Variation Of Mechanical Properties Research Articles

Effect of material characteristics of lead rubber isolators on seismic performance of box girder bridge

Near-field (NF) earthquakes have distinct ground motions, forward directivity pulses, and fling-step motions, causing structural responses to differ from far-field (FF) earthquakes. Seismic isolation is regarded as a developed and successful technology that may be applied to enhance a structure’s functionality and safeguard it against catastrophic earthquake effects. The variation in mechanical properties of seismic isolation also significantly influences bridge seismic response. The study investigates the influence of lead rubber (LRB) isolators and the characteristics of ground motions on seismically isolated bridges, aiming to determine optimal parameters for minimal earthquake response. Key parameters include ground motion characteristics, characteristic strength (Q), and isolator flexibility. The study modeled the force-deformation behavior of isolators using bilinear behavior, reflecting the Bouc-Wen hysteric model. CSI Bridge was used to model seismically isolated steel box girder bridges, with eight natural accelerograms assessing a 2% probability of exceedance in 50 years. The peak responses of pier displacement (MPD), isolator hysteric energy (HED), base shear, and deck acceleration are chosen as the response parameters for the comparison. To evaluate the response parameters, the earthquake data are scaled to the three studied peak ground acceleration (PGA) levels of design level (0.2 g), extreme level (0.4 g), and rare-extreme level (0.8 g). The findings offer insight on the relevance of isolator stiffness and its influences on the seismic performance of isolated bridges. The study identifies minimum values for pier displacement, hysteric energy, deck acceleration, and base shear at specific Q/weight sustained by isolator (W) and time period (T) values. Recommendations are made for the preliminary seismic isolation design of bridges with LRB isolators, highlighting the importance of PGV to PGA ratio in earthquake damage assessment.

Compositional, Structural, and Biomechanical Properties of Three Different Soft Tissue-Hard Tissue Insertions: A Comparative Review.

Connective tissue attaches to bone across an insertion with spatial gradients in components, microstructure, and biomechanics. Due to regional stress concentrations between two mechanically dissimilar materials, the insertion is vulnerable to mechanical damage during joint movements and difficult to repair completely, which remains a significant clinical challenge. Despite interface stress concentrations, the native insertion physiologically functions as the effective load-transfer device between soft tissue and bone. This review summarizes tendon, ligament, and meniscus insertions cross-sectionally, which is novel in this field. Herein, the similarities and differences between the three kinds of insertions in terms of components, microstructure, and biomechanics are compared in great detail. This review begins with describing the basic components existing in the four zones (original soft tissue, uncalcified fibrocartilage, calcified fibrocartilage, and bone) of each kind of insertion, respectively. It then discusses the microstructure constructed from collagen, glycosaminoglycans (GAGs), minerals and others, which provides key support for the biomechanical properties and affects its physiological functions. Finally, the review continues by describing variations in mechanical properties at the millimeter, micrometer, and nanometer scale, which minimize stress concentrations and control stretch at the insertion. In summary, investigating the contrasts between the three has enlightening significance for future directions of repair strategies of insertion diseases and for bioinspired approaches to effective soft-hard interfaces and other tough and robust materials in medicine and engineering.

Passive mechanical properties of adipose tissue and skeletal muscle from C57BL/6J mice

Skeletal muscle and adipose tissue are characterized by unique structural features finely tuned to meet specific functional demands. In this study, we investigated the passive mechanical properties of soleus (SOL), extensor digitorum longus (EDL) and diaphragm (DIA) muscles, as well as subcutaneous (SAT), visceral (VAT) and brown (BAT) adipose tissues from 13 C57BL/6J mice. Thereto, alongside stress-relaxation assessments we subjected isolated muscles and adipose tissues (ATs) to force-extension tests up to 10% and 30% of their optimal length, respectively. Peak passive stress was highest in the DIA, followed by the SOL and lowest in the EDL (p<0.05). SOL displayed also the highest Young’s modulus and hysteresis among muscles (p<0.05). BAT demonstrated highest peak passive stress and Young’s modulus followed by VAT (p<0.05), while SAT showed the highest hysteresis (p<0.05). When comparing data across all six biological specimens at fixed passive force intervals (i.e., 20-40 and 50-70 mN), skeletal muscles exhibited significantly higher peak stresses and strains than ATs (p<0.05). Young’s modulus was higher in skeletal muscles than in ATs (p<0.05). Muscle specimens exhibited slower force relaxation in the first phase compared to ATs (p<0.05), while there was no significant difference in behavior between muscles and AT in the second phase of relaxation. The study revealed distinctive mechanical behaviors specific to different tissues, and even between different muscles and ATs. These variations in mechanical properties are likely such to optimize the specific functions performed by each biological tissue.

