scholarly journals Influence of Soil Heterogeneity on the Contact Problems in Geotechnical Engineering

2021 ◽  
Vol 11 (9) ◽  
pp. 4240
Author(s):  
Hao Gu ◽  
Kang Liu
Keyword(s):  
Young’S Modulus ◽  
Penalty Method ◽  
Young's Modulus ◽  
Geotechnical Engineering ◽  
Contact Problems ◽  
Soil Heterogeneity ◽  
Contact Forces ◽  
Horizontal Scale ◽  
Normal Contact ◽  
Scale Of Fluctuation

Contact problems are widely encountered in geotechnical engineering, such as the contact between soils and concrete used in earth and rockfill dams, tunnels and coastal levees. Due to the unknown contact region and contact forces, the contact problems have strong boundary nonlinearity. In addition, soils have been recognized as heterogeneous materials in geotechnical engineering. The existence of the soil heterogeneity increases the nonlinearity of the contact problems. Currently, the contact problems are mostly analysed without considering the soil heterogeneity, which may not reflect the contact behavior well. In order to investigate the influence of soil heterogeneity on the contact problems, in this paper, a simple plane-strain contact problem is analysed as an example. In this example, Young’s modulus is taken to be a spatially variable. The local average subdivision (LAS) is used to model the heterogeneity of Young’s modulus. The penalty method is utilised to determine the contact behavior. By the first use of linking the penalty method with the LAS, the proposed approach can be used to analyse the contact problems considering soil heterogeneity. The results show that the influence of soil heterogeneity on the elastic contact problems is significant. The contact forces of the heterogeneous case present apparent variation compared to the results of the homogeneous case. The distribution of the contact force at a specific point is also normal when Young’s modulus is normally distributed, moreover, the coefficient of variation (COV) and the horizontal scale of fluctuation of Young’s modulus affect the extent of variation of the normal contact forces. The standard deviation of the normal contact force increases with the increase of the COV and decreases with the increase of the horizontal scale of fluctuation of Young’s modulus. From the analyses, to better predict the deformation/stress in the contact problems, heterogeneity needs to be considered.

Evaluation of Young’s modulus of construction materials by instrumented indentation using a ball indenter

2021 ◽  
Vol 87 (8) ◽  
pp. 64-68
Author(s):  
V. M. Matyunin ◽  
A. Yu. Marchenkov ◽  
N. Abusaif ◽  
M. V. Goryachkina ◽  
R. V. Rodyakina ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
High Surface ◽  
Construction Materials ◽  
Contact Problems ◽  
Indentation Load ◽  
Test Material ◽  
Elastic Displacement ◽  
Large Radius ◽  
Instrumented Indentation

Methods for evaluation of Young’s modulus (Em) of structural materials by instrumented indentation using ball indenter have been considered. All these techniques are based on the solution of elastic contact problems performed by H. Hertz. It has been shown that registration of the initial elastic region in the «load – displacement» indentation diagram provides the Em determination for metals and alloys. However, it is necessary to evaluate accurately the elastic compliance of a device, to use an indenter with a large radius R, and ensure a high surface quality of the test material in advance. Methods for Em determation, when indentation diagrams are recorded in the elastoplastic indentation region, should include the effect of plastic deformation on the elastic displacement calculated by H. Hertz expression. However, it appeared essential to determine the relation between the elastic αel and plastic h components of the total elastoplastic displacement α and the elastic displacement α0 estimated by H. Hertz expression for a definite indentation load. A close correlation between α0 and αel is revealed for steels, aluminum, magnesium, and titanium alloys when using indenters with a radius of R = 0.2 – 5 mm (diameter D = 0.4 – 10 mm) and maximum indentation load Fmax = 47 – 29430 N (4.8 – 3000 kgf). It is also shown that a gradual decrease in Em is observed with an increase in R(D) at the same degree of loading F/D2 for the same material. This fact was explained by the scale factor effect.

Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials

2007 ◽  
Vol 129 (6) ◽  
pp. 904-912 ◽  
Author(s):  
David C. Lin ◽  
Emilios K. Dimitriadis ◽  
Ferenc Horkay
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Full Range ◽  
Soft Materials ◽  
Adhesive Contact ◽  
Colloid Interface ◽  
Inhomogeneous Materials ◽  
Dugdale Model ◽  
Normal Contact ◽  
Adhesive Interactions

In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon’s approximation (2000, “General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load,” J. Colloid Interface Sci., 226(1), pp. 166–171) of the Maugis–Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement–Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young’s modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young’s modulus close to those obtained with Hertzian models for the extension curves. The Pietrement–Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis–Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon’s empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young’s moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.

Friction Analysis in Needle Insertion Into Soft Tissue

2021 ◽  
Author(s):  
Yingda Hu ◽  
Murong Li ◽  
Yong Lei
Keyword(s):  
Friction Coefficient ◽  
Young’S Modulus ◽  
Friction Force ◽  
Young's Modulus ◽  
Surface Friction ◽  
Needle Insertion ◽  
Contact Forces ◽  
Diagnostic Methods ◽  
Tissue Pressure ◽  
Preoperative Diagnostic

Abstract As one of the preoperative diagnostic methods, needle insertion is widely used for its safety and effectiveness. Recently, robotic needle insertion systems have been under active developments. Hence needle insertion experiments are essential for system verifications, in which the interactions between needle and tissue is a major focus for needle-tissue interactive models, and the friction between the needle and tissue is an important factor. In these experiments, the friction coefficient can be affected by many factors, such as insertion speed, needle-tissue deformation and contact forces. In this paper, to study and analyze the influence of various variables on friction force and friction coefficient, three variables, i.e., tissue pressure on needle, needle insertion velocity and Young’s modulus of the tissue, are systematically studied by constructing a testbed, in which the radial surface friction is converted into equivalent plane friction based on the assumption that the distribution of the normal force and friction force on the needle is uniform for the whole needle outer surface. The experimental results show that the variation range of friction coefficient is 0.122–0.341. The friction coefficient decreases with the increase of pressure and increases with the increase of velocity, while Young’s modulus have a small effect on the friction coefficient.

The Influence of the Suspension on the Phenomena of Wheel-Rail Contact

2015 ◽  
Vol 809-810 ◽  
pp. 1061-1066
Author(s):  
Ioan Sebeşan ◽  
Valeriu Ştefan
Keyword(s):  
Contact Surface ◽  
Contact Problems ◽  
Contact Forces ◽  
Dynamic Loads ◽  
Friction Forces ◽  
Normal Contact ◽  
The Moment ◽  
The Relationship ◽  
Contact Pressures ◽  
Pivoting Friction

Efficient use of adhesion between wheels and rails involves a good knowledge of this phenomenon, in order to equip the vehicle with adequate facilities and systems that protect the vehicle and the rail. The loading of the vehicle's axle with dynamic loads in vertical and horizontal planes, are to be developed in the area of contact, both normal stress and shear distributed stress, their sum giving the friction force and the moment of pivoting friction (spin). This makes the wheel-rail contact problems take the two aspects of the study, namely the problem of normal and tangential contact issue. The normal contact problem involves regular geometric shape bodies, determining the size of the resulting contact surface, the distribution of the normal contact pressures and the relationship between the proximity of the bodies and the normal contact force. Solving the problem of the tangential wheel-rail contact is about to establish the correlation between the creepage, normal contact forces and friction forces, and also the ratio between the adherent contact surface and the nominal contact surface where the creepage ocurs.

scholarly journals Contact problems for an inhomogeneous elastic wedge with variable Poisson’s ratio

2021 ◽  
pp. 63-71
Author(s):  
D. A Pozharskii ◽  
E. D Pozharskaia
Keyword(s):  
Young’S Modulus ◽  
Integral Equations ◽  
Contact Pressure ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Elastic Equilibrium ◽  
Contact Problems ◽  
Poisson's Ratio ◽  
Polar Coordinates ◽  
Angular Coordinate

