Mechanical Theory Research Articles

Resurrecting Tradition

This paper reviews Kelly Brown Douglas’s Resurrecting Hope and brings it into conversation with certain themes in Catholic theology and with the theory of the scapegoat mechanism articulated by the French intellectual, René Girard.

Study on Micro-Pressure Drive in the KKM Low-Permeability Reservoir

Kazakhstan has abundant resources of low-permeability oil reservoirs, among which the KKM low-permeability oil reservoir has geological reserves of 3844 × 104 t and a determined recoverable reserve of 1670 × 104 t. However, the water flooding efficiency is only 68%, and the recovery efficiency is as low as 32%. The development of the reservoir faces challenges such as water injection difficulties and low oil production from wells. In order to further improve the oil recovery rate of this reservoir, our team developed micro-pressure-driven development technology based on pressure-driven techniques by integrating theories of fluid mechanics and artificial intelligence. We also combined this with subsequent artificial lift schemes, resulting in a complete set of micro-pressure-driven process technology. The predicted results indicate that after implementing micro-pressure-driven techniques, a single well group in the KKM oilfield can achieve a daily oil production increase of 32.08 t, demonstrating a good development effect.

A theory of the neural mechanisms underlying negative cognitive bias in major depression.

The widely acknowledged cognitive theory of depression, developed by Aaron Beck, focused on biased information processing that emphasizes the negative aspects of affective and conceptual information. Current attempts to discover the neurological mechanism underlying such cognitive and affective bias have successfully identified various brain regions associated with severally biased functions such as emotion, attention, rumination, and inhibition control. However, the neurobiological mechanisms of how individuals in depression develop this selective processing toward negative is still under question. This paper introduces a neurological framework centered around the frontal-limbic circuit, specifically analyzing and synthesizing the activity and functional connectivity within the amygdala, hippocampus, and medial prefrontal cortex. Firstly, a possible explanation of how the positive feedback loop contributes to the persistent hyperactivity of the amygdala in depression at an automatic level is established. Building upon this, two hypotheses are presented: hypothesis 1 revolves around the bidirectional amygdalohippocampal projection facilitating the amplification of negative emotions and memories while concurrently contributing to the impediment of the retrieval of opposing information in the hippocampus attractor network. Hypothesis 2 highlights the involvement of the ventromedial prefrontal cortex in the establishment of a negative cognitive framework through the generalization of conceptual and emotional information in conjunction with the amygdala and hippocampus. The primary objective of this study is to improve and complement existing pathological models of depression, pushing the frontiers of current understanding in neuroscience of affective disorders, and eventually contributing to successful recovery from the debilitating affective disorders.

Avalanche scaling law for heterogeneous interfacial fracture

A new approach is proposed to study the statistical law of avalanches due to the fracture of a heterogeneous interface. Firstly, a discrete interface is considered as a bundle of fibers clamped with two elastic circular plates, fiber strength being either a random variable or a stochastic field. Based on the theory of solid mechanics, equations governing the dynamic fracture process of fibers under tension are exactly derived and solved. The statistical law of fracture avalanches is accurately obtained. By tuning parameters, the model covers the whole scheme of stress-transfer mechanism due to fiber breaking from local load sharing to equal load sharing. Results show that the distribution of avalanche size of interfacial fracture follows a power-law relation, with the power exponent in the range [1.5,2.5], depending on both disorders of interface and stiffness of plates. Particularly, the exponent monotonically increases with plate stiffness to the value 2.5, a universal constant obtained by Hemmer and Hansen (1992). Then, the fracture of a laminated interface is analyzed. By discretizing the interface to a set of prismatic elements, the problem reduces to that of a discrete interface. Similar statistical behaviors are also observed. Furthermore, the temporal variation of avalanche scaling law is investigated. It is shown that in the vicinity of collapse point, the exponent of each time window is smaller than the exponent evaluated with the whole time series of event, probably a precursor for imminent catastrophic failure of interface.

