ECD and EFL functions is then used to compute the dimensionless Stress Intensity Factors (SIFs) in order to determine the stability behavior of TEBM weakened by an ICP. The numerical results provided demonstrate the dimensionless SIFs at the crack tips. These results exhibit excellent agreement with previous studies conducted on the subject. Additionally, it is observed that the dimensionless SIFs at the crack tips are influenced by factors such as the ratio of Elastic Constants (ECR), the geometry of the cracks, and the coefficients associated with the Electric Current Density (ECD).

Thermal and mechanical investigation of proton exchange membrane fuel cells under combined loading conditions

Mechanical performance of PEM fuel cells under combined loadings is one of critical issues in improving cell performance and reliability. In this study, thermal and mechanical performance of the PEM fuel cell under clamping force and temperature load are investigated by experiments and three-dimensional dynamic simulations. In experiments, pressure distributions between gas diffusion layer and flow field are measured by pressure sensitive films. The experimental results show that the local pressure increases with clamping load, and pressure distribution is much uneven in the midstream. Meanwhile, a three-dimensional model of the cell combined transient heat transfer and mechanical response of components is developed, which is validated by experimental data. The modeling results show that under combined loadings, the porosity of gas diffusion layer under the rib decreases, attributed to compressive deformation caused by thermal gradient and clamping pressure, leading to higher effective thermal conductivity and electrical conductivity. When at a higher temperature, the overall stresses of gas diffusion layer decrease and the minimum stress is located under the center rib, forming a concave stress distribution pattern. Distribution and variation patterns of local deformations and stresses for the membrane are similar to those of gas diffusion layer, but the maximum stress and deformation are much lower. A dimensional stress coefficient is proposed to determine the stress distribution uniformity under the rib. With the increase of clamping torque, dimensionless stress coefficients under lower ambient temperature change slightly. As temperature increases, dimensionless stress coefficients increase significantly and decrease with the clamping torque, indicating the decreasing role of temperature load on mechanical response of the cell.

Influence of the ground motion directionality on the global ductility of 3D RC structures

This study examines the influence of ground motion directionality on global ductility μ_s of framed reinforced concrete structures. Suitable values of angle of attack θ, longitudinal reinforcement ratio ρ_l, dimensionless axial stress υ and mechanical ratio of transverse reinforcement ω_wd were assumed. Detailed nonlinear modeling was adopted to reproduce the behavior of reinforced concrete elements in the plastic field considering, also, the confinement effect on concrete mechanical properties. Nonlinear static simulations were carried out with the capabilities of the OpenSees code to evaluate the capacity curves and the corresponding global ductility. The results show that plastic hinges develop on the columns for the combined effect of bending moments transmitted by the beams framing into the same joint for values of the angle θ equal to 30° and 45°. Consequently, the formation of soft-storey mechanisms significantly reduces the global ductility μ_s. A design formula is proposed to avoid such collapse mechanism for framed reinforced concrete structures in ductility class high

Design of equi-strength annular disks made of functionally graded materials

This research proposes a robust method for designing functionally graded disks subject to internal and external pressures. The design objective is to find the profile of equi-strength disks. The von Mises yield criterion controls the initiation of plastic yielding. The yield stress and Young’s modulus are entirely arbitrary functions of the polar radius. Poisson’s ratio is constant. The solution is facilitated using the dimensionless yield stress as an independent variable instead of the polar radius. In particular, a numerical technique is only required to solve two ordinary differential equations. Moreover, one of these equations is independent of the other. Therefore, the equations can be solved individually, simplifying the solution method. The limitation imposed by the thickness gradient on the acceptability of plane stress conditions is considered. Particular designs are proposed assuming that the power function describes the radial distribution of material properties. A critical condition that allows for deriving relatively simple design solutions is emphasized. It is shown that this condition is satisfied for many specific material property distributions used in the literature.

A simple stress field solution for conical indentation

Classical contact mechanics has revealed the theoretical conical indentation solution of a stress field for ideal elastic–plastic materials based on the expansion cavity model and elastoplastic theory. This study proposes an equivalent stress analytical equation for the representative volume element of the median energy density point under conical indentation. For materials whose constitutive relations conform to power-law hardening, the equivalent stress solution is defined as the characteristic stress factor, and a simple stress field solution characterized by the logarithmic distribution law of dimensionless stress for conical indentation is presented. The verification results of finite element analysis showed that the proposed solution can uniformly describe the distribution of equivalent stress and three principal stresses in the material deformation region near the cone tip.

Investigation on the microscale memory dependence effect of thermo-viscoelastic rod based on fractional strain theory

Based on fractional strain theory and considering microscale memory dependent effect, the transient response of a one-dimensional micro-nano-structured viscoelastic rotating rod under the action of a moving heat source is investigated in the paper. The rod is placed in a magnetic field of constant strength and its outer surface is unconstrained. The effects of the kernel function, time lag factor, fractional order strain parameter, rotational parameter, visco-thermoelastic relaxation time, and nonlocal parameter on the distribution of the physical field in the rod are obtained by solving the governing equations through the Laplace integral transform and its numerical inverse transform. The results show that the fractional strain parameters and rotational angular velocity have little effect on the dimensionless temperature, but have significant effects on the dimensionless displacement, stress, and strain. The kernel function, time delay factor, viscoelastic relaxation time, and nonlocal parameter have different degrees effects on temperature, displacement, stress, and strain.

Analytical modelling of a multifunctional heterogeneous beam-bending analysis

Pores have a crucial role in shaping the features of functionally graded materials. If the distribution of pores is permitted to gradually rise from the outside inwards towards the center, many more features can be incorporated. A shear shape function is used to analyze the bending response of a two-directional functionally graded porous beam (FGPB), which can be considered a multifunctional heterogeneous material while accounting for both even as well as uneven porosity distributions. The power law is adapted to modify the material properties of FGPB through out the length and thickness dimensions. The notion of virtual displacements is applied when establishing equilibrium equations in FGPB. The Navier method is applied to clamped-clamped, clamped-free boundary conditions and simply supported boundary conditions to offer solutions to FGPB. The proposed methodology is supported by the numerical results of functionally graded beams from earlier studies. The dimensionless deflections and stresses under study are affected by gradient exponents, porosities, and aspect ratios.

Thermoelastic response of an elastic rod under the action of a moving heat source based on fractional order strain theory considering nonlocal effects

In this paper, based on fractional order strain theory and nonlocal heat conduction theory, the thermoelastic response of an elastic rod rigidly fixed at both ends and subjected to a moving heat source is investigated. The nonlocal fractional order strain control equation is established, and the analytical expressions of dimensionless temperature, displacement, and stress are solved using the Laplace integral transformation and numerical inverse transformation. The distribution law of physical quantities such as temperature, displacement, and stress when the fractional parameters, heat source moving speed, and thermal nonlocal parameters change is obtained. The results show that strain parameters and thermal nonlocal parameters have less influence on thermal–mechanical waves, while heat source velocity has a significant influence on thermal–mechanical waves.