Modulus Theory Research Articles

Research on triaxial compressive mechanical properties and damage constructive model of post-thawing double-fractured quasi-sandstones with different angles

Joints and fractures lead to different failure mechanisms in rock masses under different environments. The mechanical properties and failure mechanisms of rocks with fissures are key problems in rock mass engineering. Parallel double-fracture quasi-sandstone specimens with different dip angles were prepared and subjected to triaxial compression tests after a single freeze-thaw cycle. Pore development, crack propagation, damage evolution, and failure characteristics were analysed. Combined with the strength distribution theory of microelements and the static elastic modulus theory, a damage constitutive model of double-fracture quasi-sandstone under freeze-thaw cycles and loads was established. This study explored the pore development, fracture propagation, damage evolution, and failure characteristics of fractured sandstone after thawing. The results showed that the compression wave velocity of the thawed specimens decreased, the nuclear magnetic resonance (NMR) T2 curve shifted to the right, and the frost heave force promoted the development of the internal porosity in the specimens. With an increase in the crack dip angle, peak stress, expansion stress, cohesion and internal friction angle, the specimen showed a ‘U’ shaped change trend, compression cracks, and rock bridge penetration rate after failure decreased, and mixed failure of tension and shear gradually changed into shear failure. When the dip angles were 30° and 60°, the double fractured quasi-sandstone had larger total damage and more obvious brittle failure characteristics.

Universal predictions of Siegel modular invariant theories near the fixed points

We analyze a general class of locally supersymmetric, CP and modular invariant models of lepton masses depending on two complex moduli taking values in the vicinity of a fixed point, where the theory enjoys a residual symmetry under a finite group. Like in models that depend on a single modulus, we find that all physical quantities exhibit a universal scaling with the distance from the fixed point. There is no dependence on the level of the construction, the weights of matter multiplets and their representations, with the only restriction that electroweak lepton doublets transform as irreducible triplets of the finite modular group. Also the form of the kinetic terms, which here are assumed to be neither minimal nor flavor blind, is irrelevant to the outcome. The result is remarkably simple and the whole class of examined theories gives rise to five independent patterns of neutrino mass matrices. Only in one of them, the predicted scaling agrees with the observed neutrino mass ratios and lepton mixing angles, exactly as in single modulus theories living close to τ = i.

Behaviour of short and long columns made from bamboo scrimber subjected to uniaxial compression

Engineered bamboo has been getting recognition as a forerunner in terms of desirable mechanical properties and a sustainable construction material. One of the most widespread variants is bamboo scrimber, also known as Parallel Bamboo Strand Lumber (PBSL). This paper presents a holistic investigation into the uniaxial compressive capacity of short bamboo scrimber columns in terms of failure mode, size effect, aspect ratio and failure strain. The studies in focus have been collated from published articles in literature. Furthermore, intermediately slender to long columns have been investigated with respect to the most common international timber standards and, elastic and inelastic theories. It is shown that the dominant failure mode affects the ultimate strength, especially a failure mode called kinking/local buckling. A size effect was observed and discussed with respect to the failure modes. In addition, a tangent modulus theory was proposed from a constitutive model called the Full-range Ramberg Osgood model that could better predict the critical buckling stress of intermediate-long columns over the conventional theory. Moreover, a modified AS1720 design approach was proposed to accommodate the inherent column behaviour of bamboo scrimber. Finally, a modified Newlin-Gahagan approach was proposed which produced consistent predictions for the experimental buckling stress for columns with varying slenderness across four different studies.

A fatigue damage model of asphalt mixture considering tensile and compressive modulus decay

In practical asphalt pavement engineering, asphalt mixture experiences both tensile and compressive stresses, and the stress state plays a pivotal role in determining fatigue performance. This study thoroughly explores the fatigue damage characteristics of asphalt mixture, specifically emphasizing a meticulous analysis of the differences between tensile and compressive moduli. Initially, the compressive and tensile moduli of the asphalt mixture were calculated based on the dual modulus theory. Subsequently, differences in tensile and compressive moduli, along with fatigue performance characteristics, were evaluated through indirect tensile tests. Ultimately, a comprehensive fatigue damage model was proposed to ascertain the critical damage degree of the asphalt mixture, integrating both modulus decay and fatigue damage. The findings reveal that decay rates for the tensile modulus were higher than those observed for the compressive modulus. The tensile damage should be considered more in the design of pavement structures. Upon comparing the critical damage degree determined using the traditional modulus decay model with the comprehensive fatigue damage model, it can be deduced that the latter shows favorable applicability. The compressive fatigue modulus can better characterize the fatigue damage behavior. The model proposed in this study integrates modulus decay and fatigue damage information, offering a more comprehensive depiction of asphalt mixture damage behavior during fatigue processes.