Experimental Study on Dynamic Tensile Mechanical Behavior and Fracture Mechanical Characteristics of Sandstone with a Single Prefabricated Fissure

The structural stability of engineering rock mass under dynamic disturbance is directly associated with the fracture mechanics properties in engineering practice. Fully understanding the rock’s fracture mechanical behavior and crack evolution caused by stress concentration at the crack tip in engineering rock mass under dynamic load can offer useful insight into the rock’s dynamic fracture mechanism. A dynamic test using split-Hopkinson pressure bar (SHPB) test system was performed on a single prefabricated fissure sandstone centrally cracked Brazilian disk (CCBD) specimens. Based on the theory of fracture mechanics and one-dimensional stress wave theory, the dynamic crack initiation criterion of CCBD specimen is proposed, and the regression model of sandstone’s dynamic fracture toughness under the coupling effect of fissure angle and strain rate is established by using response surface methodology (RSM). The influence of strain rate and fissure angle on stress wave characteristics, dynamic tensile mechanical behavior, and fracture mechanics characteristic was investigated in this study. The findings demonstrate that: (1) The fissure angle plays a pivotal role in determining the failure mode of sandstone. As the fissure angle increases, three distinct failure modes emerge in the sandstone specimens, while variations in strain rate have minimal impact on the fracture mode of these specimens. (2) Alterations in the fissure angle result in changes to the waveform of transmitted waves. When the fissure angle is below 30°, the transmitted wave exhibits “double peak” characteristics; when it exceeds 30°, a “single peak” waveform is observed. This phenomenon can be attributed to diffraction principles governing incident waves. (3) When the impact pressure is 0.2 MPa, the peak load initially exhibits an increase followed by a decrease, with the peak load reaching its maximum at a fracture angle of 60°; when the impact pressures are 0.3 and 0.5 MPa, there exists a negative correlation between the peak load and the fissure angle. (4) The influence of strain rate on sandstone’s fracture resistance is predominant, with alterations in fissure angle exerting an auxiliary effect on this property. The research results can provide a theoretical and experimental basis for dynamic disaster prevention in urban underground space.

Evolution mechanism of scratch removal based on the implementation of magnetorheological finishing.

Scratches on optical components induce laser damage and limit the increase in laser power. Magnetorheological finishing (MRF) is a highly deterministic optical manufacturing technology that can improve the surface roughness of optical components. Although MRF has exhibited significant potential for reducing subsurface damage and removing scratches, the principle and mechanism behind the scratch removal are not sufficiently understood. In this study, the theory of fluid mechanics is used to analyze the pressure, velocity, and particle trajectory distribution near a scratch. A physical model was developed for the differential removal of scratches at the bottom and surface of the optical components. The morphological evolution of the scratch was predicted during removal, and detailed experiments were performed to verify the effectiveness of the proposed model. The results indicate that scratches expand laterally rather than being completely removed. Furthermore, scratch removal efficiency is greater when the removal direction is perpendicular to the scratch rather than being parallel. This study offers an intrinsic perspective for a comprehensive understanding of the MRF technique used for scratch removal, which can be beneficial for removing scratches from aspherical optical systems.

A unified analytical disk cam profile generation methodology using the Instantaneous Center of Rotation for educational purpose

Cam design is a fundamental part of the Mechanism and Machine Theory (MMT) and is included in the vast majority of MMT books. Cam profile design is usually determined with graphical and analytical methods. Graphical methods are didactically very successful to introduce the theory of cam profile generation in a simple way. In turn, analytical methods allow computer implementations of cam profile generation in order to reproduce it accurately. Most modern MMT books describe analytical methods using geometric equations and envelope theory. However, the analytical profile definition depends on the specific type of follower and there is a lack of a general formulation. This work presents a unified and general analytical formulation for the disk cam profile determination. Based on the Instantaneous Center of Rotation and the kinematic inversion, the formulation provides analytical expressions of the cam profile and is applicable to any type of follower. Thus, the unified formulation can be used in forthcoming books on this discipline.

