Uniaxial Tension Research Articles

Understanding plasticity in multiphase quenching & partitioning steels: Insights from crystal plasticity with stress state-dependent martensitic transformation

This study develops a novel crystal plasticity (CP) model incorporating deformation-induced martensitic transformation (DIMT) and transformation-induced plasticity (TRIP) effect to predict the complex interplay between microstructural evolution and mechanical behavior in a third-generation advanced high-strength steel QP980. This model introduces phenomenological theory of martensite crystallography (PTMC) based TRIP theory and DIMT kinetics grounded on nucleation-controlled phenomenon. Notably, the DIMT model is improved by utilizing a geometric approach for calculating shear band intersections. A virtual multiphase representative volume element (RVE) based on the Voronoi tessellation is generated for the QP980 steel, which comprises ferrite, martensite, and retained austenite (RA). The study highlights how phase transformation affects mechanical properties, notably the strengthening from transformed martensite and the mechanical alterations in RA due to the TRIP effect. The DIMT kinetics dependent on stress states such as uniaxial tension (UT), uniaxial compression (UC), plane strain tension (PST), and equi-biaxial tension (EBT) are analyzed using the developed model. The role of microstructural surroundings on martensitic transformation is also examined. Furthermore, analysis under biaxial loading angles using the model reveals an asymmetric yield surface, with more pronounced changes in yield stress in the tensile region due to accelerated transformation behaviors, as opposed to the more gradual transformations in the compressive region. This study provides valuable insights into the deformation mechanisms of the third-generation advanced high-strength steels including relationship between plastic anisotropy, transformation kinetics, and microstructural evolution.

Development of an enhanced damage law for typical steel fiber reinforced concrete based on uniaxial compression and tension tests

Understanding the stiffness of a concrete structure is crucial to analyze it, particularly for statically indeterminate structures. Stiffness degradation – commonly referred to as damage – occurs with the onset of cracking or large compressive strains. For most conventional and specialized types of concrete, damage studies and models for predicting damage development are available. However, more information is needed about the damage behavior for the most common steel fiber reinforced concrete in Europe with strength class C30/37 and modern end-anchored high-strength fibers in dosages of 20–40 kg/m3. Therefore, in this study, these common steel fiber concretes were subjected to multiple load cycles in (1) uniaxial compression tests on cylinders and (2) direct tensile tests on bone specimens to investigate their damage behavior. The resulting damage was then compared to known damage laws, but none of the models predicted accurate damage results. Finally, an existing damage law for plain concrete was modified as a function of the residual flexural tensile strength—the relevant parameter for describing the performance of the steel fiber reinforced concrete. Hereby, we were able to decisively improve the agreement between experimental results and the theoretical prognosis by utilizing our modified damage law.

Environmental Bond Degradation of Different Laminated Glass Panels.

Since buildings are designed to endure over time, it is crucial to comprehend how laminated glass (LG) windows, and consequently, the polymer interlayer materials, respond to weathering. This paper explores the impact of accelerated humidity on the mechanical properties of several polymer interlayer materials and LG sections. The study specifically focuses on three polymer interlayer materials of industrial interest: polyvinyl butyral (PVB), ethylene-vinyl acetate (EVA), and ionomer (SG). To examine the environmental effects, testing setups were devised to subject the polymeric materials and LG panels to specific conditions. Uniaxial tension coupons and LG disks were submerged in a water bath to simulate the environmental effect. A dedicated testing fixture was designed and manufactured for the LG disks. The results showed that the properties of EVA, including strength, maximum strain, and toughness, were not significantly affected by the environmental conditions. However, the properties of SG5000 were notably impacted, with a significant reduction in its bond strength due to water immersion.

A numerical study on tensile strength of low-density Kagome networks made of brittle fibers

