International Journal of Structural Stability and Dynamics

Hydroxyapatite (HAP) is a naturally occurring calcium phosphate mineral that resembles human hard tissue in structure and composition. Its unique structure makes it suitable for a variety of applications such as biomedical implants, pollution control, nuclear waste management. The hexagonal structure of HAP endows it with five independent elastic constants, and a comprehensive understanding of their role and properties is essential for large scale adoption of HAP in various applications. However, the limited experimental and computational estimates currently available exhibit a wide scatter and occasional inconsistencies, and little effort has been made to quantify the influence of operating temperature on HAP elastic response. In this paper, we calculate the five elastic constants of hexagonal HAP first from Density Functional Theory (DFT)-based stress–strain relations derived using ultrasoft pseudopotential with Perdew–Burke–Ernzerho (PBE) exchange-correlation functional under generalized gradient approximation (GGA) on the 44 atom single unit cell, and then with molecular dynamics (MD)-based stress–strain relations derived from $4\times 4\times 6$ unit cells using three distinct families of force fields. These force fields are differentiated by how they model the non-bonded interactions: Lennard–Jones, Born–Mayer–Huggins and Buckingham types. We conduct the MD studies in the temperature range of 10–500 K. We find DFT to slightly overestimate the unit cell volume (a known consequence of using GGA) compared to X-ray powder diffraction-based experimental values reported in the literature. The predicted elastic constants satisfy Born’s criterion for mechanical stability. All potential models agree with DFT that HAP exhibits higher stiffness along $c$-axis. Lattice parameters are found to increase with temperature, while the elastic constants decrease. Their rate of change, however, differs based on the force field. Among the three, the force field based on Buckingham potential appears to perform the best and agrees qualitatively with DFT and experimental results.

A numerical model for hydride embrittlement in Zirconium alloy (Zr–2.5Nb) is developed utilizing the extended finite element method (XFEM). Hydride embrittlement reduces the ductility and failure time of a metal/alloy. During hydride embrittlement, stress-directed hydrogen diffusion, metal-hydride phase transformation, mechanical deformation, and hydride precipitation occur simultaneously. The present model incorporates all these processes and is able to predict the hydrogen concentration and the hydride fraction distribution under any externally applied stress field. In this work, both the steady and transient hydrogen diffusion cases are evaluated. Further, the XFEM is utilized to develop a model of hydride embrittlement in the presence of a crack. The first step of the hydride embrittlement process is the diffusion of hydrogen. According to Fick’s law of diffusion, hydrogen diffusion is directly dependent on hydrostatic stresses and hydrogen concentration gradient under external stresses. The next step is the hydride precipitation in hydride embrittlement, where the expansion of material takes place that changes the hydrostatic stress field. Thus, studying the effect of precipitation of hydride on hydrostatic stresses is essential. Moreover, the process of hydride embrittlement is highly influenced by residual stresses in the structure. Hence, the effect of residual stress present in the zirconium alloy pressure tube (PT) is also evaluated. The results indicate that the residual tensile stresses contribute to the growth of hydride, which will reduce the material failure time.

Fiber metal laminates are the advanced composite materials, in which the metal and FRP layers are stacked alternatively to achieve the desired properties. The presence of FRP layers enhances the fatigue, fracture properties and weight savings. Durability and plasticity of the metal plays a significant role in the design of fiber metal laminates. This study evaluates the role of middle metal layer (core) thickness on the behavior of Carall fiber metal laminates under low velocity impact loading. Two types of Carall 3/2 with middle layer of varying thickness are considered. The metal volume fraction is same for both the laminates. Finite element simulations have been carried out for the laminates considered according to the standard ASTM D7136. Johnson–cook plasticity and damage model and two-dimensional Hashin damage criteria have been used to model the aluminum and CFRP respectively. From the study, it was found that the placement of thicker layer at the middle position in the Fiber metal laminate enhances the impact resistance of Carall. The energy absorption studies also indicate that the presence of thicker layer at the middle position increases the energy absorption capability.