Variation of Mechanical Properties and Temperature Control in Hot Asphalt Mixtures through the Incorporation of Glass Powder, Province of Huancayo

Variation of Mechanical Properties and Temperature Control in Hot Asphalt Mixtures through the Incorporation of Glass Powder, Province of Huancayo

Tunable amorphous carbon films formed on ultralow wear, Pt–Au alloys

The mechanocatalytic formation of carbonaceous films at the interface between sliding metallic contacts is simultaneously advantageous for reducing friction and adhesion in several tribological applications and detrimental for electrical contacts as they can induce device failure by increasing the contact resistance. Yet, remarkably little is still known about the chemistry, structural and mechanical properties, and tunability of these interfacial layers. In this study, we performed contact pressure-dependent tribological experiments in dry nitrogen containing trace organics on four, nanocrystalline Pt–Au alloys ([Au] from 0 at.% to 10 at.%) – a promising class of alloys for ultralow wear and electrical contact applications. The ex-situ, multi-technique characterization results did not only provide insights into the chemical nature and mechanical behavior of the mechanocatalytic, carbon-rich films formed on Pt–Au surfaces, but also revealed the interplay between catalytic and mechanochemical tribofilm formation controlled by the composition-dependent electronic structure of the Pt–Au substrate and the applied contact pressure. The results of this work provide guidelines for tailoring nanocrystalline alloys to control their mechanocatalytic activity on the basis of variations of the alloy mechanical properties and element's electronic structure with the alloy stoichiometry.

Investigation of the variation of mechanical and durability properties of elements manufactured with rubber substituted SCMs with element height

Controlling the homogeneous distribution of granulated rubber materials added to self-compacting concrete/mortars along the height is of great importance in terms of preserving and defining the holistic behavior of structural elements. In this study, the effect of EPDMGR (ethylene propylene diene monomer granulated rubber) ratio (0 %, 5 %, 10 %, 15 %, 20 % and 25 %), test age, L/D (slenderness ratio) and element test zone (bottom, middle and top) on the mechanical properties (flexural and compressive), durability properties (porosity and sorptivity) of the elements produced with SCM were evaluated. The results obtained were statistically evaluated by GLM-ANOVA. It was observed that flexural tensile strength was strengthened up to 5 % substitution rate due to the hydrophobic properties and elasticity properties of EPDMGR used, while porosity values increased with height in the upper regions compared to the lower regions due to the placement properties of SCM. Differences in compressive strength appeared in the upper and lower sections after 5 % EPDMGR substitution. This indicates that for the mixture properties used, the properties examined in terms of mechanical and durability test results may have different properties with limited variability in terms of L/D ratio depending on the EPDMGR ratio used and the region where the element was taken.

Study on Rock Mechanical Properties of Deep Volcanic Rock Reservoir

Volcanic rocks exhibit complex mechanical properties due to their special diagenetic forms. Laboratory tests were conducted to study the influence of confining pressure changes on the mechanical properties of deep volcanic rocks, and outcrop volcanic rocks single triaxial tests were conducted simultaneously to study the mechanical properties of deep volcanic rocks. The maximum deviatoric stress and elastic modulus are used to study the variation of mechanical properties of volcanic rocks with confining pressure. The maximum deviatoric stress of underground core increases linearly with the increase of confining pressure. The elastic modulus reaches its maximum at 80MPa confining pressure. Although the variation trend of mechanical parameters of underground core with confining pressure is similar to that of outcrop core with confining pressure, the underground core shows a larger maximum deviatoric stress and elastic modulus. It can be seen from the 80MPa confining pressure comparison test that the mechanical properties of underground core under high confining pressure are superior to those of outcrop core. The mechanical properties of outcrop core under high confining pressure are significantly affected by natural fractures, while the mechanical properties of underground core are less affected by natural fractures.The brittleness index of volcanic rocks decreases with the increase of confining pressure, and the decreasing range is relatively low. The brittleness index of outcrop volcanic rocks decreases with the increase of confining pressure, but its sensitivity to confining pressure is much higher than that of underground core.

