Stress Discontinuities Research Articles

Thermal stress concentration points and stress mutations in nano-multilayer film structures

In the multilayer film-substrate system, thermal stress concentration and stress mutations cause film buckling, delamination and cracking, leading to device failure. In this paper, we investigated a multilayer film system composed of a substrate and three film layers. The thermal stress distribution inside the structure was calculated by the finite element method, revealing significant thermal stress differences between the layers. This is mainly due to the mismatch of the coefficient of thermal expansion between materials. Different materials respond differently to changes in external temperature, leading to compression between layers. There are obvious thermal stress concentration points at the corners of the base layer and the transition layer, which is due to the sudden change of the shape at the geometric section of the structure, resulting in a sudden increase in local stress. To address this issue, we chamfered the substrate and added an intermediate layer between the substrate and the transition layer to assess whether these modifications could reduce or eliminate the thermal stress concentration points and extend the service life of the multilayer structure. The results indicate that chamfering and adding the intermediate layer effectively reduce stress discontinuities and mitigate thermal stress concentration points, thereby improving interlayer bonding strength.

A permeability model considering the dynamic effect of stress on gas adsorption under discontinuous compression.

With the continuous advance of coal mining, the normal stress in front of coal seams will continue to increase, resulting in changes of internal structure and permeability of coal seams. During the continuous advance of mining face, the increase of vertical stress somewhere in front of coal seams may not be a transient process, but a gradual change process. Therefore, this paper carried out the seepage test of gas-containing coal under discontinuous loading axial stress. The stress, deformation and permeability of coal specimens were measured and recorded during the test, and the influence of discontinuous loading axial stress on the deformation, internal structure and seepage properties of coal specimens were discussed. On this basis, considering the influence of stress on the gas adsorption state, Klinkenberg effect and other factors, combined with Shi-Durucan permeability model, a new permeability model considering the dynamic adsorption state of coal specimens was developed.

A Strain-Controlled Finite Strain Model for CRD Consolidation of Saturated Clays Considering Non-Linear Compression and Permeability Relationships

Consolidation is the combined phenomenon of the compression and groundwater seepage of clay. Accurate evaluation of the consolidation characteristic is essential for the design, construction, and long-term stability of geotechnical structures. In this study, a strain-controlled non-linear finite strain model for constant rate-of-deformation (CRD) consolidation was developed for quickly and reliably predicting the consolidation behavior of clay soils. The model can account for any form of non-linear compression and permeability relationships, thus considering variations in the coefficient of consolidation. Being strain-controlled, it overcomes the limitations of stress-controlled models which require complex numerical iteration. The validity and accuracy of this model were verified through rigorous comparisons with both numerical simulations and experimental data. For normally consolidated soils, a non-linear e-lgσ′compression model was used instead of a linear compression model. For overconsolidated soils, the Harris function compression model was determined to be recommended to overcome the discontinuities in total stress and pore pressure caused by the traditional piecewise e-lgσ′ model. It was also found that determining the steady state of consolidation for normally consolidated soils should use the non-linear method, while the linear method is suggested to be adopted for overconsolidated soils.

Questioning Copernicus: cosmological principles on the eve of the Scientific Revolution

Abstract This paper examines the issues arising from Nicolaus Copernicus’s heliocentric theory when it is considered in the context of historical controversies over the planetary order. It will investigate the terms of this issue as they were available to Copernicus, and will stress both continuities and discontinuities with Ptolemaic astronomy. The consequences of heliocentrism for celestial physics will also be considered. Some of the consequences are inherent to heliocentrism, although not all of them were accounted for in De revolutionibus and certain outcomes may have been unforeseen by Copernicus or discordant with his theory.

