Indentation Force Research Articles

穴盘苗基质块仿真粘结参数标定与试验

To accurately simulate the interactions between the plug seedlings and the planter during the planting process and explore the damage mechanism of the plug seedling substrate block, the bonding parameters of plug seedlings substrate block were calibrated by the discrete element method. The physical puncture test showed that the average of maximum force of the cone indenter on substrate block measured by texture analyzer was 4.633 N. A Hertz-Mindlin with the bonding model was established for the substrate block in EDEM software. A virtual calibration experiment was designed with the puncture force of substrate block as the evaluation index. The two-level factorial test and the steepest climbing test were used to screen out the significant parameters and the optimal interval. Then, the Box-Behnken test and the optimization solution were used to obtain the optimal bonding parameter combination of the substrate block particles. Finally, the optimal parameter combination was simulated and verified. The relative error of the maximum puncture force between the simulated value and the measured value was 1.88 %, which indicated that the bonding parameters of the substrate block obtained by calibration were accurate and reliable.

Chemical short range order and deformation mechanism of a refractory high entropy alloy HfNbTaZr under nanoindentation: An atomistic study

Refractory high entropy alloys (RHEA) are promising potential used as structural materials owing to the remarkable mechanical properties, such as excellent thermal stability and strength. However, the dynamic nanoindentation response of the nanocrystalline RHEA at atomic scale is not fully revealed. Here, the mechanical behaviour of the as-cast and annealed nanocrystalline HfNbTaZr RHEA under nanoindentation is investigated for first time using a large scale molecular dynamics simulation, in the terms of indentation force, microstructural evolution, stress distribution, shear strain distribution, and surface topography. The results show the annealed nanocrystalline HfNbTaZr RHEA has obvious chemical short-range ordered structure (CSRO), including Ta enrichment and Hf–Nb segregation. The elastic modulus of the annealed RHEA is larger than that of random RHEA, agreeing with the previous experiment. CSRO improves the indentation force and work hardening, due to the inhibition of dislocation nucleation and motion. Interestingly, the hardening behavior is found in the unloading stage, which is rarely reported in traditional alloys. The crystal-to-amorphous phase transition takes place under the loading, and the inverse phase transformation occurs under the unloading. The increase rate of high Von Mises stress and hydrostatic stress region is lower than the change rate of the high strain region. Certainly, almost all atoms move to consume stored energy after unloading, leading to the decrease of stress and strain. The current study not only gives an insight into probing the mechanical behavior of the nanocrystalline RHEA, but also provides an avenue to design high performance RHEAs based on the heat treatment process.

Molecular dynamics models of tapping mode atomic force microscopy

Macro-mechanical simulation software cannot easily simulate the atomic resolution of the tapping mode atomic force microscope (TM-AFM), so the accuracy of the corresponding mechanical model is questioned. In this paper, a TM-AFM simulation model is established using classical molecular dynamics (MD). The model simulated the tapping of gold (Au) and aluminum (Al) by probes with various amplitudes. The simulation yielded the z-direction force curves, trajectory curves and indentation curves of the probe. The amplitude change and the phase shift of the probe at various amplitudes were calculated from the direct measurement results. A contact jump and detachment jump become evident and are significant to energy and force results. The recovery ability of Al after indenting is smaller than that of Au. The energy calculations can be fitted to a high goodness of fit, reaching 0.99 and better; hence, the amplitude and phase shift variations of the probe can be used to fit the stored and dissipated energies, the sample energies when the sample is tapped. In this way, the TM-AFM is able to calculate the mechanical properties of the sample, and thus characterize the sample.