In this paper, we present a numerical study on the tensile strength of low-density Kagome networks made of brittle fibers. First, an elastic beam model is employed to analytically predict the effective elastic properties and tensile strength, as well as the critical condition for buckling of the fibers in Kagome networks. A series of finite element analyses are then conducted to simulate the elastic deformation and failure of Kagome networks under tension. The numerical results based on unit-cell models reveal four possible failure modes of the Kagome networks subject to uniaxial tension, summarized in a phase diagram in terms of the relative density and the fiber strength. The pre-buckling failure mode is restricted to cases with relatively high density and low fiber strength. A low-density Kagome network is likely to fail by one of the post-buckling modes, with an effective tensile strength much lower than the prediction by the elastic beam model. For Kagome networks consisting of a large number of unit cells, the effect of boundary conditions on the tensile strength is examined. Under periodic boundary conditions, the effective tensile strength is nearly identical to that predicted by the unit-cell model, independent of the model size. Under a roller boundary condition, with damage initiation near the free edges followed by a diffusive damage progression, the effective tensile strength is lower than that under periodic boundary conditions for the cases of relatively low fiber strengths. Under a clamped boundary condition, the effective tensile strength is higher than that under periodic boundary conditions for the cases of relatively high fiber strengths, where fiber buckling is largely suppressed by the clamped boundaries. Finally, the effect of a crack-like defect on the effective tensile strength is studied for Kagome networks under the clamped boundary condition. With a small defect, the effective strength is nearly independent of the defect size. In contrast, with a relatively long defect, the effective strength decreases almost linearly with the length of the crack-like defect. The effective toughness for damage initiation and steady-state damage progression in the Kagome networks is discussed from an energetic perspective.

Predicting the band gap of kinked Mo6S6 nanowires based on band folding theory

Transition-metal chalcogenide (TMC) nanowires are an important building block for semiconductor components, which is conducive to the miniaturization and integration for nano-electronic devices and optoelectronic functional devices. Here, using density-functional theory (DFT) methods, we unveil intriguing electronic properties of kinked Mo6S6 nanowires (Mo6S6-NWs.) The results demonstrate that the shorter kinked Mo6S6 nanostructures exhibit distinct semiconductor behavior compared to the intrinsic Mo6S6-NWs, with the band gap being highly dependent on the length of the intrinsic Mo6S6-NWs between the kinks. Importantly, the band gap of kinked Mo6S6-NWs can be predicted by the band-folding theory, and the predicted value is extremely close to the actual calculated value. In addition, under uniaxial tension and compression strain, the band gap of long kinked Mo6S6-NWs changes within a narrow range, indicating their excellent electronic stability. This is mainly attributed to the small contribution of Mo/S atoms in the kinked part to valence band maximum (VBM) and conduction band minimum (CBM). Our work provides a useful theoretical insight for electronic properties of kinked Mo6S6-NWs, which open up the possibility of tailoring the properties of TMC nanowires, providing an ideal candidate material for the construction of flexible nanodevices.

Uniaxial tensile‐induced deformation of spherulite: combining experimental and simulation methods

AbstractA combination of experimental and simulation methods is adopted to study the relationship between micro‐stress and micro‐strain of a single spherulite upon uniaxial tensile deformation. To verify the simulation results and establish a suitable spherulite model, large‐sized isotactic polypropylene spherulite is first cultured with isothermal crystallization, whose structural deformation upon application of uniaxial tension is recorded using a polarizing optical microscope. A nanoindenter is used to measure the elastic modulus of the spherulite and amorphous region, preparing the property parameters for numerical simulation. Modeling and meshing of the single spherulite are conducted with the finite element software ABAQUS. The entire deformation of the spherulite is analyzed with fixed strain as the boundary condition, and the microscopic stress and strain distribution inside and outside of the spherulite is obtained. The higher micro‐stress region mainly locates at two poles in the equatorial direction, where might be the origin of craze. Generally, the simulation result is basically consistent with the experimental deformation process, which provides a new idea for the study of microscale structure and performance. © 2024 Society of Chemical Industry.

A testing theory for simultaneously determining asphalt mixture’s dynamic modulus in compression and tension by use of IDT test