Plane contact problems of the elasticity theory are investigated for a wedge when Poisson’s ratio is an arbitrary smooth function with respect to the angular coordinate while shear modulus is constant. For this case Young’s modulus is also variable with respect to the angular coordinate. A finite contact domain is given on one wedge face, it does not include the wedge apex, while the other wedge face is rigidly fixed (problem A) or stress-free (problem B). To reduce the problems to integral equations with respect to the contact pressure, we use the general Freiberger type representation for the solution of elastic equilibrium equations written in polar coordinates with variable Poisson’s ratio. Exact solutions of auxiliary problems are constructed with the help of Mellin integral transforms. The regular asymptotic method employed is effective for contact domains relatively distant from the wedge apex. It is shown that logarithmic terms appear in the asymptotic solutions for the inhomogeneous material which are missing in the well-known asymptotics for the homogeneous one. In contact problem C which is corresponding to problem A, the friction and roughness are taken into account in the contact region. The roughness of the wedge surface is simulated by a Winkler type coating. The collocation method is used for solving integral equations of the second kind. Unlike problem A, in problem C the contact pressure does not have square root singularities at end-points where it takes finite values. Calculations are made for the cases when Poisson’s ratio and Young’s modulus increase or decrease from the surface of the wedge.

Linear Complementary Formulations Involving Frictional Contact for Elasto-Plastic Deformable Bodies

1997 ◽  
Vol 64 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Maocheng Li ◽  
Desong Sha ◽  
K. K. Tamma
Keyword(s):  
Frictional Contact ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Small Deformation ◽  
Contact Problems ◽  
Tangential Direction ◽  
Normal Direction ◽  
Contact Forces ◽  
Contact Boundary ◽  
Normal Contact

In the present study, an incremental variational inequality is described for frictional contact problems with material non linear behavior assumed to be elasto-plastic for the contacting bodies. On the contacting boundaries, the constraint conditions include noninterpenetration along the normal direction of the contact boundary and Coulomb friction law in the sliding direction. After numerical discretization using the finite element method, an effective linear complementary formulation is then established with two unknown variables and two complementary variables for each contact nodal pair. The proposed developments permit a reduced number of unknown variables which are chosen as the gap function for the normal direction and the norm of the incremental sliding displacements for the tangential direction; and the complementary variables are taken as the normal contact forces and slack variables in the tangential directions. The resulting linear complementary equations are then solved employing an explicit Conjugate Gradient Based Projection (CGBP) method in conjunction with a generalized Newton-Raphson iteration procedure to account for the material nonlinear behavior. The methodology is valid for three-dimensional frictional contact representations; however, for purposes of illustration of the proposed approaches, attention is confined to applications involving two-dimensional static elasto-plastic problems under small deformation. Numerical examples are presented which clearly show that the developments satisfy the problem physics and contact conditions with features to include high accuracy and reduced computational costs.

scholarly journals Sliding Interaction for Coated Asperity with Power-Law Hardening Elastic-Plastic Coatings

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2388
Author(s):  
Bin Zhao ◽  
Hanzhang Xu ◽  
Xiqun Lu
Keyword(s):  
Friction Coefficient ◽  
Yield Strength ◽  
Young’S Modulus ◽  
Contact Force ◽  
Young's Modulus ◽  
Contact Forces ◽  
Geometrical Parameters ◽  
Asperity Contact ◽  
Strength Ratio ◽  
Modulus Ratio

Sliding between asperities occurs inevitably in the friction pair, which affects the efficiency and reliability in both lubricated and non-lubricated conditions. In this work, the contact parameters in the coated asperity sliding process are studied, and the universal expressions of the average contact force and the friction coefficient are obtained. The effect of the interference between asperities, the material and geometrical parameters including the Young’s modulus ratio and yield strength ratio of the coating and substrate, and the hardening exponent and thickness of the coating on the average contact forces and friction coefficient is considered. It shows both normal and tangential contact forces increase with the increasing interference, increasing Young’s modulus ratio, decreasing yield strength ratio, and decreasing coating thickness; while the trend is different for the effect of the hardening exponent of the coating. The normal force increases and the tangential force decreases as the hardening exponent increases. Based on this, the influence of these parameters on the effective friction coefficient is obtained further. It reveals that the friction coefficient increases as the interference and Young’s modulus ratio enlarge and decreases as the yield strength ratio, the coating’s hardening exponent, and thickness increase. The universal expressions for the contact force and friction coefficient in the sliding process are obtained. This work might give some useful results to help choose the optimum coatings for specific substrates to reduce friction in cases where the asperity contact exists, especially in the focused field of the journal bearing in the marine engine under poor lubrication conditions.

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