Gradient Variation and Correlation Analysis of Physical and Mechanical Properties of Moso Bamboo (Phyllostachys edulis).

This study aimed to investigate the gradient properties of bamboo at the microscopic level and provide a basis for improving the utilization rate of bamboo. Using moso bamboo (Phyllostachys edulis (Carrière) J. Houz.) as a research subject, the variation of vascular bundle area percentage, chemical content, relative crystallinity (CR), mechanical properties of different bamboo slivers, and correlation between those parameters were analyzed. From the bamboo green layer (BGL) to the bamboo yellow layer (BYL), the distribution of vascular bundles changed from dense to sparse. Cellulose and lignin mass content decreased gently, and hemicellulose mass content showed gradual increases. The CR showed an order of bamboo middle layer (BML) > BGL > BYL. The tensile modulus of elasticity, tensile strength, bending modulus of elasticity, and bending strength decreased from BGL to BYL. The order of influence degree on mechanical properties of moso bamboo was vascular bundle area, hemicellulose content, lignin mass content, density, and CR, and these factors correlated with mechanical properties at a significant level (p < 0.05). Vascular bundle area had a decisive effect on the mechanical properties of bamboo. The vascular bundle area and density were linearly correlated with mechanical properties, while the lignin mass content and CR were curve-linearly correlated with mechanical properties.

Effect of functional fillers in solvent‐free polyurethane adhesives: Processing and characterization

AbstractThe present work is focused on the study of polyurethane adhesives in the presence of functional fillers (encapsulated enzymes) intended to make them degradable. This is part of a general strategy aiming to recycle multilayer films for packaging, at their end of life, by means of separating the constituent layers as a result of adhesives degradation. Primarily, it was found that the presence of small quantities of functional filler greatly affects both, the quality of the coating process and the kinetics of the adhesive curing. The former, because of the dependency on particle size distribution, leads to high variations in thickness and mechanical properties of multilayers and, the latter, because of a significant catalytic effect (higher curing rates). Indeed, an assessment of the adhesives' kinetics by rheology showed that the pot‐life and the cross‐over point (G′ = G″) for the enzyme‐containing system were obtained three times faster in comparison to the control formulation. These findings were also confirmed by differential scanning calorimetry measurements. On the other hand, by reducing and homogenizing the filler's particle size using separated sieved material (≤50 μm), improvements in coating control as well as in the quality and final properties of the multilayers were evidenced.Highlights Recycling multilayer plastic films for flexible packaging. Encapsulated enzymes to degrade the polyurethane adhesive in specific conditions. The presence of functional fillers affects the coating process. Process optimization to ensure the coating quality control.

Effect of annealing temperature on the evolution of microstructure, texture, and mechanical properties of hot-rolled 12Cr-ODS steel

To achieve high thermal efficiency, today's nuclear reactor structures are exposed to higher temperatures and pressures, which requires the use of high-strength steels with specific properties, such as ODS steels. There is a need to clarify the evolution of the microstructure and properties of steels at elevated temperatures. This study systematically investigates the evolution of microstructure, texture, and mechanical property variations of 12Cr-ODS steels after hot-rolling and subsequent annealing at 1000 °C and 1200 °C. The investigation utilizes optical microscopy, electron backscatter diffraction technique, and mechanical property measurements. The microstructure of hot-rolled samples shows a layered alternating distribution, which is distinguished by a notable presence of the α-fiber texture. Following annealing at 1000 °C, the martensite grains are smaller with a reduced hardness, while maintaining a strong α-fiber texture. After annealing at 1200 °C, there is a rapid increase in the growth of martensite grains, a significant rise in hardness, a reduction in the α-fiber texture characteristics, and an improvement in the γ-fiber texture characteristics. Moreover, the maximum intensity of the α-fiber texture diminishes as the annealing temperature increases. The mechanical properties of the samples deteriorated after annealing at 1200 °C, which can be attributed to the coarse martensite grains and the texture components containing the {001} cleavage plane dominating the occurrence of brittle cleavage fracture. The 0.1Y sample after annealing at 1000 °C exhibits an excellent combination of strength (1458 MPa) and ductility (20.3%), which is owing to the unique heterogeneous grain structure and the evolution of favorable texture.