Advances and applications of the strut-and-tie method in reinforced concrete design: A state-of-the-art review

The Strut-and-Tie Method (STM) is a versatile and powerful approach widely used in the design and analysis of reinforced concrete structures, particularly in regions with complex stress distributions and discontinuities. This review article delves into the theoretical foundations, practical applications, and experimental validations of the STM. The article begins by exploring the fundamental principles of the STM and its historical development, with a focus on its application in predicting the capacity of reinforced concrete members. Additionally, the STM efficacy in designing deep beams and comparisons with other analytical methods are thoroughly examined. Notably, the review includes a discussion on the application of STM in concrete beams, highlighting its ability to accurately predict capacity. Several studies investigating the behavior of reinforced concrete deep beams with openings, shear-strengthened deep beams, and continuous deep beams using the STM approach are critically analyzed, providing valuable insights into its reliability and practicality. Furthermore, the review delves into advancements in computational tools and finite element analyses that have been integrated with the STM, offering a more comprehensive and robust approach to design and analysis. The article also evaluates practical applications of STM in engineering scenarios, such as the design of bridge pier caps and complex regions, showcasing its versatility and adaptability. In conclusion, this review underscores the pivotal role of the Strut-and-Tie Method in modern reinforced concrete design and analysis. It serves as a valuable resource for engineers, researchers, and practitioners seeking to apply this method effectively in various structural configurations and challenging scenarios. Ultimately, the article emphasizes the significance of STM as a reliable and efficient tool for optimizing the design and ensuring the safety and performance of reinforced concrete structures.

Tensile damage evolution of unidirectional ceramic matrix composites under thermal stress

Ceramic matrix composites (CMCs) have been widely used in aerospace thermal-structures due to their excellent high-temperature performance. It is essential to understand the damage evolution of CMCs. However, in previous research work, the effect of thermal stress induced damage during CMCs fabrication on tensile response was often ignored. A damage evolution model that considers axial and radial thermal stresses to predict tensile response of unidirectional ceramic matrix composites was proposed in this study. The average relative errors between the current prediction and experimental data in the literature were calculated as 1.64 % and 1.91 %, validating this approach. Meantime, the damage evolution laws of interface debonding and the critical stress of matrix cracking in the Budiansky–Hutchinson–Evans (BHE) model were corrected to satisfy the discontinuous interfacial shear stress. According to the experimental data, the current model predicted critical stresses of matrix cracking better than the BHE model, with error rate reductions of 6.52 % and 15.38 %.

Bioinspired stiff–soft gradient network structure for high-performance impact-resistant elastomers

Traditional impact-resistance materials relying on the combination of supporting materials and energy-dissipation elastomers can effectively reduce shock load, yet the sharp interface between two types of materials causes discontinuous stress transfer and cracking. Here, inspired by the squid beak, we report a type of high impact-resistance gradient elastomers with large-scale modulus gradient with about three orders of magnitude (modulus range of 7 × 103 ∼ 7 × 106 Pa) and high energy dissipation (loss factor > 0.6) over a wide temperature range by diffusively introducing stiff polymers in a highly damping elastomer with controlled mechanical properties. Under the action of an external force, our gradient elastomers exhibit soft-while-stiff attributes, combining cushioning and support. In drop hammer impact tests, our gradient materials can reduce impact strength by 80 %, significantly better than commercial protective gear. It is worth mentioning that the modulus of the bottom layer matches that of the tissues for better protection.

Stable nanofacets in [111] tilt grain boundaries of face-centered cubic metals

Grain boundaries can dissociate into facets if that reduces their excess energy. This, however, introduces line defects at the facet junctions, which present a driving force to grow the facets in order to reduce the total number of junctions and thus the system's energy. Often, micrometer-sized facet lengths are observed and facet growth only arrests for kinetic reasons. So far, energetically stable, finite-sized facets have not been observed, even though theoretical stability conditions have already been proposed. Here, we show a case where nanometer-sized facets are indeed stable compared to longer facets in [111¯] tilt grain boundaries in Cu by atomistic simulation and transmission electron microscopy. The facet junctions lack a Burgers vector component, which is unusual, but which removes the main energy cost of facet junctions. Only attractive interactions via line forces remain, which result from a discontinuity of grain boundary excess stress at the junction. Atomistic simulations predict that the same phenomenon also occurs in at least Al and Ag. Published by the American Physical Society 2024