The compressive and tensile moduli of asphalt mixtures are not equal. As a result, in order to obtain reasonable response calculation results, asphalt pavement mechanical analysis should first determine the compressive and tensile moduli of asphalt mixtures separately. Then, it should assign an appropriate modulus to the FEM element based on the stress state of the element. However, conventional uniaxial compression modulus testing protocol is typically unable to determine the actual asphalt pavement's coring specimen due to the limitation that general dynamic modulus testing protocol requires a larger size of specimen and conventional coring specimen from field usually cannot meet the requirement in regard to specimen size. In this case, the dynamic modulus of the asphalt mixture can only be ascertained using the IDT test method.Nevertheless, the current IDT test protocol is unable to distinguish between the compressive and tensile moduli of asphalt mixtures, and the testing results are usually different from those obtained by using the conventional uniaxial compression or tension method. This is because the current IDT test method for determining the dynamic modulus of asphalt mixtures generally treats asphalt mixtures as a kind of ideal elastic material and considers its compressive modulus is equal to its tensile modulus.Consequently, this paper presents a new theory, based on Ambartsumyan's bi-modulus constitutive relation theory, that can use the IDT test method to simultaneously determine the dynamic modulus of an asphalt mixture in both compression and tension. This theory assumes that the stress-strain relationship of asphalt mixture complies with the bi-modulus constitutive relation, and obtains the vertical deformation or horizontal deformation of the IDT specimen by solving a definite integral for the displacement of a small segment on the vertical or horizontal axis, which utilizes the results of the mathematical analysis of the stress distribution of the IDT specimen under distributed strip load. Then, the specimen's dynamic modulus in compression and tension can be obtained via back-calculating method, if the specimen's vertical and horizontal displacement are measured by a physical test in the lab. Obviously, this theory addresses the limitation of the conventional IDT method that cannot reflect the distinction of compressive modulus with tensile modulus, and can be better utilized to simultaneously determine compressive and tensile modulus of cored specimen from field. The verification test also demonstrates, the dynamic modulus determined by this theory are in line with the results of the conventional uniaxial test and is highly practicable.

Experimental research of the effect of manufacturing holes and defects on the mechanical characteristics of laminated polymer composite

The paper presents a developed methodology for experimental research of the mechanical characteristics of a laminated polymer composite, taking into account manufacturing holes and defects. The results of experimental determination of mechanical characteristics are presented, the influence of the filler material, the type of fabric fiber weave, holes and manufacturing defects on the mechanical characteristics of laminated carbon fiber reinforced plastic are analyzed. The test specimens were made from carbon fiber 200T, 200P, ACM C300X and binder “Inject SL(B)”. Static tests of specimens for uniaxial tension, compression and three-point bending were performed.

Fracture and multiple-cracking modelling of strain-hardening cementitious composites

Strain-hardening cementitious composites (SHCC), composed of short fibres embedded within brittle matrix, exhibit distinctive pre-peak strain-hardening characteristics and remarkable tensile ductility. The fracture and failure process of SHCC, involving both hardening and softening stages as a result of matrix multiple micro-cracking and strain localization, is highly complex and poses a significant challenge for numerical modelling. In the present paper, a novel numerical framework, characterized by the bi-layer superposed cohesive zone strategy, is developed for the numerical modelling of fracture and multiple cracking of SHCC, at both the material scale and structural scale. The developed model is based on diffused cohesive interface model, but with adaptions to consider fibre bridging mechanism. The crack interface is simulated by two cohesive elements sharing the same nodes: one for the matrix-cohesion effect and the other for the fibre-bridging effect. Cohesive constitutive relations of matrix cohesion and fibre bridging are carefully assigned. The proposed model is first validated on the material scale through a uniaxial tension test. With the aid of a random material field, multiple-cracking phenomenon and stress fluctuation are successfully predicted by the model. The model is then applied to the structural fracture modelling, where four case studies, including both pure mode I and mixed mode fracture, are performed. The size effect and boundary effect on the fracture behaviour are well captured by the numerical modelling. The model proposed in the current work has the potential to be extended to the multiple cracking modelling of other materials.

Mechanical response of 3D printed irregular sutural tessellations with Voronoi tile patterns under tension

The mechanical response of bio-inspired irregular sutural tessellations with Voronoi tile patterns are designed and fabricated via multi-material 3D printing. The effective mechanical properties of the designs were characterized via uni-axial tension mechanical experiments on the 3D printed specimens. Systematic nonlinear finite element simulations are conducted to explore the damage initiation and evolution of the designs. The influences of important design parameters, including tile length aspect ratio R, tile size irregularity Cstd, suture amplitude irregularity Astd, and stiffness ratio between the soft and hard phases, were evaluated. The effective stiffness, Poisson’s ratio, strength, toughness, and failure mechanisms are systematically quantified. The results demonstrate that an optimized level of suture irregularity exists for maximizing the modulus of toughness. The results provide a general design guideline for designing functionally graded two-phase tessellations with high mechanical performance.