Synergistic enhancement of strength and ductility in novel solid-stir continuous extrusion: Influence of heterogeneous microstructure and alloy chemistry

Friction stir-derived solid-state processes leverage the synergistic effect of frictional heating and intense shear deformation to achieve localized microstructural modification for the improvement of mechanical properties. In the present work, a novel processing route called solid-stir extrusion (SSE) has been explored for continuous, high-rate extrusion of a high strength non-age-hardenable-AlMgSc alloy. In the current study, loss of strength associated with frictional heating during the process is mitigated as elevated strength is observed in as-extruded condition, thereby eliminating the need for post process heat treatment. The effect of process attributes on mechanical property and microstructure evolution was investigated. The SSE process caused extensive grain refinement and fragmentation of thermally stable Al3Sc intermetallic periodically at shear bands, which contributes to the elevated mechanical strength. The spatial variation in mechanical properties and microstructural heterogeneity was characterized using nanoindentation and microstructural correlation. The current findings indicate the significance of the process-specific alloy design approach to increase performance of material in as-processed condition.

Relationship between mechanical properties and height-diameter ratio of moso bamboo

Systematic tests of longitudinal compression, bending, longitudinal shear, and longitudinal tensile strength of bamboo were conducted to study the variation of mechanical properties and the height-diameter ratio of bamboo. The predictive relations of mechanical properties and height-diameter ratio were fitted by linear regression analysis. The results showed that the mechanical properties of longitudinal compression, bending, longitudinal shear, and longitudinal tensile strength of bamboo increased with the increase of the height-diameter ratio. In this paper, the method of deducing the relationship between mechanical properties and height-diameter ratio of bamboo through the linear fitting relationship between mechanical properties and height-diameter ratio was shown to have high applicability and accuracy for bamboo. This paper has a certain reference value for the evaluation of mechanical properties of bamboo and has a certain practical value for reducing the testing cost.

Experimental and damage model study of layered shale under different moisture contents

To investigate the mechanical properties and damage evolution law of layered shale under varying moisture contents, we conducted triaxial compression experiments on rock samples with different bedding angles and moisture levels. This study analyzed the variations in mechanical properties of layered shale under different conditions, and established a predicted model for elastic modulus based on different bedding angles and moisture content. Additionally, the damage constitutive model of layered shale was improved. The study revealed that shale’s mechanical properties display anisotropy, which is influenced by the bedding angles and moisture contents. The elastic modulus of the rock increases with the rise of bedding angle, exhibiting a ‘U’-shaped change. Conversely, the mechanical properties of rocks deteriorate, and their brittleness weakens with the increase in moisture content. When the confining pressure increased, the overall mechanical properties of shale were enhanced, and the influence of bedding on shale was weakened, but the deteriorating effect of water on rocks was hardly affected. Based on the above experiments, a predicted model of equivalent elastic modulus of shale considering the coupling effect of bedding and different moisture contents was proposed, which could effectively predict the elastic modulus of layered shale with different moisture content under different confining pressures. Furthermore, based on the predicted model of elastic modulus, an improved damage constitutive model of layered shale under triaxial loading was established, and the damage accumulation trend of layered shale was obtained, which showed an “S”-shaped change with strain. Under the coupling effect of bedding and different moisture contents, the damage of shale was advanced, but the accumulation rate of damage slowed down. With the increase of confining pressure, the influence of bedding and moisture content on the damage characteristics of shale decreased, and the damage curves under different conditions gradually tended to isotropy. The developed damage constitutive model for layered shale under different moisture contents provides theoretical support for the study of reservoir fracturing and wellbore stability.

Design of metadevices based on isotropic materials for eigenfrequency recovery in lightened structures

This work presents a novel approach for the design of metadevices conceived to recover a prescribed set of the natural eigenfrequencies of a structure lightened by machining arbitrary shape holes, using classical topology optimization (TO) techniques. This TO metadevice design (TOMD) is performed by minimizing the error of an eigenfrequency recovery task, using the finite element method (FEM) as an analysis tool, ensuring manufacturability via the solid isotropic material with penalization (SIMP) approach with Heaviside filtering to reduce intermediate-density areas. The spatial variation of mechanical properties derives from the macroscopically distinguishable dual material distribution obtained from the TOMD problem. The methodology was first tested on lightened thin steel plates and then extended to a real-world 3D mechanical component with additional mechanical performance testing. In all cases, the optimized metadevice yielded lower error in recovering eigenfrequencies compared to the lightened component without the metadevice. Furthermore, the metadevice generally achieved further mass reduction, demonstrating its potential for lightweight design while restoring its original eigenfrequencies.