Influence of reversible swelling and preload force on the failure behavior of a lithium-ion pouch cell tested under realistic boundary conditions

Safety of lithium-ion batteries plays an important role in the context of advancing electrification for vehicles. Pouch cells suffer from low structural strength and are often constrained within a battery module to guarantee mechanical integrity. The effect of constraints and SOC-dependent changes on the mechanical abuse behavior was not sufficiently investigated.A total number of 36 pouch cells were indented with a flat-end cylinder under different boundary conditions until mechanical failure and thermal runaway occurred. The pouch cells were constrained at 30 % SOC with a preload force of 0, 300 or 4000 N and charged to 0 %, 30 %, 60 % or 100 % SOC before indentation.The maximum indentation force, corresponding indentation, initial stiffness and failure behavior indicated a dependency on the preload force. The stiffness at greater indentation was similar for all boundary conditions indicating a pre-compression and flattening of unevenness. Internal stress within the separator resulted in earlier short circuit and mechanical failure for increasing preload force. The mechanical constraint led to increased gas pressure during thermal runaway.The results in this publication give rise to an additional consideration of preload force and boundary conditions imposed by a battery module in abuse testing and simulation approaches in the future.

Nanoindentation test of a DLC coated high-speed steel substrate using a two-dimensional axisymmetric finite element method

Diamond-Like Carbon is a thin coating that has high hardness, chemical inertia and low coefficient of friction characteristics that can improve the performance of cutting tools and mechanical components. To identify the characteristics of this film it is important to carry out mechanical tests, such as nanoindentation, which can provide important information in understanding and improving coating techniques and, when combined with the finite element method, leads to more detailed results of material behavior during testing. Considering this, the present work aimed to study and apply a nanoindentation test simulation of a Diamond-Like Carbon coated high-speed steel specimen. The results of the indenter penetration versus load were compared with experimental data seeking correlation of the model. A great proximity was observed between the experimental results and the results obtained in the simulation. When comparing the final indentation force, a proximity of 93.9 % and 95.5 % was found for the model with only one indentation and with partial indentations, respectively, thus validating the created model. The impact of modifying the indenter tip radius for the partial indentation method was also evaluated. The tip radius variation did not have a significant impact on the results of final indentation force and material hardness. The material hardness was also obtained in the simulation, which was equal to the experimental: 9.25 GPa.

Probing measurements of the Meyer hardness index of radial, tangential and cross section of various types of wood

The Meyer index is a power exponent appearing in Meyer hardness power law, which describes the dependence of the indenting force on the diameter of the indentation caused by the ball (or alternatively a cylinder). A perfectly plastic material should have a Meyer hardness index of 2 and a perfectly elastic material of 3. Previous research by the author and co-workers indicated that the Meyer index of beech wood is 2.5 and for metals aluminum 2.25, copper 2.0. This gave rise to the hypothesis that the hardness index of each wood is about 2.5. It was decided to verify this hypothesis for different types of wood, different anatomical cross-sectional directions. Research on such diversity must therefore be of a probing nature. Nevertheless, these probing measurements indicate that different types of wood in given sectional planes have similar Meyer indexes, but in each section it is a different value. The measured mean value in the radial section was 2.41, in the tangential section 2.28 and in the cross section 1.98. Thus, the initial hypothesis of the value 2.5 was confirmed only for the radial section, and for the tangential and cross sections, new values of 2.25 and 2.0 were hypothesized. Only the extreme values of the Meyer indexes (on the radial and cross section) turned out to be statistically significantly different.

Grain and twin boundaries dependent mechanical behavior of FeCoCrNiCu high-entropy alloy