Multiscale modeling on the multi-physical behaviors of high temperature superconducting magnets based on a combined global homogenization and local refinement scheme

The safe and stable operation is a crucial issue in the development of high-field high temperature superconducting (HTS) magnets. In this paper, we construct a multiscale model which couples the homogenized global (macroscopic) behavior and the refined local (mesoscopic) characteristics to simulate the coupled electromagnetic-mechanical-thermal behaviors of the HTS magnets. In the model, the numerical homogenization method is adopted to simulate the macroscopic behavior of the magnets and identify the ‘dangerous region’ of the magnet which are prone to damage or quench. Then, a refined local sub-model which coupling with the macroscopic homogenization model is established by considering the microstructure and physical parameters of each components of the HTS tapes in the ‘dangerous region’. Thus, a combined global homogenization and local refinement scheme which balances the computational efficiency and numerical accuracy is developed to simulate the coupled multi-physical behaviors of the HTS magnets including the quench and its propagation. Our results show that the refined local sub-model can simulate the electromagnetic field and the stress-strain at the scale of the tape more accurately. Characteristics, such as the discontinuous stress distribution across the interfaces between different layers and the current shunt from the HTS layer to metallic layers during the quench process of HTS tapes, which are beyond the capability of the homogenization model, have also been well depicted by the refined sub-model.

Development of governing partial differential equations of reinforcing thin films

In this paper, a novel interface model for elastic isotropic thin films perfectly bonded to the surrounding elastic media is introduced. Considering an average stress and displacement through the thin film thickness, the shear stress discontinuity across the interface is expressed in terms of spatial and time derivatives of displacement components. The derived interfacial equations are presented in a general form. As such, they are applicable to asymmetric elastodynamic problems of anisotropic solids with thin film interfaces. Employing the introduced interface model and Hankel transform technique, static Green's functions of an elastic isotropic half-space reinforced by a buried thin film are obtained. Results of some special cases, including axisymmetric loading, inextensible membrane, unreinforced half-space, and surface-coated half-space, are also presented. The robustness and effectiveness of the proposed interface model are shown by two solved numerical examples, and some elastic responses are plotted to show the impact of thin film stiffness. According to the numerical results, modeling elastic thin films as inextensible membranes can significantly alter the elastic responses.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

Finite element investigations for chip scraping during orthogonal cutting process with micro-textured tools

Compared with the conventional tool (CT), the micro-textured tool (MTT) has the advantages of reducing cutting forces, lowering cutting temperatures and inhibiting tool wear. However, the chip scraping phenomenon generated in the cutting process has negative effects and degrades cutting performance when using the MTT with grooves perpendicular to the cutting edge. Due to the difficulty in observing and characterizing chip scraping in situ by experiments, its mechanism and influence on specific cutting forces and tool wear are not fully understood. To this end, finite element (FE) method is employed for simulating the cutting process with MTT. The simulation model is validated by comparing the predicted and measured specific cutting forces. The average prediction error of specific cutting and feed forces is 12.4 % and 18.8 %, respectively. The simulation results indicate that chip scraping mainly results from the discontinuity, non-uniformity and high contact stress state of the tool-chip interface. The minimum specific cutting force is achieved when the advantages of micro-texture and the chip scraping effects are balanced. The MTT rake face wear is subdivided into a severe and a sliding wear zone. This partition characteristic is closely associated with normal contact stress and temperature distributions. The work in this paper contributes to improving the understanding of chip scraping, optimizing micro-texture and cutting parameters, and promoting MTT applications in the manufacturing industry.