The dynamics of three-dimensional (3D) slender systems such as statues, obelisks, monuments, museums, and household objects are highly nonlinear. In this study, a numerical model for rigid blocks in 3D, referred to as the physical model (PM), is developed to explore and view the motion of the slender blocks to base excitations. The model can represent the dynamics of both symmetric and mass-eccentric 3D blocks for unidirectional and bidirectional excitations. Keeping the kinematics of the system in view, the PM is developed as an assemblage of different subsystems in the Simscape Multibody Library. The rigid block supported by four tiny spheres at the corners is resting on a rigid table. Physical interaction between the table and the rigid body is simulated by introducing a virtual plane characterized by a spring and a damper that follows the visco-elastic Kelvin model. The values of the depth of the virtual plane, parameters of the Kelvin model, and the dimension of the tiny spheres are suitably chosen for such interaction. Adequately large values for kinetic and static friction are used in the virtual plane to prevent the body from sliding during its rocking motion. The motion of the table is described by choosing the inertial reference frame with origin at a fixed point and another parallel frame fixed with the tabletop. The response of the rigid body is described by the asymmetric Euler sequence. A third set of the frame, i.e. the body-fixed reference with the origin at the centre of mass of the corresponding symmetric body is introduced by a Bushing joint. A calculated amount of mass-eccentricity is generated by adding very small square blocks to the side-faces of the 3D symmetric block. The response of mass eccentric systems to trigonometric base excitations applied in-plane and out-of-plane of the eccentricity is computed using the PM, and a comparison of the same to the results derived analytically confirms the adequacy of the model. In the sequel, representative case studies are presented and interpreted to uncover the complex dynamics of the mass eccentric rocking systems. The PM can also serve as the basis of analyzing and viewing the motion of blocks with arbitrary geometry.

In this study, finite element (FE) analysis of underground structure is carried out, which is subjected to the internal blast loading and the structure is surrounded with soil media. Three different methods to analyze the effect of blast loading on structure, i.e. ConWep, smooth particle hydrodynamics (SPH), and couple Eulerian-Lagrangian (CEL) are used for the simulation of blast loading using ABAQUS/Explicit^®. Concrete damage plasticity (CDP), Mohr–Coulomb, Johnson–Cook (JC) plasticity model, Jones–Wilkins–Lee (JWL) equation of state and ideal gas are utilized for defining behavior of concrete, soil, steel, explosive and air, respectively. FE analysis is performed to compare the behavior of structure under different blast modelling methods. The effect of different explosive weights is considered to see the impact of the blast load on the structure. For parametric analysis, three explosive weights, 3kg, 5kg, and 10kg of TNT (trinitro toluene), and three concrete grades, M30, M35, and M40 are considered to see the stability of the structure. The effect of varied explosive weights and varied concrete grades is compared in terms of stress, pressure, and displacement at critical locations of the structure. The outcome of this shows that the change in explosive weight and concrete grade considerably affects the stability of the structure. As the explosive weight increases, damage to the structure increases, and with the increase in the concrete grade, the blast load resistance capacity of the structure increases. It is observed that buried part of the structure is more resistant to blast load compared to the structure visible above ground.

Utilizing the inherent capacity of energy dissipation, liquid tanks are nowadays being employed as tuned liquid dampers (TLDs) for controlling unwanted structural vibration. The effective liquid mass that participates in convective mode controls the tank’s overall dynamic response. The stagnant liquid mass, which does not participate in sloshing at the bottom corners of the conventional rectangular and cylindrical TLDs, increases the total liquid mass and has no role in the vibration control of the supporting structure. The hydrodynamic behavior of the sloped wall tank under resonance conditions is demonstrated under harmonic excitation over a range of frequencies close to the fundamental sloshing frequency of the tank. However, the present study focuses on the effect of the modified geometrical configuration due to the bottom-mounted object on the slosh displacement and hydrodynamic base shear. A 2D finite element model developed employing the potential flow theory is used for the present numerical investigation. Compared to a conventional flat-bottom tank, the sloped wall tank exhibits a considerable increase in hydrodynamic base shear near resonance excitation. The dynamic impulsive and the convective response components of the base shear force have been successfully estimated. Also, the effectiveness of the proposed sloped wall tank with bottom-mounted internal object is examined under EL-Centro EW earthquake motion.