The nanoindentation response of FeCoCrNiCu high-entropy alloy is revealed through molecular dynamics simulation. The influences of various grain sizes and twin lamellae thicknesses on the mechanical characteristics and plastic deformation are carefully studied. The result indicates that the indentation force and substrate hardness increase as the grain size increases from 55.16 Å to 114.46 Å and the twin layer thickness rises from 6.74 Å to 30.04 Å, which reveals the inverse Hall-Petch effect in the relationship between the material strength versus grain size and the twin lamellae thickness. The shear strain and residual stress are converged around the indentation regions and then enhanced deep into the substrate along the grain boundary and twin boundary. The presence of grain boundaries significantly affects the movement of the atoms, resulting in an asymmetric dispersion of the atomic displacement vector during the deformation. Moreover, the surface morphology reveals that the pile-up height generally increases with increasing the grain size and decreasing the twin lamellae spacing. The microstructural evolution suggests that the rotation of the grain related to grain boundary sliding and the migration of the grain boundary are the dominant mechanism in the deformation with grain size reduction. Moreover, the dislocation nucleation at the intersections of the twin and grain boundaries is also a remarkable characteristic, which significantly affects the plastic deformation of the material. The result also shows that the dislocation density tends to increase with increasing grain size and twin lamellae thickness. The figure shows the simulation model of FeCoCrNiCu high-entropy alloy (a), atomic displacement vectors of samples with different grain sizes (b), atomic configuration of the specimens with various twin lamellar thicknesses (c). ● The inverse Hall-Petch effect is recognized with the variation of grain size and twin lamellae thickness. ● The deformation mechanism of FeCoCrNiCu HEA is significantly dependent on the grain/twin boundaries. ● The rotation of grain related to grain boundary sliding and the grain boundary migration are dominant mechanism. ● The dislocation nucleation at the intersections of the twin and grain boundaries is also a remarkable characteristic.

Milk protein-based cryogel monoliths as novel encapsulants of probiotic bacteria. Part I: Microstructural, physicochemical, and mechanical characterisation

The implementation of cryogels as alternative xero-carriers for embedding labile bioactive compounds including probiotic living cells is becoming more popular. In the present work, milk protein-based cryogels were developed by freeze-drying of indirectly acidified protein gels (10% wt. in sodium caseinate or whey protein isolate blended at varying mass ratios i.e., 1:0, 3:1, 1:1, 1:3 and 0:1) comprising Lacticaseibacillus rhamnosus GG (LGG) living cells, trehalose (5% wt.), glucose (1% wt.) and glycerol (2.5% wt.). The physicochemical, microstructural, and mechanical characteristics of the cryogels conveying LGG were measured. The acid gel contraction during the fermentation notably influenced the macroscopic (volume contraction) and microscopic aspects (porosity, thickness, and uniformity of the wall material construct) of the cryogels. The amount of monolayer water content (11.5−14.0 g.100 g−1), and total surface area (403−488 m2 g−1) as well as the glass transition temperature (Tg = 33−46 °C), of the cryogels increased proportionally to the whey protein content. X-ray microtomography analysis revealed that the mixed protein cryogels were characterised by lower porosities than their individual protein exemplars. However, the uniformity and the structure conformation of the protein network constructs were altered according to the milk protein composition of the cryogels. All the cryogels exhibited a brittle and plastic behaviour when subjected to indentation forces, with the hardest and stiffest cryogels exerting the lowest water reconstituting capacity. The microstructural assessment of the wall material at nanoscale level evidenced a satisfactory intrenching of the LGG cells, which substantiates the feasibility of the cryogels as novel probiotic xero-scaffolds.

The Improvement of the Rheological Model of Leather

Fibrous capillary-porous materials, such as woven materials and leather, used in the light industry for clothing and footwear, differ sharply from metallic materials. These differences manifest themselves in a complex relationship between stress and strain, which depends on the strain rate and loading time. A method for determining the identified new rheological parameter of the inert resistance of a capillary-porous material (for example, leather) of accelerated deformation is presented in the article; it consists in determining the indentation force of a conical indenter at a constant speed and the coefficient that considers shear zones, and the angle formed by the boundaries of the material deformation zone and application of force value. An equation for an improved rheological model of leather is derived; it consists of the Kelvin model, the Bingham-Shvedov model, and the Khusanov model, expressed in terms of the rheological parameter in the form of a deformation inertness coefficient. The inclusion of the model of deformation inertness in the form of a coefficient into the rheological model of leather will allow the mathematical description of the rheological parameters of leather and the development of engineering methods for their calculation. The implementation of the developed method will allow obtaining numerical values of the rheological parameter of the inert resistance of the capillary-porous material under its accelerated deformation, namely, a new property of the capillary-porous material, which must be taken into account in various technological processing operations, for example, when treating moisture-saturated leather.