Reviewer acknowledgments and awards: Recognition awards for distinction of reviewing in 2023

In 2023, members of the Mechanism and Machine Theory journal's Editorial Board and many independent reviewers contributed their time and expertise in reviewing manuscripts. This process greatly benefits our editors, contributing authors, and ultimately our readers. In fact, the high standard and reputation of the journal is strongly shaped by the expert knowledge, generous time contribution, and commitment to mechanism and machine science of the body of reviewers. Both, Elsevier, the publisher, and the editor-in-chief of the journal, would like to publicly pay tribute to all of the 824 reviewers who completed a total of 2118 reviews during the year of 2023. We are extremely grateful for their outstanding contributions and we are look forward to working with them in 2024!

A Lie group variational integrator in a closed-loop vector space without a multiplier

Abstract. As a non-tree multi-body system, the dynamics model of four-bar mechanism is a differential algebraic equation. The constraints breach problem leads to many problems for computation accuracy and efficiency. With the traditional method, constructing an ODE-type dynamics equation for it is difficult or impossible. In this exploration, the dynamics model is built with geometry mechanic theory. The kinematic constraint variation relation of a closed-loop system is built in matrix and vector space with Lie group and Lie algebra theory respectively. The results indicate that the attitude variation between the driven body and the follower body has a linear recursion relation, which is the basis for dynamics modelling. With the Lie group variational integrator method, the closed-loop system Lagrangian dynamics model is built in vector space, with Legendre transformation. The dynamics model is reduced to be the Hamilton type. The kinematic model and dynamics model are solved using Newton iteration and the Runge–Kutta method respectively. As a special case of a crank and rocker mechanism, the dynamics character of a parallelogram mechanism is presented to verify the good structure conservation character of the closed-loop geometry dynamics model.

Progressive Irreversible Proprioceptive Piezo2 Channelopathy-Induced Lost Forced Peripheral Oscillatory Synchronization to the Hippocampal Oscillator May Explain the Onset of Amyotrophic Lateral Sclerosis Pathomechanism.

Amyotrophic lateral sclerosis (ALS) is a mysterious lethal multisystem neurodegenerative disease that gradually leads to the progressive loss of motor neurons. A recent non-contact dying-back injury mechanism theory for ALS proposed that the primary damage is an acquired irreversible intrafusal proprioceptive terminal Piezo2 channelopathy with underlying genetic and environmental risk factors. Underpinning this is the theory that excessively prolonged proprioceptive mechanotransduction under allostasis may induce dysfunctionality in mitochondria, leading to Piezo2 channelopathy. This microinjury is suggested to provide one gateway from physiology to pathophysiology. The chronic, but not irreversible, form of this Piezo2 channelopathy is implicated in many diseases with unknown etiology. Dry eye disease is one of them where replenishing synthetic proteoglycans promote nerve regeneration. Syndecans, especially syndecan-3, are proposed as the first critical link in this hierarchical ordered depletory pathomechanism as proton-collecting/distributing antennas; hence, they may play a role in ALS pathomechanism onset. Even more importantly, the shedding or charge-altering variants of Syndecan-3 may contribute to the Piezo2 channelopathy-induced disruption of the Piezo2-initiated proton-based ultrafast long-range signaling through VGLUT1 and VGLUT2. Thus, these alterations may not only cause disruption to ultrafast signaling to the hippocampus in conscious proprioception, but could disrupt the ultrafast proprioceptive signaling feedback to the motoneurons. Correspondingly, an inert Piezo2-initiated proton-based ultrafast signaled proprioceptive skeletal system is coming to light that is suggested to be progressively lost in ALS. In addition, the lost functional link of the MyoD family of inhibitor proteins, as auxiliary subunits of Piezo2, may not only contribute to the theorized acquired Piezo2 channelopathy, but may explain how these microinjured ion channels evolve to be principal transcription activators.