Dynamic performance of functionally graded composite structures with viscoelastic polymers

The functionally graded composite structures with viscoelastic polymers inherits the excellent performance of functionally graded composites and also possesses large damping performance, which has broad application prospects in the aerospace and mechanical engineering fields. However, due to the complexity of the structure itself, there is limited literature available on its theoretical modeling for efficient solutions. To predict its dynamic performance, a simplified dynamic model of the functionally graded composite structures with viscoelastic polymers is established. This model takes into account the displacement transfer relationship between the functional graded composite layer and the viscoelastic polymer layer. The governing differential equations are obtained by applying the Navier method and complex modulus theory. These equations are then solved using the Rayleigh–Ritz method. The validity of the theoretical model is confirmed by comparing it with existing literature and the results obtained from ANSYS software. Additionally, the model that has been developed is used to analyze how the graded index and elastic modulus of the structure, as well as its geometric parameters, affect its vibration and damping characteristics.

Computer homogenization of porous piezoceramics of different ferrohardness with random porous structure and inhomogeneous polarization field

The article is concerned with the homogenization problems, in which the effective moduli of porous piezoceramic composites are determined taking into account the inhomogeneity of the polarization field. The homogenization problems are solved by the finite element method in the framework of the theory of effective moduli and the Hill energy principle using the ANSYS package. To this end, in static problems of electroelasticity, the displacements and electric potential, which are linear in spatial variables, are specified on the boundary of a representative volume to provide constant stress and electric induction fields for a homogeneous reference medium. After solving a set of boundary value problems under different boundary conditions and determining the volume-averaged stress components and the electric induction vector, a complete set of effective moduli for the piezoelectric composite is calculated. A representative volume of the piezocomposite is created in the form of a regular finite element mesh consisting of cubic elements. Pores in the representative volume are assumed to be filled with a piezoelectric material with extremely small moduli. Finite elements with pore properties are selected according to a simple random algorithm. The inhomogeneous polarization field is found by solving an electrostatic problem, in which the polarization process in the representative volume is modeled based on a simplified linear formulation. The local coordinate systems for individual finite elements of the composite matrix are specified by the directions of the polarization vectors. In the following, when solving the problems of electroelasticity, these local coordinate systems associated with the elements of the piezoelectric matrix allow recalculating the material properties according to the formulas of transformation of the tensor components as the coordinate systems rotate. In addition, consideration is given to different models describing the change in the moduli of the material from an unpolarized state to a polarized one as a function of the polarization vector. Computational experiments were carried out for three types of piezoceramics: soft ferroelectric piezoceramics PZT-5H, piezoceramics PZT-4 of medium ferrohardness, and piezoceramics PZT-8 with higher degree of ferrohardness. The dependences of the effective moduli on porosity are compared for different laws of polarization inhomogeneity and different kinds of piezoceramic material of the composite matrix.

REPRESENTATIVE VOLUME AND EFFECTIVE MATERIAL CHARACTERISTICS OF PERIODIC AND STATISTICALLY UNIFORMLY REINFORCED FIBER COMPOSITES

In the deformable solid mechanics, there are concepts associated with continuum points (displacements, relative elongations, shifts) and a set of continuum points – an elementary volume (mass, energy, stresses). The role of such volume in the mechanics of composite materials is played by the representative volume element (RVE).This concept was first introduced by R. Hill (1963). Modern authors use the W.J. Drugan, J.R. Willis (1996) formulation. Based on the analysis of the RVE concept, we formulated its essential features: RVE is the minimum possible sample for numerical tests to determine the effective material parameters of the composite; under any RVE loading, its macroscopic stress-strain state is uniform. Its significance for the mechanics of composite materials is revealed: the existence of RVE for a composite is a criterion for applying the effective modulus theory to the analysis of its stress-strain state; the dehomogenization of a stressed-state composite material at a point is a solution to the micromechanics problem of the RVE stress-strain state determination; the characteristic size of RVE limits the size of the sampling grid in the numerical study. An iterative algorithm for constructing a representative volume of a periodic structure composite and its effective material thermoelastic characteristics is proposed. It is shown that the geometric shape of such a composition is a rectangular parallelepiped. The RVE construction algorithm for periodic compositions is extended to the composites statistically uniformly reinforced with continuous fibers. A method for modeling such materials with a following regular structure is suggested described: in the section perpendicular to the fibers, fiber centers should be located at the vertices of regular triangles. Examples of constructing RVE and thermoelastic material characteristics of specific compositions are given. The calculation results are compared with the data obtained using certified software products.