Effect of twist on indentation resistance

With mechanical metamaterials that display force-torque coupling receiving recent attention, we tested the effect of twist on indentation resistance. We hypothesised that the force required to indent a twisting lattice to a set depth would increase with the amount of transverse deformation caused by twist. Based on previous work, various chiral lattices were designed to twist by up to 1.3° per 1 % compression. These lattice designs were 3D-printed in Nylon-12, then tested, with the experiments replicated in finite element simulations. Indentation resistance increased with twist; the lattice with maximum twist required ∼70 % higher indentation force (when normalised to compressive stiffness) than the non-twisting (antichiral) one during spherical indentations to 1 % of sample thickness. Further, we calculate the expected effects of twist on indentation resistance by combining the established micropolar and Willis’ plane stress moduli with classical Hertzian indentation equations. We found reasonable agreement (within 10 %) between 2D calculation methods use here and previous 3D calculation methods. The indentation resistance calculated using the micropolar plane stress modulus followed the same trends as the simulations and experiments. The calculated indentation force was within 10 % of the simulations and experiments.

Comment on “Lubauer J, Lohbauer U, Henrich M, Munz M, Lube T, Belli R. Intricacies involving the evaluation of fracture toughness obtained by the surface‐crack‐in‐flexure method. J. Am. Ceram. Soc., 2022;105(12) 7582–7599”

AbstractWe have evaluated over fifty materials using small semi–elliptical controlled surface flaws with the Newman–Raju factors. Although occasionally there were nuances and peculiarities, the results were sound and comparable to other methods. So, despite the lengthy discussions and numerous plots in Lubauer et al.’s paper, what is evident is that if one simply follows the guidelines in ASTM C 1421 and the other standards for most ceramics including the SL200B sintered silicon nitride, and polish off the recommended 4.5 to 5 h material, one will obtain the correct results. Excessive indentation forces and excessive material removal to obtain sharp corner, shallow surface cracks are unwise. Removing more than 5 h should only be done to remove lateral cracks. In such cases the Strobl et al. solutions may be useful. These solutions are an interesting alternative to the reputable Newman–Raju factors, but much more experience and verification is needed before they can be accepted. They and the extension of their analysis for precrack angles χ < 70° need to be vetted in a major engineering journal.

Atomic Force Microscopy Micro-Indentation Methods for Determining the Elastic Modulus of Murine Articular Cartilage.

The mechanical properties of biological tissues influence their function and can predict degenerative conditions before gross histological or physiological changes are detectable. This is especially true for structural tissues such as articular cartilage, which has a primarily mechanical function that declines after injury and in the early stages of osteoarthritis. While atomic force microscopy (AFM) has been used to test the elastic modulus of articular cartilage before, there is no agreement or consistency in methodologies reported. For murine articular cartilage, methods differ in two major ways: experimental parameter selection and sample preparation. Experimental parameters that affect AFM results include indentation force and cantilever stiffness; these are dependent on the tip, sample, and instrument used. The aim of this project was to optimize these experimental parameters to measure murine articular cartilage elastic modulus by AFM micro-indentation. We first investigated the effects of experimental parameters on a control material, polydimethylsiloxane gel (PDMS), which has an elastic modulus on the same order of magnitude as articular cartilage. Experimental parameters were narrowed on this control material, and then finalized on wildtype C57BL/6J murine articular cartilage samples that were prepared with a novel technique that allows for cryosectioning of epiphyseal segments of articular cartilage and long bones without decalcification. This technique facilitates precise localization of AFM measurements on the murine articular cartilage matrix and eliminates the need to separate cartilage from underlying bone tissues, which can be challenging in murine bones because of their small size. Together, the new sample preparation method and optimized experimental parameters provide a reliable standard operating procedure to measure microscale variations in the elastic modulus of murine articular cartilage.