C=Anything and the switchback effect in Schwarzschild-de Sitter space

We investigate observables within the framework of the codimension-one C=Anything (CAny) proposal for Schwarzschild-de Sitter (SdS) space under the influence of shockwave sources. Within the proposal, there is a set of time-reversal invariant observables that display the same rate of growth at early and late times for a background with or without shockwave sources. Once we introduce shockwaves in the weak gravitational coupling regime, there is a decrease in the late-time complexity growth due to cancellations with early-time perturbations, known as the switchback effect. The result shows that some CAny observables in SdS may reproduce the same type of behavior found in anti-de Sitter black holes. We comment on how our results might guide us to new explorations in the putative quantum mechanical theory.

Erosion mechanism of point bar retreat under the protection of a flexible mattress

Channel retreat can be responsible for the significant loss of banks, farmland, and wetlands, leading to drastic changes in fluvial sediment and local river regimes. Although current studies focus on the erosion process of natural river channels, the mechanism by which revetments, such as the flexible mattress, influence bank evolution is still unclear. Hence, by conducting a generalized model experiment, this study investigates the point bar failure process under the mattress protection, i.e., the episodic event when the soil reaches the static equilibrium state. Specifically, a scour hole develops at the junction between the soft and hard materials, causing mattress suspension on the bank toe’s side wall and resulting in a reduction coefficient for transverse scouring rate ranging from 0.08 to 0.15. Based on the theories of soil mechanics and river dynamics, the critical conditions for point bar instability were deduced, and a mechanical model describing its erosion process under the mattress protection was established. Furthermore, our model calculated the bank morphology and total erosion volume at different periods in the flume experiment, demonstrating a good agreement with the measured data. Additionally, variations in stability coefficient and forces exerted on soil (including shear strength, gravity, and fluid pressure) of the typical sections during point bar retreat were analyzed. Sensitivity analysis of the bank toe stability emphasized the controlling effect of soil mechanical properties and the negative feedback of mattress weight. The results reveal the interaction mechanism between the mattress protection and point bar failure, theoretically guiding the bank erosion strengthening and river management planning.

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.

On the Use of Foam Rubber for Sealing Applications

O-rings made from foam rubber are often used in sealing applications. Foam rubber have low (macroscopic) elastic modulus E0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_0$$\\end{document} resulting in a low nominal contact pressure when squeezed against a countersurface. In most cases the foam rubber is covered by a thin surface film with the effective elastic modulus E1>E0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_1 > E_0$$\\end{document}. We show that the nominal contact pressure may not be high enough for the contact area to percolate and the O-ring seal will leak. For the leakage calculations we use the Persson multiscale contact mechanics theory, and the (modified) Bruggeman effective medium theory for the fluid flow conductivity. The experimental input for the theory are surface roughness power spectrum, which was obtained from stylus topography measurements, and the elastic properties (E0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_0$$\\end{document} and E1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_1$$\\end{document}) of the rubber O-ring. As an application of this calculation method, we have used the preliminary as well as the final results of the laboratory gas tightness tests of the 136 New Small Wheel Micromegas Quadruplets performed at CERN, from February 2019 to May 2021, in the framework of the ATLAS Experiment upgrade. In the integration quality control, a novel method for gas tightness measurement, that we have called “Flow Rate Loss”, has been used as a baseline method.Graphical

Adaptive directed support vector machine method for the reliability evaluation of aeroengine structure