Insights into molecular and bulk mechanical properties of glassy carbon through molecular dynamics simulations and mechanical tensile testing

With increasing interest in the use of glassy carbon (GC) for a broad range of application areas, the need for developing a fundamental understanding of its mechanical properties has come to the forefront. Furthermore, recent theoretical and modeling works that highlight the synthesis of GC via the pyrolysis of polymer precursors has explored the possibilities of a revisit to the investigation of their mechanical properties at a fundamental level. Although there are isolated reports on the experimental determination of its elastic modulus, insights into the stress-strain behavior of a GC material under tension and compression obtained through simulations, either at the molecular level or for the bulk materials, are missing. This study fills the gap at the molecular level and investigates the mechanical properties of GC using molecular dynamics (MD) simulations, which model the atomistic-level formation and breaking of bonds using bond-order-based reactive force field formulations. The molecular model considered in this simulation has a characteristic 3D cage-like structure of five-, six-, and seven-membered carbon rings and graphitic domains of a flat graphene-like structure. The GC molecular model was subjected to loading under varying strain rates (0.4, 0.6, 1.25, and 2.5 ns−1) and temperatures (300 K–800 K) in each of the three axes: x, y, and z. The simulations show that the GC nanostructure has distinct stress-strain curves under tension and compression. In tension, MD modeling predicted a mean elastic modulus of 5.71GPa for a single GC nanostructure with some dependency on the strain rate and temperature, whereas, in compression, the elastic modulus was also found to depend on the strain rate and temperature and was predicted to have a mean value of 35 GPa. To validate the simulation results and develop experimental insights into the bulk behavior, mechanical tests were conducted on dog-bone-shaped testing coupons that were subjected to uniaxial tension and loaded until failure. The GC test coupons demonstrated a bulk modulus of 17 ±2.69 GPa in tension, which compares well with those reported in the literature. However, comparing MD simulation outcomes to those of uniaxial mechanical testing reveals that the bulk modulus of GC in tension found experimentally is higher than the modulus of single GC nanostructures predicted by MD modeling, which inherently underestimates the bulk modulus. With regard to failure modes, the MD simulations predicted failure in tension accompanied by the breaking of carbon rings within the molecular structure. In contrast, the mechanical testing demonstrated that failure modes are dominated by brittle failure planes largely due to the amorphous structure of GC.

Effect of the end conditions on the response of glass textile reinforced cementitious composites under uniaxial tension

Effect of the end conditions on the response of glass textile reinforced cementitious composites under uniaxial tension

Dynamic recrystallization in a near β titanium alloy under different deformation modes – Transition and correlation

During the thermoforming of TC18 titanium alloy multi-cavity components, different deformation modes always exist and change, such as uniaxial compression (UC), shear-compression deformation (SCD), uniaxial tension (UT) and shear-tension deformation (STD). Dynamic recrystallization (DRX) of β grains occurs during the single-phase field deformation and has a great influence on the performance of components. In this study, the types and mechanisms of DRX in TC18 titanium alloy as well as transition and correlation under different deformation modes are investigated. It is found that discontinuous dynamic recrystallization (DDRX) initiates through grain boundary bulging at a low strain and dominates in different modes of deformation. Continuous dynamic recrystallization (CDRX) initiates at different strains depending on deformation modes, and the mechanisms vary, subgrain rotation within grains and lattice rotation near GBs under UC and STD, while only subgrain rotation under UT, in addition to these two mechanisms, grain fragmentation is also involved under SCD. Secondary dynamic recrystallization (SDRX) only occurs at a high strain under SCD and STD. Deformation modes lead to differences in orientation, slip and rotation of grains, further result in different dislocation density, distribution and accumulation, which contribute to the occurrence and transition of different types of DRX. Meanwhile deformation modes result in differences in the difficulty of GB migration and lattice rotation, ultimately in the initiation and degree of DDRX and CDRX. The shear stress in SCD and STD promotes the occurrence of CDRX. The present results can provide a guidance for obtaining good performance of the titanium alloy components.