This paper proposes a novel intensity measure (IM) based on the geometric mean of acceleration response spectral ordinates to assess the probabilistic performance of structures subjected to seismic loading. Instead of relying solely on the fundamental period, the proposed IM is evaluated across a fixed period range for all structural systems, which allows consideration of higher mode effects and period changes due to nonlinearity. The proposed seismic IM is evaluated using two established indices sufficiency and efficiency. Sufficiency quantifies the independence of an engineering demand parameter at a specific intensity level with ground motion characteristics such as seismic magnitude $(M)$ and distance from site to fault plane $(R)$. It is calculated by linear regression analysis, or using gradient-based relative sufficiency measures. On the other hand, efficiency is measured as dispersion across ground motions at a given intensity level for any physical response quantity. It helps to reduce computational demand for failure probability assessment by considering a smaller number of records compared to an inefficient IM for similar confidence levels. The effectiveness of the proposed IM along with 10 other IMs is demonstrated on single degree of freedom systems with various fundamental periods by performing nonlinear time history analysis using a far-field ground motion record set. The study is also extended to five degree of freedom lumped mass stick models, 2D models (4-, 8-, and 12-story archetype steel frames), and 3D reinforced concrete shear wall building model. The results indicate that the proposed IM limits dispersion to within 10% for long-time period structures, and demonstrates improved sufficiency across different structural systems. For example, gradient of the proposed IM with respect to magnitude $M$ and site-to-source distance $R$ for a 12-story steel frame is reduced by 42.9% and 94%, respectively, compared to spectral acceleration at fundamental time period. Potential application of this research lies in efficiently conducting seismic reliability assessment and design for structural systems.

Composite nanobeams with carbon nanotube (CNT) reinforcement are crucial components in various applications due to their unique mechanical and thermal properties. The present work investigates the frequency–aspect ratio relationship in composite nanobeams with CNT reinforcement, particularly under varying temperatures, magnetic field strengths, and Winkler elastic stiffnesses. The non-dimensional frequency variation with aspect ratio, influenced by temperature differences, reveals distinct behavior patterns. The introduction of a magnetic field alters frequency characteristics, with uniform distribution (UD) nanobeams displaying higher frequencies. The impact of Winkler elastic stiffness, temperature differences, and magnetic field strengths on frequency elucidates differing responses between UD, $X$-type distribution (XD), and $V$-type distribution (VD) nanobeams. Nonlocal strain gradient theory proves essential in capturing dynamic characteristics influenced by CNT distribution. These findings shed light on the intricate dynamics of composite nanobeams, providing valuable insights for the design of future nano-devices employing CNT-reinforced composite beams as fundamental elements.

Early fault detection and diagnosis of rolling element bearing is of paramount importance in wind turbines as it contributes to around 70% of gearbox and 21%–70% of generator failure. When a rolling element bearing strikes a local fault in the inner or outer race, a shock (high frequency) is introduced, and repetitive impact occurs due to continuous rotation. Extracting the fault-sensitive repetitive impact frequency component from the measured signal containing multiple frequencies (discrete gear and shaft frequency, bearing fault frequency and high-frequency noise) is challenging. This paper presents two vibration techniques based on enhanced envelope analysis and blind deconvolution technique for bearing fault identification. The improved envelope analysis diagnosis bearing faults using the three-step process of removing gear and shaft frequency components by auto-regression model, followed by spectral kurtosis to extract fault-sensitive features and envelope analysis to identify bearing faults.

On the contrary, the enhanced blind deconvolution extracts the fault-sensitive component by finding the best inverse finite impulse response filter from the measured vibration signal by adaptively demodulating resonance bands due to repetitive impact and reducing the periodic noise component in a single step. The application of the two bearing fault diagnosis techniques and their comparative study has been demonstrated through numerical simulations and two industrial testrig bearing benchmark datasets. Investigations concluded that both methods extract the transient impulse features due to bearing fault; however, the enhanced blind deconvolution technique outperforms the envelope analysis in the case of measured vibration signal with outliers.