Machine learning methods have been widely applied to structural reliability analysis, due to the excellent performance in modeling precision and efficiency. In this paper, an adaptive directed support vector machine model (ADSVM) is proposed by integrating the adaptive sampling technology (AST) and the developed directed support vector machine (DSVM), to improve the efficiency and accuracy of turbine blade reliability analysis. In the developed method, the AST is adopted to extract high quality samples, in respect of distributed probability density and the distances between sample values and response values. The DSVM was developed by introducing the penalty coefficients for all the slack variables, to improve the modeling accuracy of SVM approach. One numerical example and the reliability analysis of aeroengine high-pressure turbine blade were performed to validate the developed methods. As illustrated in this numerical investigation, the modeling precision of DSVM is improved by alleviating the lag effect of support vector regression. From the comparison of methods, it is demonstrated that the ADSVM has higher accuracy, efficiency and stability in reliability simulations, which are improved by ∼20 % and ∼46.2 %, respectively. The main efforts of this study are to propose a promising approach, ADSVM, for the reliability analysis of complex structures besides turbine blades, which hold the academical significance in enriching and developing mechanical reliability theory.

Three-Dimensional Probabilistic Semi-Explicit Cracking Model for Concrete Structures

This paper introduces a three-dimensional (3D) semi-explicit probabilistic numerical model for simulating crack propagation within the framework of the finite element method. The model specifically addresses macrocrack propagation using linear volume elements. The criteria governing the macrocrack propagation is based on the softening behavior observed in concrete under uniaxial tension. This softening behavior corresponds to a dissipated cracking energy that is equal to the mode I critical fracture energy (GIC) used in the Linear Elastic Fracture Mechanics theory (LEFM). The probabilistic nature of this model revolves around the random distribution of two mechanical properties: tensile strength (ft) and fracture energy, which varies based on the volume of finite elements. The scattering of the fracture energy increases as the volume of finite elements decreases in order to consider the strong heterogeneity of the material. This work primarily aims to estimate the relationship between the standard deviation of GIC and the volume of finite elements through the development of the numerical model. For this purpose, an inverse analysis is conducted based on a fracture mechanical test simulation. This test involves macrocrack propagation in a large Double Cantilever Beam (DCB) specimen with a crack length exceeding two meters. The proposed inverse analysis procedure yields highly significant results, indicating that the numerical model effectively evaluates both crack length and crack opening during propagation.

Transformation of 2,4,6-tribromophenol in the acetylperoxyl radical based oxidation process and formation of brominated byproducts

Acetylperoxyl radical (CH3C(O)OO•), as a peracetic acid (PAA) derived specific radical, has a promising future in environmental remediation. However, the research about the transformation mechanism of halogenated organics with CH3C(O)OO• and the subsequent formation of disinfection byproducts (DBPs) is still in the gap stage. 2,4,6-tribromophenol (2,4,6-TBP) was chosen as a target brominated compound to study its transformation and the formation mechanism of brominated byproduct in the neutral Co(II)/PAA system. The results showed that 94.7 % of 2,4,6-TBP with 50 µM was transformed and its corresponding pseudo-first-order kinetic constant is about 0.540 min−1. Interestingly, CH3C(O)OO• and reactive bromine species were found to dominate 2,4,6-TBP transformation. 2,4,6-TBP had the best transformation under neutral conditions· H2O2, HCO3–, and natural organic matter (NOM) significantly inhibited 2,4,6-TBP transformation, while Cl− had little effect on 2,4,6-TBP transformation. In addition, the main transformation pathways of 2,4,6-TBP, including debromination, C–C coupling, self-coupling, and CH3C(O)OO• cross-coupling were proposed based on the analysis of transformation products by LC-MS/MS and DFT theoretical calculations. In identified intermediates, there are some DBPs, including bromate, bromoform, and dibromoacetic acid. These DBPs increased gradually in approximately 24 h, moreover, Suwannee River NOM improved DBPs production. Therefore, the formation mechanism of DBPs during the treatment of brominated organics with CH3C(O)OO• was proposed for the first time, which extended the theory of the formation mechanism of DBPs in CH3C(O)OO•-based water treatment.