Nanoindentation characteristics of nanocrystalline tungsten via atomistic simulation

ABSTRACT Molecular dynamics simulations are performed to explore nanoindentation characteristics of tungsten, and the influences of grain size, indenter velocity, indenter size, and temperature are discussed. The results illustrate that the hardness reduces as the grain size (5.00 ∼ 24.62 nm) decreases. There is no phase change observed during the whole deformation process. For monocrystalline W, the dislocation nucleation and propagation dominate the deformation mechanisms. Differently, the primary deformation mode of nanocrystalline W is the grain split and motion of GBs. Dislocations primarily nucleate below the contact surface of the indenter and substrate and then glide in the grain core. The monocrystalline W has better pattern-forming ability than nanocrystalline. Besides, the pattern-forming ability of nanocrystalline W is negatively correlated with the average grain size (5.00 ∼ 24.62 nm). The von Mises stress is mainly concentrated in the interface between the indenter and substrate, the dislocation area for monocrystalline, and grain boundaries for nanocrystalline. The indentation force and hardness are positively correlated with indenter radius size (30 ∼ 80 Å), negatively correlated with temperature (10 ∼ 1500 K), and insensitive to the indenter velocity when velocity is lower than 3.0 Å /ps (300 m/s).

An analytical model describing the mechanics of erythrocyte membrane wrapping during active invasion of a plasmodium falciparum merozoite

The invasion of a merozoite into an erythrocyte by membrane wrapping is a hallmark of malaria pathogenesis. The invasion involves biomechanical interactions whereby the merozoite exerts actomyosin-based forces to push itself into and through the erythrocyte membrane while concurrently inducing biochemical damage to the erythrocyte membrane. Whereas the biochemical damage process has been investigated, the detailed mechanistic understanding of the invasion mechanics remains limited. Thus, the current study aimed to develop a mathematical model describing the mechanical factors involved in the merozoite invasion into an erythrocyte and explore the invasion mechanics.A shell theory model was developed comprising constitutive, equilibrium and governing equations of the deformable erythrocyte membrane to predict membrane mechanics during the wrapping of an entire non-deformable ellipsoidal merozoite. Predicted parameters include principal erythrocyte membrane deformations and stresses, wrapping and indentation forces, and indentation work. The numerical investigations considered two limits for the erythrocyte membrane deformation during wrapping (4% and 51% areal strain) and erythrocyte membrane phosphorylation (decrease of membrane elastic modulus from 1 to 0.5 kPa).For an intact erythrocyte, the maximum indentation force was 1 and 8.5 pN, and the indentation work was 1.92 × 10−18 and 1.40 × 10−17 J for 4% and 51% areal membrane strain. Phosphorylation damage in the erythrocyte membrane reduced the required indentation work by 50% to 0.97 × 10−18 and 0.70 × 10−17 J for 4% and 51% areal strain.The current study demonstrated the developed model's feasibility to provide new knowledge on the physical mechanisms of the merozoite invasion process that contribute to the invasion efficiency towards the discovery of new invasion-blocking anti-malaria drugs.

Effect of Poisson's ratio on the indentation of open cell foam

We tested whether conventional and auxetic (negative Poisson's ratio) foam indentation response fits with classical indentation theory. We first made foam cubes with 20–25 mm sides, and Poisson's ratios spanning negative and positive values (−0.35 to 0.3). These foam cubes were compression tested, and indented by the curved face of two cylinders (10 and 50 mm diameters) and a stud (12 mm diameter), to 20% of their thickness. Full-field true strains were measured by digital image correlation, to obtain Poisson's ratios and to study foam deformation during indentation. Indentation force vs. displacement was measured and calculated using incremental Poisson's ratios and tangent moduli. Normalised root mean square errors between measured and calculated indentation forces were ∼5% of measured values. Foam densification during indentation, and compression towards sample edges, increased with the magnitude of negative Poisson's ratio; these may both increase indentation resistance beyond predictions from indentation theory.