Moduli of spaces with prescribed homotopy groups

We describe a homotopy-theoretic approach to the theory of moduli of realizations of Blanc-Dwyer-Goerss, reproducing their obstructions to realizing a given Π-algebra as homotopy groups of a pointed space. Our techniques are based on the ∞-category PΣ(Sph) of product-preserving presheaves on finite wedges of positive-dimensional spheres, leading to more conceptual and streamlined arguments.

Structural optimization to improve the dynamic performance of novel co‐curing damping sandwich composites

AbstractCo‐cured damping composite structures have broad application prospects in high‐tech fields such as aerospace and space vehicles because of their low weight, large damping, and sufficient stiffness. In order to improve dynamic properties of conventional composite structures, a new type of damping composites embedded with multilayer viscoelastic film is proposed in this paper. Based on the complex modulus theory and vibration mechanics of composite plates and shells, vibration differential equation of composite plates with multilayer viscoelastic film is derived. The constitutive relation of the complex structure is established. The consistency of theoretical derivation and numerical simulation results provides a reference for the optimization of dynamic performance of damping sandwich composites. The effects of the distribution of viscoelastic film and the geometric structure parameters on dynamic performance of co‐cured damping composites are also discussed. The results show that the embedding of multi‐layer viscoelastic film can greatly enhance the loss factors of co‐cured composite structures under same damping layer thickness. This work lays a foundation for optimization of dynamic performance of lightweight and large damping composite structures.

Virtual Riemann–Roch theorems for almost perfect obstruction theories

This is the third in a series of works devoted to constructing virtual structure sheaves and K-theoretic invariants in moduli theory. The central objects of study are almost perfect obstruction theories, introduced by Y.-H. Kiem and the author as the appropriate notion in order to define invariants in K-theory for many moduli stacks of interest, including generalized K-theoretic Donaldson–Thomas invariants. In this paper, we prove virtual Riemann–Roch theorems in the setting of almost perfect obstruction theory in both the non-equivariant and equivariant cases, including cosection localized versions. These generalize and remove technical assumptions from the virtual Riemann–Roch theorems of Fantechi–Göttsche and Ravi–Sreedhar. The main technical ingredients are a treatment of the equivariant K-theory and equivariant Gysin map of sheaf stacks and a formula for the virtual Todd class.

Evaluation of tensile properties and fracture surface morphology of woven fabric-polymer composites filled with micro SiC and Al2O3 particulates

The current research aims to study the influence of hybridisation on the tensile and fracture surface morphology of plain weave glass fibre/epoxy composites. The polymer resin is primarily filled with inorganic particles such as silicon carbide and alumina, and the corresponding modified resin is termed as effective matrix. This effective matrix is further reinforced by plain weave glass fibre to fabricate the hybrid composite. Elastic properties of the composites are estimated after developing Micro-mechanical-model-based formulation considering different analytical model like Mori-Tanaka, Paul, Ishai-Cohen model along with equivalent modulus theory. Experiments are conducted to estimate the elastic constants and post-tensile fractured surface morphology of these composites. The tensile modulus predicted using Mori-Tanaka and equivalent modulus theory matches well with the experiments and found to be in good convergence compared to the other models. Detailed analyses of the fractured surface of the tensile samples express the positive effect of hybridisation on the tensile and failure behaviour. It is found that the tensile strength and elastic modulus of the composites increase with an increase in particulate content.

Characterization of strength, modulus, and fatigue damage properties of cement stabilized macadam based on the double modulus theory