Comparative study of metallic foil friction stir welded and conventional friction stir welded AZ61 Mg alloy butt joints: Biomedical and engineering applications

Metallic Foil Friction Stir Welding (MFFSW) was newly developed from the Friction Stir Welding (FSW) technique. Magnesium (Mg) alloys were the most trending alloys in the aerospace, automobile, and biomedical industries. This study aims to investigate the variation in mechanical, corrosive, microstructural, and fractographic properties of MFFSW as a process innovation when compared with FSW. The metallic foil of pure manganese (Mn) with a thickness of 500 μm was inserted between two AZ61 Mg alloys. The tensile strength, impact strength, and hardness were noted as mechanical properties of the output. Potentiodynamic corrosion tests were performed to reveal the corrosion properties. An optical microscope was used to examine a distinct transverse section of the weld. Fractography tests with scanning electron microscopic analysis were conducted on destructive tensile specimens. The ultimate tensile strength, impact energy, yield strength, and microhardness increased to 16%, 32%, 12%, and 19.17%, respectively, compared to FSW. MMFSW shows a lower elongation of up to 33% than FSW. MMFSW (9.61 mm/A) shows a lower corrosion rate than FSW (11.02 mm/A), which employs improved corrosion properties. Optical microscopy images of the stir zone in both MFFSW and FSW revealed that adding a Mn alloying element improved grain growth uniformity and eliminated unexpected grain growth patterns. Hence, the experiment’s conclusion shows that MFFSW has the edge over FSW for mechanical and corrosion properties. Thus, the Mn strip improves the properties of MFFSW.

Preparation of high thermal conductivity aluminium nitride ceramics with low oxygen impurity for power semiconductors

AbstractEnergy transmission efficiency and stability place higher demands on electrical power systems. Aluminium nitride (AlN) ceramics, which possess high thermal conductivity and electrical insulation, are gradually used in heat dissipation systems for high‐power semiconductors. However, oxygen impurity has been one of the key factors limiting the thermal conductivity of AlN ceramics. The pre‐reduction treatment was used to reduce the powder oxygen content. AlN ceramics with low oxygen impurities were then obtained by hot‐pressing sintering. The decrease in the oxygen content of the powder shows a hindering effect on densification, which increases the sintering temperature to 1750°C. The pre‐reduced powders transform the grain edge phase from YAP to YAM, which is more favourable for purifying the lattice. The variations in grain size and mechanical properties are also discussed. Eventually, AlN ceramics with a thermal conductivity of 201 W m−1 K−1 and a flexural strength of 376 MPa are obtained.

Using miniature experiments to reveal strength gradients in battery casings

Complex metallic structures are often manufactured through multi-step forming or casting processes that induce severe mechanical property variations within the final part. Instead of using the virgin material properties to predict the final part performance, the local material properties after manufacturing need to be known. A novel comprehensive testing methodology is presented allowing the resolution of spatial gradients in the plasticity and fracture properties in metallic structures. It involves using a recently-developed miniature linear-motion system that probes the material within 2 mm wide gage sections (uniaxial, notched and central hole tension, in-plane shear). Additionally, a novel mini-bulge testing system is presented along with a mini-punch system to provide further insight into the local material response for biaxial loading conditions. A full testing campaign comprising 60 miniature samples is performed on all sides of a prismatic aluminum casing for Li-ion battery cells. The results demonstrate significant property variations with more than 30 % higher yield stresses for the side walls as compared to the bottom section. The miniature specimens allow identifying a location-dependent anisotropy, which would otherwise be missed by standard-sized samples. Furthermore, it is shown that the anisotropic Yld2000 plasticity model and the stress-state dependent Hosford-Coulomb fracture initiation model can be fully identified using results from experiments on miniature specimens only.