Experimental Analysis of Transseptal Puncture to Investigate the Mechanical Properties of Fossa Ovalis

Background/Objective: Optimization of needle characteristics for trans-septal puncture is of paramount importance to reduce the extent of tissue deformation. This was achieved by studying the mechanical behavior of fossa ovalis (FO) in lamb hearts. The fossa ovalis tissue samples obtained after dissection were subjected to experimental indentation and tensile tests to determine tissue deformation. Methods: Lamb hearts (n = 20) were dissected to obtain fossa ovalis tissue samples. These were subjected to indentation and tensile tests to determine the puncture and rupture forces respectively. Indentation tests were performed using two different indenters: A steel indenter with a hemispherical tip and a Brockenbrough (BRK) needle (bevel tip). Tensile tests were formed using Zwick Roell (Z005) tensile machine at 100 N load cell. ImageJ analysis was also performed to determine the diameter and shape of FO. Results: Indentation results demonstrated that the hemispherical indenter requires a greater punch force compared to the puncture force with the BRK needle. The mean punch force of the hemispherical indenter (15.57 N) was nearly 3 times greater than the puncture force of the BRK needle (5.47 N). Variations between the two indenters provide an insight into the importance of device geometry on trans-septal procedures. The tensile test results illustrated a typical failure pattern with a toe region, linear region, and failure region. The mean rupture force determined was 10.51 N. ImageJ analysis confirmed an oval shape of FO and the diameters measured were in the range 9.0–15.3 mm. Conclusions: The mechanical aspects of fossa ovalis in lamb hearts were successfully studied through a series of experimental indentation and tensile tests. This study serves as a guide to dissecting the challenging FO sample. The procedures for indentation and tensile tests are detailed with common experimental challenges encountered addressed. The correlation of the parameters involved in these experimental tests to the collagen fiber orientation in tissues is also discussed, providing an insight into the deformation of tissues and variations in fiber orientation before and after trans-septal procedures.

Mechanical Characterization of Aluminum Sandwich Structures with Woven-Ply Pineapple Leaf/Glass Fiber-Reinforced Hybrid Composite Core

ABSTRACT Fiber-metal laminates consisting of alternating metal and fiber-reinforced polymer layers have displayed remarkable performance in several engineering applications. This work aims to identify the feasibility of incorporating pineapple leaf fiber to partially supersede glass fiber in thermoplastic-based fiber-metal laminates. Fiber-metal laminates made of pineapple leaf/glass/polypropylene/aluminum were fabricated using the hot press molding technique. The tensile, flexural, Charpy impact and quasi-static indentation tests were performed. The findings indicated that the hybridization of glass with pineapple leaf fibers improved the mechanical properties of the laminates. The results are particularly promising in [G/P/G] laminates in which their tensile and flexural strengths are 38.98% and 20.19% higher than [P/P/P] laminates. In addition, the Charpy impact strengths of [G/P/G] laminates are also 236.66% and 175.68% greater than those of [P/P/P] laminates. In terms of indentation properties, the maximum indentation forces of [G/P/G] laminates are 16.71% and 13.76% higher than those of [P/P/P] laminates at indenter diameters of 12.7 and 20.0 mm, respectively. Interestingly, in-plane and out-of-plane properties of [G/P/G] laminates were comparable to [G/G/G] laminates. Thus, it is anticipated that the hybridization concept could escalate the utilization of natural fibers as a potential reinforcement for engineering applications.

A 3D surface nanomechanical property mapping method with a magnetic-drive orthogonal cantilever probe.

