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Abstract: In the present paper, the mechanics of axisymmetric adhesive contact of rough surfaces involving power-law graded materials is investigated analytically. A series of general analytical solutions have been obtained with use of the cumulative superposition and equivalent energy release rate approaches. These solutions provide closed-form expressions of equilibrium relations among applied load, indentation depth and contact radius. Based on these solutions, an effective macroscopic description of the contact evolution is obtained for a general punch profile with surface roughness. Our analysis results reveal that the simultaneous presence of surface roughness and graded material properties can influence the pull-off force and energy dissipation due to adhesion hysteresis significantly. Moreover, it is found that both the adhesion strength and toughness can be optimized by adjusting the surface topography and material parameters of power-law graded solids appropriately. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials as special cases and therefore can also serve as the benchmarks for checking the validity of numerical solution results. [Copyright &y& Elsevier]

Abstract: The present paper analytically investigates the adhesive behavior of power-law graded elastic solids under a combined action of external normal loading and a substrate stretch-induced mismatch strain with the effect of mode-mixity taken into account. A plane strain non-slipping model, a plane strain non-coupling model and an axisymmetric non-coupling model have been analyzed, respectively. Our results show that under a finite normal force, the equilibrium of the adhesive system may lost its stability at a critical value of mismatch strain, which significantly depends on both the graded material constants and the degree of mode-mixity. This indicates that the strongest or weakest adhesion strength under substrate stretching can be achieved by designing the physical constants of the adhesive system appropriately. These results provide a theoretical foundation for novel applications of functional graded materials in adhesion systems. [Copyright &y& Elsevier]

Abstract: In previous work about axisymmetric adhesive contact on power-law graded elastic materials, the contact interface was often assumed to be frictionless, which is, however, not always the case in practical applications. In order to elucidate the effect of friction and the coupling between normal and tangential deformations, in the present paper, the problem of a rigid punch with a parabolic shape in non-slipping adhesive contact with a power-law graded half-space is studied analytically via singular integral equation method. A series of closed-form analytical solutions, which include the frictionless and homogeneous solutions as special cases, are obtained. Our results show that, compared with the frictionless case, the interfacial friction tends to reduce the contact area and the indentation depth during adhesion. The magnitude of the coupling effect depends on both the Poisson ratio and the gradient exponent of the half-space. This effect vanishes for homogeneous incompressible as well as for linearly graded materials but becomes significant for auxetic materials with negative Poisson’s ratio. Furthermore, influence of mode mixity on the adhesive behavior of power-law graded materials, which was seldom touched in literature, is discussed in details. [Copyright &y& Elsevier]

Abstract: In this paper, adhesive contact of a rigid cylinder on an elastic power-law graded half-space is studied analytically with the theory of weakly singular integral equation and orthogonal polynomial method. Emphasis is placed on the coupling effect between tangential and normal directions which was often neglected in previous works. Our analysis shows that the coupling effect tends to reduce the contact area in the compressive regime. The effect of bending moment on the adhesion behavior is also examined. Like a pull-off force, there also exists a critical bending moment at which the cylinder can be bended apart from the substrate. However, unlike pull-off force, the critical bending moment is insensitive to the gradient exponent of the graded material. [Copyright &y& Elsevier]

Abstract: The aim of the present paper is to investigate the adhesive behavior between a transversely isotropic piezoelectric half-space and a cylinder punch subjected to combined mechanical and electric loads under plane-strain condition. The effect of adhesion is described by using a generalized JKR-model which can account for the non-slip condition in the contact regions. Analytical function theory is employed to find the solution of the resulting singular integral equations. Our analysis shows that the adhesive contact behavior for different types of piezoelectric materials may be quite different. The results obtained in this paper may be helpful to understand the contact mechanics of piezoelectric materials at micro-scale. [Copyright &y& Elsevier]

This paper extends the double-Hertz model of Greenwood and Johnson (1998) to the plane strain problem of adhesive contact between a wavy surface and a flat surface, named as the double-Westergaard model. The adhesive force within the cohesive zone near contact edge is described by the difference between two Westergaard pressure distribution functions with different contact widths. Closed-form analytical solutions are obtained for different equilibrium states during loading and unloading stages. The proposed model captures a transition between Westergaard and JKR contact models through a dimensionless transition parameter. Depending on two dimensionless parameters, transitions between partial and full contact during loading/unloading are characterized by one or more jump instabilities. Decreasing waviness size by decreasing both the amplitude and period with a fixed curvature is found to enhance adhesion both by increasing the magnitude of the pull-off force and by inducing more energy loss through adhesion hysteresis. [ABSTRACT FROM AUTHOR]

A multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials. The model developed is based on the higher-order homogenization theory with multiple spatial and temporal scales in one dimensional case. The amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non-Fourier heat conduction due to material heterogeneity and non-local effect of the homogenized solution. By separating the governing equations into various scales, the different orders of homogenized non-Fourier heat conduction equations are obtained. The reduced time dependence is thus eliminated and the fourth-order governing differential equations are derived. To avoid the necessity of C1 continuous finite element implementation, a C0 continuous mixed finite element approximation scheme is put forward. Numerical results are shown to demonstrate the efficiency and validity of the proposed method. [Copyright &y& Elsevier]

The self-organisation behaviour of dislocation upon loading is still a mechanistically mysterious phenomenon. The present article aims to present a computationally tractable dislocation dynamics model, which can be used for helping analyse the mechanism behind dislocation pattern formation. With an integrated use of asymptotic analysis and machine learning tools, the discrete dislocation dynamics on two parallel slip planes is self-consistently reformulated at a coarse-grained level. For the present case, asymptotic analysis helps in 1) reformulating the original globally discrete problem by a continuum model underpinned by a database resolving the almost singular short-range elastic interaction of discrete dislocations; 2) identifying the proper input and output quantities for implementing machine learning tools; 3) digging out a hidden but explicit interrelation between mean-field quantities to reduce the dimensionality of the data space. Machine learning tools serve for 1) inferring the inherently implicit interrelationships between continuum quantities; 2) capturing a low-dimensional manifold in the data space corresponding to the local flow stress. The non-monotonically increasing profile of the flow stress - density relationship, as revealed by machine learning, is found to play a key role in the onset of dislocation patterning behaviour seen in the simulation results. A scaling law relating the applied stress to pattern wavelength is also derived, providing a rationale to the widely used empirical similitude relation. The experimentally observed swing in similitude coefficient value is attributed to the randomness in slip plane distributions. In a methodological viewpoint, the treatment of using asymptotic analysis to help design the curriculum for implementing machine learning tools, offers a paradigm for self-consistently upscaling more complicated multiscale systems. [ABSTRACT FROM AUTHOR]

Materials possessing tension-compression asymmetric behavior can be simulated by a bi-modulus constitutive relation, which assumes the materials have different moduli in tension and compression. Traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model. In this paper, a new computational framework is established. Solution procedures under both small and finite deformations, which have asymptotically quadratic rate of convergence, have also been proposed and implemented in ABAQUS with UMAT. Numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena. [ABSTRACT FROM AUTHOR]

Many engineering and biological materials have been found to have tension–compression asymmetry properties. An extension of the linear thermoelastic behavior called a bi-modulus constitutive model is proposed to study the impact of thermo-mechanical coupling in such materials and structures. The well-posedness of the corresponding bi-modulus thermoelasticity problems is confirmed via a variational approach. An efficient numerical analysis method is developed for such nontrivial material behavior and is further employed for structural topology optimization. The importance of the proposed analysis and design framework is demonstrated by the significant impact of the tension–compression asymmetry and thermal effect on structural responses and optimum structural configurations. • A thermo-mechanical constitutive model considering TCA is constructed. • The well-posedness of the bi-modulus thermoelasticity theory is demonstrated. • An efficient analysis algorithm of thermoelastic structures with TCA is proposed. • MMC-based design optimization of thermoelastic structures with TCA is developed. [ABSTRACT FROM AUTHOR]

A theoretical model of a power-law graded elastic half-space in contact with a randomly rough rigid surface is established by combining the Greenwood–Williamson rough contact model and the JKR type adhesion model for power-law graded materials. The rough surface is modeled as an ensemble of non-interacting asperities with identical radius of curvature and Gaussian distributed heights. By applying the JKR type theory for power-law graded solids to each individual asperity of the rough surface, the total normal forces for the rough surface are derived for loading and unloading stages, respectively, and a prominent adhesion hysteresis associated with dissipation energy is revealed. Our results include the solutions for homogeneous materials and Gibson solids as special cases and describe the complete transition between these two limiting situations. A dimensionless adhesion parameter, which influences both the total pull-off force and the energy dissipation due to adhesive hysteresis, is also identified. It is found that a small adhesion parameter results in higher energy dissipation and pull-off force, while a large adhesion parameter leads to lower energy dissipation and pull-off force. [ABSTRACT FROM AUTHOR]

Abstract: A cohesive zone model for two-dimensional adhesive contact between elastic cylinders is developed by extending the double-Hertz model of Greenwood and Johnson (1998). In this model, the adhesive force within the cohesive zone is described by the difference between two Hertzian pressure distributions of different contact widths. Closed-form analytical solutions are obtained for the interfacial traction, deformation field and the equilibrium relation among applied load, contact half-width and the size of cohesive zone. Based on these results, a complete transition between the JKR and the Hertz type contact models is captured by defining a dimensionless transition parameter μ, which governs the range of applicability of different models. The proposed model and the corresponding analytical results can serve as an alternative cohesive zone solution to the two-dimensional adhesive cylindrical contact. [Copyright &y& Elsevier]