Continuum Model of Peridynamics for Brittle Fracture Problems

The article investigates the nonlocal method of peridynamics, which makes it possible to simulate the brittle fracture of a solid body without using spatial derivatives. The basic motion equation of a particle with a given volume is written in integral form. A model combining the key features of continuum mechanics and of the nonlocal method is considered. To determine the forces of pair interaction, the dependence of the Cauchy stress tensor on the rate-of strain tensor was used. This formulation correctly describes the behavior of the material during damage and allows to get rid of the limitations inherent to simple bond-based model and ordinary state-based model. The maximum value of the tensile stress is used as a criterion of fracture, which describes the process of nucleation and evolution of damage. To test the implemented model, tasks in a two-dimensional formulation were used. Using the example of the elastic problem about uniaxial tension of a thin rod, the convergence of the numerical solution is shown with a decrease of interaction horizon and an increase of particles number. The second task demonstrates the capabilities of the implemented model to describe the nucleation and evolution of a crack under uniaxial load on a plate with an initial horizontal defect.

Experimentally calibrated viscoelastic phase-field fracture method of thermoplastic resins

In the past few years, there has been considerable emphasis on investigating fracture behavior in composite materials using the phase-field fracture (PFF) method. However, accurately characterizing the viscoelasticity of the matrix necessitates employing the viscoelastic PFF method, and there remains an ongoing debate regarding the precise determination of the viscous driving force introduced in this methodology. This study aims to propose a feasible calibration method for quantifying the viscous driving force. To achieve this goal, benchmark experiments utilizing Polyetheretherketone (PEEK), a typical thermoplastic resin, are carried out by designing uniaxial tension tests, three-point bending tests, as well as compression tests at various strain rates. Through employing the viscoelastic PFF method, we discuss the effect of strain rate and viscous driving force on mechanical response. Our findings reveal a non-linear relationship between the influence of viscous driving force and strain rate with an initial increase followed by a subsequent decrease. By combining simulation results with experimental data analysis, the viscous driving force value is determined. The results demonstrate that our proposed approach is reliable for quantifying the viscous driving force in the viscoelastic PFF method, laying a foundation for investigating the mechanical response of composite materials.

Correlating mechanical properties of Al/Al bimetal composite and its constituents using combined experiment and microstructure-based multiscale modeling approach

A combined experiment and multiscale modeling approach was presented to correlate the mechanical properties of a roll-bonded AA1050/AA3004 bimetal clad sheet and constituents. The mechanical responses of the 2-ply AA1050/AA3004 and constituents were measured under various loading conditions. For the measurements, each constituent was separated from the clad sheet using electrical discharge machining and uniaxial tensile tests. Continuum-scale yield functions such as isotropic von Mises and anisotropic/non-quadratic Yld2000-2d were developed for the two constituents and the bimetal clad sheet. A grain-scale crystal plasticity finite element (CPFE) simulations were also performed incorporated with newly developed representative volume element considering measured microstructural attributes. These CPFE predictions were used to identify the anisotropy coefficients for Yld2000-2d. Using the identified yield functions, finite element modeling was followed in which the mechanical properties of each constituent sheet were addressed separately. This is a new approach developed in the current work and it enables a fundamental correlation between multilayered material and its constituents. The mechanical properties of the bimetal clad sheet under the uniaxial tensions were predicted using those of the constituents and compared with calculations based on known rule of mixture (ROM) approach. The two approaches well reproduced stress–strain curves and r–value evolutions. The two FE modeling approaches were also applied to an independent test (i.e., the limiting dome height). The predictions were in good agreement with the experimental data. Finally, the mechanical properties of the bimetal clad sheet and constituents were correlated, and proper modeling scheme for multilayered materials is proposed.

Mechanical Properties of Additively Manufactured Polymeric Materials-PLA and PETG-For Biomechanical Applications.

The study presented herein concerns the mechanical properties of two common polymers for potential biomedical applications, PLA and PETG, processed through fused filament fabrication (FFF)-Material Extrusion (ME). For the uniaxial tension tests carried out, two printing orientations-XY (Horizontal, H) and YZ (Vertical, V)-were considered according to the general principles for part positioning, coordinates, and orientation typically used in additive manufacturing (AM). In addition, six specimens were tested for each printing orientation and material, providing insights into mechanical properties such as Tensile Strength, Young's Modulus, and Ultimate Strain, suggesting the materials' potential for biomedical applications. The experimental results were then compared with correspondent mechanical properties obtained from the literature for other polymers like ASA, PC, PP, ULTEM 9085, Copolyester, and Nylon. Thereafter, fatigue resistance curves (S-N curves) for PLA and PETG, printed along 45°, were determined at room temperature for a load ratio, R, of 0.2. Scanning electron microscope observations revealed fibre arrangements, compression/adhesion between layers, and fracture zones, shedding light on the failure mechanisms involved in the fatigue crack propagation of such materials and giving design reference values for future applications. In addition, fractographic analyses of the fatigue fracture surfaces were carried out, as well as X-ray Computed Tomography (XCT) and Thermogravimetric (TGA)/Differential Scanning Calorimetric (DSC) tests.