Numerical investigations are conducted to examine the penetration depth of ellipsoid-shaped projectiles into semi-infinite aluminum targets under conditions of hypervelocity impact. These results are then compared against empirical equations developed by various researchers for spherical projectiles. The semi-infinite aluminum target, sized at $150\times 150\times 50$mm, is composed of Al7075-T651. The projectiles are fashioned from Al-7075-T651, steel, and boron carbide. The projectile’s shape factor was determined using the L/d ratio, specifically for the symmetrical ellipsoidal shape. Employing Ansys Autodyn, a 3-dimensional finite element model (FEM) is created and calibrated using existing experimental findings from the literature. The validation utilized the Johnson–Cook (JC) and Johnson–Holmquist (JH-2) material models for both the targets and projectiles. These validated models are subsequently employed to analyze how the ellipsoid projectile’s shape and density influenced their interaction with the semi-infinite targets. Furthermore, the investigation also encompassed an analysis of the resulting crater shapes generated by the hypervelocity impact of both metallic and nonmetallic projectiles. It is observed that for a definite SF, max${}^m$ depth of penetration is observed due to steel project as compared to boron carbide and aluminum projectile. Both the diameter of the crater and the height of the bulge ($H_c)$ are directly proportional to the impact velocity and density of projectiles, and inversely proportional to SF. However, for a particular material and impact velocity of the projectile, in the case of $H_c$, there are no clear-cut observations displayed it seems like a mixed variation.

Numerical simulations were conducted to validate computational and constitutive models for steel materials through dynamic material tests involving both tension and compression. These simulations involved the numerical modeling of the split Hopkinson pressure bar (SHPB) apparatus, with the appropriate loading applied directly in compression and indirectly in tension. To induce a tensile wave within the specimen, a shoulder, such as a coupler or collar, was interposed between the bars. The simulations were carried out using the LS-DYNA finite element code. In these numerical simulations of the SHPB tests, the MAT-15 Johnson–Cook material model was applied to represent mild steel. The resulting stress–strain relationships obtained under both compression and tension conditions were subsequently compared to corresponding experimental data. The primary objectives of these simulations were to determine the optimal placement of strain gauges on both the input and output bars of the tensile SHPB setup. Additionally, the simulations aimed to assess the influence of the gauge length-to-diameter ratio on the behavior of the mild steel specimen subjected to dynamic tension and compression. The results showed that the pulse produced due to the mechanical mismatch of the element at boundaries can be avoided using the length of the input bar smaller than the output bar. Further, the location of the strain gauge in the case of the output bar should be toward the output bar-shoulder interface, while in the case of the input bar, it should be considered at the center of the span of the bar.

Human heart is elegantly articulated to mechanically contract in response to electrical excitation. Cardiac electrical activity may be described as a multiscale process from sub-cellular to cellular to tissue level. Ion movement at the cellular level through ion channels results in an action potential that propagates as an electrical wave in tissue. A first-principles-based mathematical description of the cellular-level dynamics of cardiac electrophysiological behavior provides a better understanding of the functioning of the heart.

The mathematical models describing cellular dynamics often involve a coupled system of ordinary differential equations (ODEs) with variables including transmembrane voltage, ion concentrations and ion channel gating variables, whose evolution describes activation/inactivation of ion channels. In this study we discuss a mathematical model of the human ventricular myocyte (O’Hara–Rudy model), defined as a system of 41 ODEs, with variables involving membrane voltage, 29 gating variables describing activation of Na${}^{+}$, K${}^{+}$, Ca${}^{2+}$ channels, 11 variables describing ion concentrations and Ca${}^{2+}$ related flux. Runge–Kutta method with variable order and variable time step was adopted to solve the system numerically. We discuss the action potential (AP) profile of a healthy human ventricular myocyte and corresponding dominant ionic currents. We present a phase plot that describes the change in voltage and its rate as the system evolves over time. The phase plot seems to provide more details of the underlying events than the AP curve.

This study presents a simplified semi-analytical model to analyze the dynamic behavior of a plate with shark skin biomimetic surface modifications. The base plate is considered to be thin isotropic homogeneous and modeled using a Kirchhoff–Love plate theory, whereas the dermal denticles are modeled as a distributed array of point mass and replicated using a Dirac delta function. A semi-analytical formulation, which takes into account closed-form beam mode shapes, with the Galerkin technique to minimize errors is utilized to study the free and forced vibration response of modified plates. Harmonic analysis is carried out to understand the dynamic behavior of the modified plate both quantitatively as well as qualitatively. A parametric study varying the array spacing and the boundary conditions is carried out to understand the effect of surface modification on power radiation characteristics. It appears that adding dermal denticles reduces the peak velocity amplitude and peak radiated power at all resonance frequencies. A separate study by varying the base plate material reveals that a higher reduction in the dynamic response and the radiated power can be achieved by increasing the mass ratio. Hence, surface modification using such a shark skin layer may prove beneficial to reduce acoustic radiation and dynamic response and to optimize the design.