• Flexural tensile strengths calculated with tensile and compressive differences are reduced by nearly 20 % when compared to those calculated without tensile and compressive differences. • A power function decay model of the tension–compression moduli of cement stabilized macadam was established in the four-point bending fatigue test. • The fatigue damage model of cement stabilized macadam was established and its accuracy was verified. Cement stabilized macadam (CSM) is a mixture created by combining cement as a binding material, water, and various particle sizes of minerals. The cement stabilized macadam material exhibits different moduli in tension and compression due to both its mechanical properties and the mechanical response in the asphalt pavement structure. To explore the strength, modulus and fatigue damage characteristics of CSM under different tensile and compressive modulus, this paper carried out the research. The calculation formulas for flexural tensile strength and tension–compression modulus were derived based on the difference in tension–compression modulus. A four-point bending strength test of CSM was carried out. Four-point bending fatigue tests with varying stress ratios were performed. It reveals deterioration laws of tension–compression modulus during fatigue process. The double logarithmic fatigue equation of CSM, as well as its nonlinear fatigue damage evolution equation, are established based on fatigue life results. The results of an analytical solution for fatigue life of rectangular section beams based on damage mechanics were obtained and compared to the results of four-point bending fatigue tests. The results reveal that the modulus of CSM differs in tension and compression. The calculated flexural tensile strength with the tension and compression difference is nearly 20 % lower than without the difference. The calculation approach that does not account for the difference in tension and compression overestimates the flexural tensile strength of CSM. The tension–compression moduli of CSM exhibit a power function decay law in the four-point bending fatigue processes. In the first stage, the dynamic modulus decays at a steady rate, accounting for 90 % of total fatigue life. The second stage in the life ratio of 0.9 occurs when the decay rate of the modulus rapidly increases and enters the stage of sharp decay. Based on the results of the four-point bending test, the modulus decay model was created. The decay parameter m has an exponential relationship with the stress ratio. The relative errors between the mean values of fatigue life tests and the predicted values of the analytical solutions range from 10.8 to 30.6 percent. The established fatigue damage equation for CSM can better reflect its fatigue damage evolution law. The research findings have great significance to solve the determination of pavement materials parameters based on the difference in tension and compression modulus. It also has a specific reference value for asphalt pavement design theory and calculation method when the varied modulus of tension and compression are considered.

Structural dynamic properties of stiffened composite plates with embedded multi-layered viscoelastic damping membranes

Aiming at optimizing stiffened composite structures with embedded multi-layered viscoelastic damping membranes, we developed a dynamic analytical model based on the first-order shear deformation theory, in which the vibration equations were derived from both the modulus theory and the composite material mechanics theory. The theoretical solution that satisfied the displacement boundary conditions was obtained by employing the Navier method. Results were simulated by the finite element method to verify correctness of the dynamic analytical model. In addition, the effects of structural parameters on dynamic performance (including first-order natural frequency and modal loss factor) were studied using the developed model.

Development of simplified model for injection rate prediction of diesel injectors during transient and steady operation

Determining the injection rate of the diesel injector during the transient short injection operations is a critical matter to enhance the combustion process by improving air/fuel mixture formation. In this regard, numerous injection models have been suggested in the literature to predict the injection rate accurately. However, such algorithms have not precisely predicted the rate of injection (ROI) in transient short injection events. In addition, most of those models require many input parameters to characterize hydraulic and mechanical subsystems in the injector, which can make them inconvenient to tune for different injector specifications, in other words not suitable for universal usage. Therefore, our study aims to develop a simple injection model that can predict injection rate precisely in the short and long injection durations considering relatively fewer input parameters. The model traces the pressure variation inside the sac based on the bulk modulus theory to predict nozzle exit velocity, thus the injection rate of the injector. In the algorithm, the bulk modulus of fuel (E) and discharge coefficients of the nozzle hole and needle seat (Cd,H and Cd,N) have been considered to vary rather than set constant during the injection process since such flow parameters would have a critical impact on the flow development at the transient stage, thus affecting the injection rate of diesel injectors. With this modelling strategy, the accuracy of the new model on ROI prediction was confirmed with acceptable model error for both short and long injection durations by validating against experimental results. To understand the effect of the new model scheme on ROI prediction, ROI results with the new model have been discussed by comparing it with the ROI results predicted with constant flow parameters.

Theory of length-scale dependent relaxation moduli and stress fluctuations in glass-forming and viscoelastic liquids.

The spatiotemporal correlations of the local stress tensor in supercooled liquids are studied both theoretically and by molecular dynamics simulations of a two-dimensional (2D) polydisperse Lennard-Jones system. Asymptotically exact theoretical equations defining the dynamical structure factor and all components of the stress correlation tensor for low wave-vector q are presented in terms of the generalized (q-dependent) shear and longitudinal relaxation moduli, G(q, t) and K(q, t). We developed a rigorous approach (valid for low q) to calculate K(q, t) in terms of certain bulk correlation functions (for q = 0), the static structure factor S(q), and thermal conductivity κ. The proposed approach takes into account both the thermostatting effect and the effect of polydispersity. The theoretical results for the (q, t)-dependent stress correlation functions are compared with our simulation data, and an excellent agreement is found for qb̄≲0.5 (with b̄ being the mean particle diameter) both above and below the glass transition without any fitting parameters. Our data are consistent with recently predicted (both theoretically and by simulations) long-range correlations of the shear stress quenched in heterogeneous glassy structures.