Ultrasonic Study of Longitudinal Critically Refracted and Bulk Waves of the Heat-Affected Zone of a Low-Carbon Steel Welded Joint under Fatigue

Currently, ultrasonic methods for assessing the fatigue lifetime of various structural materials are being actively developed. Many steel constructions are made by welding. The weld heat-affected zone is the weak point of the construction, as it is most susceptible to destruction. Therefore, it is actually important to search for acoustic parameters that uniquely characterize the structural damage accumulation in the heat-affected zone of a welded joint in order to predict failure. In this work, the specimens were made from the base metal and the welded joint’s heat-affected zone. The specimens were subjected to uniaxial tension–compression under a symmetrical cycle in the region of low-cycle fatigue with control of the strain amplitude. The propagation bulk velocities of longitudinal, shear waves and subsurface longitudinal critically refracted (LCR) waves during cyclic loading were studied. The acoustic birefringence of shear waves was calculated, and a similar parameter was proposed for longitudinal and LCR waves. The dependence of the elastic modulus ratio on the cycle ratio was obtained. It was shown that the acoustic parameters change most intensively in the heat-affected zone. According to the data of the C33/C55 ratio changes measured through the ultrasonic method, a formula for calculating the remaining fatigue life in the heat-affected zone was proposed.

Determining technological parameters for obtaining ta15 titanium alloy blanks with improved mechanical characteristics using the electron-beam 3D printing method

The object of this study is the process of electron beam 3D printing of articles made of TA15 titanium alloy powder. Peculiarities of the structure and properties formation of alloy blanks, obtained by this method have been described. Influence of process parameters (electron beam power and geometric scanning parameters) on the characteristics of the material were considered. Step of displacement of the beam trajectory changed from 0.1 to 0.25 mm with an interval of 0.05 mm. Specific energy of the electron beam varied from 20 to 70 J/mm3 for every trajectory displacement step. The macrostructure was examined visually while the microstructure was studied by optical microscopy. Mechanical properties were determined by uniaxial tension and impact bending tests. It was established that depending on the 3D printing parameters the macrostructure of most samples is dense but with unfavorable parameters non-fusions or shrinkage porosity defects may form. The microstructure of the dendritic type has an α´+β lamellar-acicular morphology, its dispersity and shape of α´–phase areas vary depending on the process parameters. A scanning step of 0.2 mm and a beam energy of 40 J/mm3 allows obtaining a dispersed microstructure in which there are no non-fusions and shrinkage micropores. The value of the Rm is 27 %, and the R0.2 is 24 % higher than that of the alloy obtained by the conventional technology of electron beam melting. The A5 is 3.2 times higher. However, impact toughness of the sample with dendrite unfavorable orientation to the direction of load applying may be lower compared to conventional technology. The results could be used for devising commercial technology of high strength titanium alloys parts produced by 3D printing

A variable-node element model and its application to damage analysis of RAC using the 2D base force element method

The existing methods find it difficult to resolve the inconsistency in the nodal displacements of nodes at the interface of dense and sparse element models. Therefore, this paper proposes a new variable-node element model using the base force element method (BFEM) and successfully applies it to study the mechanical properties of recycled aggregate concrete (RAC). First, the variable-node element model with an arbitrary change of node number in the mid-edges was established, and the explicit expressions of the 2 × 2 nodal compliance matrix and nodal displacements were given. Subsequently, the triangular and quadrilateral elements of single-sides and double-sides of hanging element models were developed based on the variable-node element model. In addition, a double-notched model of RAC with different aggregate types but the same aggregate distribution position was established, and numerical simulations of uniaxial tension were performed. The results show that the compliance matrix and nodal displacement are independent of the element characteristic without Gaussian integration. The variable-node hanging element model has high numerical accuracy and applicability, and the nodes between the sparse and dense meshes do not require any construction measures. The variable-node elements ensure the coordination of the nodal displacement at the interfaces. The aggregate shape has a significant effect on the damage mode, maximum principal strain, principal stress distribution, and stress concentration, while has a negligible effect on RAC tensile strength when the aggregate distribution is the same.