Traditional force-distance curve based atomic force microscopy (FD-AFM) is limited to two-dimensional (2D) surface characterization, making the in situ mapping of three-dimensional (3D) surface nanomechanical properties (SNMP) challenging. This paper presents a multimode 3D FD-AFM based on a magnetic-drive orthogonal cantilever probe (MD-OCP) that can achieve SNMP imaging of 3D micro-nano structures with surface contour fluctuations reaching or exceeding several microns. Bending, torsion and vector tracking modes are integrated into this method for a 2D horizontal surface, 2D sidewall, and 3D surface mapping, respectively. The MD-OCP consists of a horizontal cantilever, a vertical cantilever with a protruding tip, and a magnetized bead. It can be utilized in the detection of deep trench and dense microarray units. The force analysis during 3D SNMP measurement is performed through mathematical derivation, which shows a clear relationship between effective indentation force, friction, and total tip-sample interactions. Single-point SNMP evaluation, discrete 2D SNMP imaging, and continuous omnidirectional 3D SNMP mapping of a 3D microarray unit verify the accurate and comprehensive measurement abilities of the reported method in its bending, torsion, and vector tracking modes. The experimental results demonstrate that this method can achieve excellent 3D quantitative characterization of topography and SNMP, including critical dimensions, adhesion, Young's modulus, stiffness, and energy dissipation, along a 3D device surface. This novel 3D FD-AFM technique has many potential applications in the further exploration of 3D micro-nano devices.

The rock fragmentation and crack propagation under TBM tunneling based on particle flow code

Abstract The rock fragmentation and crack propagation of anisotropic rock induced by tunnel boring machine (TBM) tunneling is studied in this paper. First, a numerical model based on the 2D particle flow code (PFC2D) is established and calibrated to reveal the four stages of rock fragmentation. In Stage I (indentation depth 0–0.4 mm), the indentation force beneath the cutterhead increases and decreases dramatically with the accumulation and release of mechanical energy. Such a phenomenon indicates that a hydrostatic core (crushed zone) can be observed. In Stage II (indentation depth 0.4–1.1 mm), many median cracks propagate dramatically with the indentation force. Meanwhile, the hydrostatic core is pushed because the mechanical energy of the cutterhead is reaccumulated in the specimen. In Stage III (indentation depth 1.1–2.6 mm), lateral cracks begin to develop due to the further increase in indentation depth. In Stage IV (indentation depth 2.6–5 mm), the lateral cracks and median cracks continue to propagate, and rock chips can be found on the sides of the cutterhead. Then, with increasing confining pressure, lateral cracks begin to gradually develop and the maximum angle of lateral cracks is 70.5°. Furthermore, the magnitude of the intrusion velocity can seriously influence the evolution of the indentation force during Stages III and IV because of the accumulation and release of mechanical energy. The accumulation and release of mechanical energy are more obvious with a higher intrusion velocity of the cutterhead.

Quasi-static indentation, low-velocity impact, and resonance responses of the laminated double-curved panel considering various boundary conditions

This research analyzes a laminated double-curved panel’s free/forced vibrational features and Low-Velocity Impact (LVI) Accordingly, the Hertz contact scheme is introduced to model the contact force between the structure and the impactor. Additionally, Hamilton’s principle and four-variable refined quasi-3D logarithmic shear deformation theory (RQ-3DLSDT) are accessible for figuring out a structure’s motion and Boundary Condition (BC) equations for the LVI. Moreover, for computing the motion equation in the displacement and time frames, respectively, the Galerkin and Newmark methods are provided. Finally, there are two subsections within the results section. The first examines the influence related to the number of laminated layers, the geometry of doubly curved panels, and the ratio associated with Young’s module on the indentation and contact force in the time frame. The second discusses the impact of Young’s module proportion, the laminated layers’ form, and geometrical attributes related to the structure on the present simulation’s free and forced vibration features with the LVI.