Fitting the Relaxation Modulus of Viscoelastic Materials Based on the IoT-Supported Mathematics Algorithm

In this paper, the theory of viscoelastic material relaxation modulus testing, testing method, and material relaxation modulus parameter solution method is studied. Based on the IoT sensor test devices and the Hertzian mathematics theory, the relationship between the compression amount, pressure, and relaxation modulus of a rigid spherical indenter pressed into a flat viscoelastic material is studied. In combination with the Boltzmann superposition principle, the relaxation modulus test method and theory for viscoelastic materials are proposed. A good fitting curve was obtained to solve the relaxation modulus parameters of various materials under the three-element Maxwell model. The experimental setup and the results of the parameter fitting were analyzed to verify the feasibility and accuracy of the results.

Characterization of Strength, Modulus, and Fatigue Damage Properties of Cement Stabilized Macadam Based on the Double Modulus Theory

Characterization of Strength, Modulus, and Fatigue Damage Properties of Cement Stabilized Macadam Based on the Double Modulus Theory

Experimental studies on glubam columns under axial compression

Glubam is a new type of structural material or bamboo based glulam. Understanding the compressive performance of glubam columns under axial compression is crucial for its application in construction field. Experimental and analytical investigations were conducted to study the mechanical performance of 45 columns fabricated by two types of glubam with different slenderness ratios. The failure modes in terms of various slenderness ratios were reported and evaluated: strength failure was the main failure mode of the short columns while buckling was typically observed for long and slender columns. For the intermediately slender columns, buckling was also accompanied by the material damage. The experimental results were compared with the column design curves specified in Chinese, American and European timber structural design codes for glued laminated timber, showing all the codes can provide adequately conservative prediction to the test results. Euler's equation, Newlin-Gahagan approach, Yoshihara et al.’s approach and tangent modulus theory were adopted to analyze the critical buckling of the columns under both elastic and inelastic conditions. A model is proposed to explain the buckling of intermediate glubam columns with partial splitting.

Bearing Capacity of Recycled Self-Compacting Concrete-Filled Circular Steel Tubular Long Columns Subjected to Axial Load

To investigate the ultimate bearing capacity and deformation of the recycled self-compacting concrete-filled circular steel tubular (RSCCFCST) long columns subjected to axial load, nine specimens with different recycled self-compacting concrete (RSCC) strength grades and slenderness ratios are tested. The experimental results indicate that the lateral deflection dominates the buckling failure of the specimens. The ultimate bearing capacity of the specimens is enhanced gradually as the RSCC strength grade increases but decreases as the slenderness ratio rises. The load-strain curves are linear and basically coincide at the elastic stage. The decrease in the slenderness ratio or increase in the RSCC strength grade contributes to the improvement of the stiffness and ultimate circumferential and axial strains of the columns gradually. Based on the combined tangent modulus theory and bearing capacity of the RSCCFCST short columns, two estimation models are presented to predict the ultimate bearing capacity of the RSCCFCST long columns. Additionally, comparisons between the calculation results of the ultimate strength demonstrate that the prediction models established in this study are more accurate than the other specifications mentioned.

Analytical model predicting the concrete tensile stress development in the restrained shrinkage ring test

Concrete structures may experience unexpected cracking at an early age. Early age cracking can be induced by restrained deformations where tensile stress generated in concrete exceeds its tensile strength. The restrained concrete ring test is often used to evaluate the ability of concrete to resist early age cracking induced by shrinkage. This paper proposed an analytical model of the restrained ring test by capturing the effect of both restrained shrinkage and tensile creep based on the age-adjusted effective modulus theory. The analytical model allows for accurately predicting the tensile stress of the restrained concrete ring based on the experimental measurements of the time-dependent development of elastic modulus, total free shrinkage, and tensile creep of concrete. A numerical finite element simulation was also successfully carried out to validate the new analytical model. Importantly, the model was validated considering a total of 21 concretes consisting of 6 strength grades ranging from 25 MPa to 100 MPa. For each grade, one fly ash blend (30%), two GGBFS blends (40% and 60%) and a reference mix without supplementary cementitious materials were tested.