The carbon-fiber laminated composites are widely used in various industrial sectors due to their magnificent mechanical and engineering properties. While designing the structures of strategic importance, the impact perforation study and prediction of impact performance of such composites are of utmost importance. This work basically concentrates on two major areas of impact perforation study, determining impact perforation characteristics and understanding the perforation process. The objective has been achieved through experimental as well as numerical investigations. Microstructural analysis have also been carried out to understand different energy-absorbing mechanisms. The pneumatic gun setup is utilized to fire the projectile. In addition, square-shaped carbon fiber laminates and projectiles are modeled in ABAQUS/Explicit. The carbon fiber laminates of different thicknesses and layup sequences are impacted with three different types of projectiles. The cross ply, angle ply and quasi-isotropic layup sequences are considered in this study. The conical, blunt and ogive nose with caliber radius head (CRH) 1.5 projectiles are modeled as analytical rigid. Hashin criteria are adopted to replicate the behavior of carbon fiber laminates. The experimental and numerical calculations are compared and are found to be in good agreement. The different perforation features are calculated and the influence of ply orientations, thickness, projectile shape and impact velocities on the performance of targets against impact are discussed. An efficient and better laminate configuration under various ballistic conditions has been sought.

Concrete is the most widely used construction material for strategic structures which are subjected to high rate of loading (impact and blast loading). Hence, the study of the concrete material becomes essential day by day for the structural engineers for the analysis and design of the concrete structures for safety and security purposes. This paper focuses on investigating the dynamic compressive response of the standard concrete (M35) and high-strength concrete (M60) under impact loading by using the newly developed split Hopkinson pressure bar setup (SHPB) apparatus. First, the calibration of SHPB performed at a 4.90ms${}^{-1}$ impact velocity generates almost similar incident and transmission trapezoidal profile waves with minor reflection showing accuracy. Second, the dynamic compression tests were performed on the standard concrete (SC) and high-strength concrete (HSC) specimens of 29.5mm in diameter and $\sim 30$mm in length with an aspect ratio of about 1($L/D\approx 1$) and a comparative study of strain rate effect and quasi-static compressive strength on the material properties has been investigated. The dynamic compression behavior of SC and HSC thus studied under varying strain rates has been presented in terms of the compressive strength, dynamic increase factor, stress–strain relationship, material failure, and fragmentation. Compressive strength increments of 114% and 41% were observed in SC and HSC as the loading condition changed from quasi-static to dynamic. In addition, the HSC described the $\sim 23$% and $\sim 18$% higher compressive strength corresponding to 290s${}^{-1}$ and 131s${}^{-1}$ strain rate as compared to SC describing that the HSC is more sensitive to the strain rate. The dynamic mechanical properties increased with an increase in the strain rate, and the DIFs were found to vary in the range of 1.42–2.14 and 1.07–1.41 for SC and HSC, respectively. The critical strain and ultimate strain were also found to be sensitive to strain rate and increased with increase in strain rate for both grades of concrete. Moreover, strain rates exert a noteworthy influence on fragmentation, leading to an increase in the percentage weight of fine fragments and a decrease in the percentage weight of large fragments as the strain rate increases. Additionally, there is an overall increase in the quantity of fragments for both SC and HSC specimens under these conditions. The flaky, elongated, angular, and irregular shape fragments were observed but their quantity and size varied significantly with strain rate.

In this work, the thickness-dependent size effect on nonlinear free vibration response of a Porous Functionally Graded (PFG) nanobeam in a hygrothermal environment is examined via nonlocal strain gradient theory (NSGT). Through the depth of the beam, hygro-thermal loadings are uniformly distributed. The mechanical properties of the beam are assumed to vary continuously in the thickness direction according to the power law expression. The equations of motion are derived using Hamilton’s principle with consideration of von-Kármán nonlinearity. The nanobeam vibration responses are obtained with the aid of the Galerkin technique and the Hamiltonian approach. A vital point of this work is to explore the effects of power law index, slenderness ratio, porosity volume fraction, and hygrothermal changes on the vibration behavior of PFG nanobeams. The results indicate how the thickness effect and porosity volume fraction significantly change the size-dependent vibration response of the FG nanobeam under hygrothermal conditions. The paper findings can be applied to improve the mechanical performance of PFG nanobeams.