Incompatibility stress at inclined grain boundaries for cubic crystals under hydrostatic stress and uniaxial stress

In a material under stress, grain boundaries may give rise to stress discontinuities. The stress state at grain boundaries strongly affects microscopic processes, such as diffusion and segregation, as well as failure initiation, such as fatigue, creep, and corrosion. Here the general condition of incompatibility stress at grain boundaries is studied with a bicrystal model for linear elastic materials. In materials with cubic crystal structures, it is proven that hydrostatic stress does not lead to a stress discontinuity at grain boundaries. For bicrystals with inclined grain boundaries under uniaxial stress, the extreme values of the incompatibility stress as a function of the inclination angle are obtained by a simulated annealing method. A simple criterion is proposed to classify cubic materials into three groups. For cubic crystals with at most moderate anisotropy, the highest incompatibility stress occurs when the grain boundary plane is perpendicular to the uniaxial stress. For highly anisotropic materials, such as alkali metals and polymorphic high-temperature phases, the highest incompatibility stress occurs on grain boundaries with an inclination of about 47o.

Geometric stress functions, continuous and discontinuous

In his work on stress functions Maxwell noted that given a planar truss the internal force distribution may be described by a piecewise linear, C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^0$$\\end{document} continuous version of the Airy stress function. Later Williams and McRobie proposed that one can consider planar moment-bearing frames, where the stress function need not be even C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^0$$\\end{document} continuous. The two authors also proposed a discontinuous stress function for the analysis of space-frames, which however suffers from incompleteness. This paper provides a discontinuous stress function for n-dimensional space frames that is complete and minimal, along with its derivation from an n-dimensional continuous stress function. The continuous stress function generalizes both Günther’s and Maxwell’s stress functions.

Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression

The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens.

Mechanics of inner core debonding of composite sandwich beam with CFRP hexagonal honeycomb

The inner core debonding of composite sandwich beams with carbon fiber reinforced polymer (CFRP) hexagonal honeycomb core is investigated theoretically and experimentally. Based on the principle of minimum potential energy, a theoretical model is established to reveal the core debonding mechanism with Timoshenko’s beam theory and Extended High-Order Sandwich Panel Theory (EHSAPT) for composite face sheets and CFRP hexagonal honeycomb core, respectively. The theoretical approach of core debonding simulation is based on the framework of the cohesive zone model (CZM). By constructing the constitutive relation of the core interface as the discontinuous stress and displacement boundary conditions, the vertical core debonding can be simulated overcoming the singularity of equilibrium equations. The crack propagation process is decomposed into three stages with the consideration of the double crack propagation mechanism. In experiments, the regular and reinforced hexagonal honeycomb sandwich beams are designed and fabricated, and the quantification of the defect degree of the core bonding interface is achieved by equivalent energy release rate obtained from the homogenized hexagonal honeycomb. The double cantilever beam (DCB) experiments are performed to determine the equivalent energy release rate and reveal the core debonding mechanism of CFRP hexagonal honeycomb sandwich beams. Comparing the load–displacement curves and debonding deformation patterns indicates that the established theoretical model can effectively predict the core debonding mechanical response. Finally, parametric analysis is carried out to discuss the impact of structural dimension parameters, defect location and defect degree on the debonding modes of CFRP hexagonal honeycomb sandwich beams.

Microstructural smoothed particle hydrodynamics model and simulations of discontinuous shear-thickening fluids

Despite the recent interest in the discontinuous shear-thickening (DST) behavior, few computational works tackle the rich hydrodynamics of these fluids. In this work, we present the first implementation of a microstructural DST model in smoothed particle hydrodynamic (SPH) simulation. The scalar model was implemented in an SPH scheme and tested in two flow geometries. Three distinct ratios of local to non-local microstructural effects were probed: zero, moderate, and strong non-locality. Strong and moderate cases yielded excellent agreement with flow curves constructed via the Wyart–Cates (WC) model, with the moderate case exhibiting banding patterns. We demonstrate that a local model is prone to a stress-splitting instability, resulting in discontinuous stress fields and poor agreement with the WC model. The mechanism of stress splitting has been explored and contextualized by the interaction of local microstructure evolution and the stress-control scheme. Analytic solutions for a body-force-driven DST channel flow have been derived and used to validate the SPH simulations with excellent agreement in velocity profiles. Simulations carried out at increasing driving forces exhibited a decrease in flow. We showed that even the simple scalar model can capture some of the key properties of DST materials, laying the foundation for further SPH study of instabilities and pattern formation.

