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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]

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]