Design of ultra-low noise amplifier for quantum applications (QLNA)

The present article primarily focuses on the design of an ultra-low-noise amplifier specifically tailored for quantum applications. The circuit design places a significant emphasis on improving the noise figure, as quantum-associated applications require the circuit's noise temperature to be around 0.4 K. This requirement aims to achieve performance comparable to the Josephson Junction amplifier. Although this task presents considerable challenges, the work concentrates on engineering the circuit to minimize mismatch and reflection coefficients, while simultaneously enhancing circuit transconductance. These efforts aim to improve the noise figure as efficiently as possible. The results of this study indicate the possibility of achieving a noise figure of approximately 0.009 dB for a unique circuit design operating at 10 K. In a departure from traditional approaches, this study employs quantum mechanical theory to analyze the circuit comprehensively. By employing quantum theory, the researchers derive relationships that highlight the crucial quantities upon which the circuit design should focus to optimize the noise figure. For example, the circuit's gain power, which depends on the circuit's photonic modes, is theoretically derived and found to affect the noise figure directly. Ultimately, by merging quantum theory with engineering approaches, this study successfully designs a highly efficient circuit that significantly minimizes the noise figure in a quantum application setting.

What are the mechanisms underlying the delivery of survivorship care information in Australia? A realist review.

Quality survivorship information is an essential component of cancer care. However, survivors often report not receiving this information and healthcare professionals report limited practical guidance on how to effectively deliver survivorship information. Therefore, this study used realist review methods to identify mechanisms reported within the published literature for communicating survivorship information and to understand the contextual factors that make these mechanisms effective. Full-text papers published in CINAHL, PubMed, Web of Science, Scopus, Cochrane Library, and Academic Search Ultimate were included. Studies included in this review were conducted in Australia between January 2006 and December 2023, and reported on how information regarding survivorship care was communicated to adult cancer survivors living in the community. This review utilized realist methodologies: text extracts were converted to if-then statements used to generate context-mechanism-outcome theories. Fifty-one studies were included and six theories for mechanisms that underpin the effective delivery of survivorship information were formed. These include: (1) tailoring information based on the survivors' background, (2) enhancing communication among providers, (3) employing dedicated survivorship staff, (4) providing survivorship training, (5) reducing the burden on survivors to navigate their care, and (6) using multiple modalities to provide information. Findings can inform practical guidance for how survivorship care information is best delivered in practice. Clinicians can apply this guidance to improve their individual interactions with cancer survivors, as can policymakers to develop healthcare systems and procedures that support effective communication of cancer survivorship information.

A thermodynamically consistent strain difference-based nonlocal damage mechanics approach for failure analysis of quasi-brittle materials

The nonlocal integral approaches are established methods known for their effectiveness in dealing with the challenges of ill-posed behaviour and mesh sensitivity during the strain softening process, especially within classical continuum theories. The present work extends the strain difference-based nonlocal approach to continuum damage mechanics (CDM) theories for predicting the failure behaviour of quasi-brittle materials. The strain difference approach is adopted for two reasons: (i) it maintains physical realism and indirectly incorporates nonlocal effects while computing both the damage variable and the damage energy release rate, and (ii) the constitutive model maintains a symmetry nature in constructing the nonlocal part of the stiffness matrix, reducing the computational cost in strain-softening problems. The state and damage evolution equations for the present nonlocal approach are formulated within the thermodynamic framework. Numerical examples involving 2D and 3D cases are solved: (i) to study the influence of nonlocal parameter ‘α’ on the damage distribution while capturing the post-peak behaviours, (ii) to demonstrate the effectiveness of the present methodology by obtaining mesh-independent results and accurately predicting damage propagation paths, and (iii) to compare the experimental results and numerical structural response for coarse mesh, highlighting both computational efficiency and reduction of mesh-bias dependency. The results obtained by the strain difference-based nonlocal damage model agree well with the experimental results in the literature.