Stress discontinuity and singularity around the vertex of a triangular inhomogeneity

The stress field around a vertex of angular inhomogeneity has been investigated by Eshelby’s equivalent inclusion method (EIM). Different from Eshelby’s problem for ellipsoidal inhomogeneity with a uniform or polynomial eigenstrain, a singular eigenstrain field is derived by Airy’s stress function and asymptotic analysis, in which the singular elastic fields can be expressed in terms of the distance to the vertex. The discontinuity of Eshelby’s tensor along the boundary has been analytically derived and are used in the stress equivalence condition at the vertex, which can be converted into an eigenvalue problem with the integral of the Green’s function and singular eigenstrain over the inhomogeneity. To verify the solution, when the opening angle 2β at the vertex approaches zero, the triangular void reduces to a slit-like crack, and the paper reproduces the classic solution of 1/r singularity. When β increases from 0 to π/2, the singularity parameter λ around the vertex of the triangular void reduces at different pace under the symmetric and antisymmetric loading conditions. When a triangular inhomogeneity exhibits nonzero stiffness and different angles, λ changes with the stiffness ratio, β, and loading conditions, and the dominant stress singularity around the vertex and stress discontinuity across the boundary are analytically provided. Particularly, the stress singularity for an adhesive interface with varying stiffness provides insight for structure repair and integration.

Effect of Twin Circular Underground Voids on Bearing Capacity of Strip Foundations

Underground voids can significantly alter the stress and strain conditions of the surrounding soil mass, consequently affecting the stability of buildings located on the surface. Numerous numerical and experimental methods have been employed to investigate the effects of voids on nearby structures. In this research, a mixed lower bound-finite element method is utilized to study the stability of strip foundations situated above twin continuous voids. The soil behavior is modeled using the Mohr-Coulomb yield function along with an associated flow rule. Three-noded triangular stress elements are used to mesh the stress field, considering stress discontinuities at the common edges of adjacent elements. The study assumes that the two voids are identical in terms of radius, distance from the footing centerline, and depth from the ground level. The primary geometrical parameters considered in the analysis are the location and radius of the voids, as well as the strength parameters of the soil. By investigating the changes in bearing capacity concerning these factors, practical charts are proposed to aid in understanding the stability of the foundation. The results of the current study reveal the existence of an unsafe zone beneath the foundations, where the impact of the twin voids on bearing capacity reduction can be significant. Understanding these effects is crucial for design and construction of structures in areas prone to underground voids and also to decide where to bore infrastructure tunnels in order to have minimum effect on stability of the above buildings.

Heterogeneities of grain boundary contact for simulation of laboratory-scale mechanical behavior of granitic rocks

From a practical point of view, grain structure heterogeneities are key parameters that control the rock response and still remains a challenge to incorporate in a quantitative manner. One of the less discussed topics in the context of the grain-based model (GBM) in the particle flow code (PFC) is the contact heterogeneities and the appropriate contact model to mimic the grain boundary behavior. Generally, the smooth joint (SJ) model and linear parallel bond (LPB) model are used to simulate the grain boundary behavior. However, the literature does not document the suitability of different models for specific problems. Another challenge in implementing GBM in PFC is that only a single bonding parameter is used at the grain boundaries. The aim of this study is to investigate the responses of a laboratory-scale specimen with SJ and LPB models, considering grain boundary heterogeneous and homogeneous contact parameters. Uniaxial and biaxial compression tests are performed to calibrate the response of Creighton granite. The stress–strain curves, volumetric dilation, inter-crack (crack in the grain boundary), and intra-crack (crack within the grain) development, and failure patterns associated with different contact models are examined. It was found that both the SJ and LPB models can reproduce the pre-peak behavior observed for a granitic rock type. However, the LPB model is unable to reproduce the post-peak behavior. Due to the large interlocking effect originating from the balls in contact and the ball size in the LPB model, local dilation is induced at the grain boundaries. This overestimates the volumetric dilation and residual shear strength. The LPB model tends to result in discontinuous inter-cracks and stress localization in the rock specimen, resulting in fine fragments at the rock surface during failure.