This research explores the ability of 60mm thick reinforced concrete (RC) plates to resist impacts from ogive-nosed hard steel projectiles. The projectiles used in the present study have a diameter of 19mm, a length of 200mm, and a mass of 0.4kg impacted on the RC plates with incident velocities ranging from 92m/s to 161m/s. Numerical simulations were conducted using ABAQUS/Explicit finite element software to validate the experimental results. The Holmquist–Johnson–Cook (HJC) material model was employed to simulate the constitutive behavior of concrete, while the Johnson–Cook (JC) material model was used to simulate the material response of reinforcing steel bars. The residual velocities obtained from the simulations closely matched the actual experimental results, showing a polynomial correlation with the incidence velocities of the projectiles. Moreover, the experimentally and numerically determined ballistic limit for the 60mm thick RC plate was found to be 108m/s and 109.5m/s, respectively. In contrast, the ballistic limit calculated using empirical mathematical expressions was 107.4m/s. This alignment between predicted, calculated, and actual ballistic limits underscores the reliability and accuracy of both numerical and empirical approaches.

Rotating machinery with flexible shafts finds application across a broad spectrum, ranging from everyday household appliances to heavy-duty industrial setups. These machines harness substantial rotational energy, which in turn induces vibrations. In step with industrial progress, modern devices are becoming smart, intelligent, and compact, with the help of microscopic devices known as Micro-Electro-Mechanical Systems (MEMS), incorporating electrical and moving mechanical parts. One noteworthy category within MEMS is Power MEMS. Operating at speeds exceeding a million revolutions per minute, these systems are employed in compact energy supply solutions for small-scale electronics, diminutive ground robots and unmanned airborne vehicles, all of which demand efficient power sources. This paper addresses the rotor dynamics associated with micro-rotating systems. The intricate dynamics and nonlinear issues witnessed in macro-scale systems are equally relevant to these tiny systems. This is why recognizing the traits and behavior of these small-scale systems and analyzing their dynamic actions within the operational context becomes a fundamental topic that influences design, control, maintenance, and safety considerations. Incorporating low friction bearings and rotor dynamics into mathematical formulation yields results that are nearly perfect models. Therefore, this study aims to conduct a comprehensive nonlinear analysis of the micro-rotor, considering the nonlinearity arising from the substantial deformation of the shaft. The influence of small-scale effects, which hold significance at the micron scale, is addressed utilizing modified couple stress theory. The study employs the Euler–Bernoulli beam theory while accounting for the axial stretching effect under conditions of significant deformation. The dynamics of the rotor, including essential parameters like spin speed, disk placement, and size dependency, are thoroughly investigated through a comprehensive parametric study presented in this work.

Metal foams are highly useful in industries because of their lightweight, energy and vibration absorption properties. This study investigated the propagation of torsional waves in an elastic layer over a fluid-saturated fractured poroelastic half-space with a metal foam coated layer. It is assumed that the interfaces are in sliding contact with two different sliding parameters. The coated layer is closed-cell aluminium foam. We use the separation variable technique and the Bessel function to solve the equation of motion in different layers. The displacement components are written in terms of the second kind Whittaker functions. Using an asymptotic formulation of the Whittaker function and appropriate boundary conditions, the dispersion equation is derived in terms of the determinant. The control of the vibration due to the metal foam-coated layer is one of the important goals of this study. Also, numerical and graphical analyses have been done with the help of Mathematica software to see the effect of different parameters on torsional wave propagation. It is found that the presence of coated metal foam layer decreases the phase velocity of the torsional wave propagation. The work may be helpful in the seismology, automobile, and aerospace industries.

In the impact application, the impactor doesn’t have to be perpendicular to the structure. This study mainly focuses on numerical low velocity oblique impact analysis performed on silicon aluminum composite foam using ABAQUS^®. In this paper, the shear failure model is used to estimate damages in silicon aluminum composite foam model for different angles of the impactor. Here, dissipation energies, impact load histories and load displacement curves for damages under different angles of impactor have been characterized. From the study, it is found that the contact force intensity and penetration time decrease as the angle of the impactor increases. In the study of energy time histories, it is seen that energy increases and penetration time decreases as the angle of the impactor increases. From the contact force study, it is found that the contact force decreases, and contact time increases as the angle of the impactor decreases. The studies for displacement show that oblique impactor displacement increases as the angle of the impactor increases.