[Translated article] Mechanical properties variations of immature bone in the earliest stages of development

IntroductionBone as a material varies its composition and mechanical properties throughout life. Although these variations are better understood in adulthood, there is little experimental information on the variation of these properties in early stages of development. The objective of this study is to analyze the mechanical behavior and chemical properties of cortical bone tissue from two animal species in these earliest stages. Material and methodologyTwenty specimens of cortical bone were manufactured from bovine and ovine species that were in different stages of development (feeding exclusively on breast milk, in the transition period to feed or pasture, and young animals but on a solid food diet). The specimens were subjected to tensile tests, recorded with a high-speed camera to obtain deformation maps. Measurements of the tensile force until the specimen broke were also carried out. A fractographic study was carried out with a scanning electron microscope to analyze the fracture surface and an analysis of the amount of calcium in each of the specimens using X-ray dispersion spectroscopy. ResultsA statistically significant and positive correlation was found between the elastic modulus of the specimens and their calcium content. A trend towards more rigid behavior with age was observed. ConclusionsYoung bone tissue tends to stiffen with age as the calcium content increases with an increase in elastic modulus.

Effect of the Heating/Cooling Rate of Nonisothermal Aging on Microstructure and Mechanical Properties of 2050 Al–Li Alloy

The effect of the heating/cooling rates of nonisothermal aging (NIA) on microstructure and mechanical properties of 2050 Al–Li alloy are investigated. The 2050 Al–Li alloy is first solid solutioned and predeformed and then heated from 130 to 220 °C at different rates of 20, 30 °C h−1, or 40 °C h−1 and then cooled to 150 °C. The results show that the mechanical properties of the alloy subjected to NIA treatment can be improved by adjusting the heating and cooling rate. When the heating and cooling rate is 30 °C h−1, the alloy achieves the best mechanical properties; the hardness, ultimate tensile strength (UTS), yield strength (YS), and elongation are 182.9 HV, 597, 571 MPa, and 9.6%, respectively. With the decrease of heating (or cooling) rate of NIA, the diameter and thickness of the T1 precipitate increase and the volume fraction decreases, resulting in the variation in mechanical properties. Therefore, herein, premier precipitation behavior and improved mechanical properties are both achieved by modifying the heating and cooling rate of NIA; the effect of the heating/cooling rate of NIA on the microstructure evolution of 2050 Al–Li alloy is revealed, and the underlying strengthening mechanism is investigated in detail.

Snow mechanical property variability at the slope scale – implication for snow mechanical modelling

Abstract. Snow avalanches represent a natural hazard to infrastructure and backcountry recreationists. Risk assessment of avalanche hazard is difficult due to the sparse nature of available observations informing on snowpack mechanical and geophysical properties and overall stability. The spatial variability of these properties also adds complexity to decision-making and route finding in avalanche terrain for mountain users. Snow cover models can simulate snow mechanical properties with good accuracy at fairly good spatial resolution (around 100 m). However, monitoring small-scale variability at the slope scale (5–50 m) remains critical, since slope stability and the possible size of an avalanche are governed by that scale. To better understand and estimate the spatial variability at the slope scale, this work explores links between snow mechanical properties and microtopographic indicators. Six spatial snow surveys were conducted in two study areas across Canada. Snow mechanical properties, such as snow density, elastic modulus and shear strength, were estimated from high-resolution snow penetrometer (SMP) profiles at multiple locations over several studied slopes, in Rogers Pass, British Columbia, and Mt. Albert, Québec. Point snow stability metrics, such as the skier crack length, critical propagation crack length and a skier stability index, were derived using the snow mechanical properties from SMP measurements. Microtopographic indicators, such as the topographic position index (TPI), vegetation height and proximity, wind-exposed slope index, and potential radiation index, were derived from unoccupied aerial vehicle (UAV) surveys with sub-metre resolution. We computed the variogram and the fractal dimension of the snow mechanical properties and stability metrics and compared them. The comparison showed some similarities in the correlation distances and fractal dimensions between the slab thickness and the slab snow density and also between the weak layer strength and the stability metrics. We then spatially modelled snow mechanical properties, including point snow stability, using spatial generalized additive models (GAMs) with microtopographic indicators as covariates. The use of covariates in GAMs suggested that microtopographic indicators can be used to adequately estimate the variation in the snow mechanical properties but not the stability metrics. We observed a difference in the spatial pattern between the slab and the weak layer that should be considered in snow mechanical modelling.