Journal of The Mechanics and Physics of Solids最新文献

The statistical mechanics of stiff polymer chains confined within narrow tubes is a foundational topic in polymer physics, extensively analyzed in prior research. For cylindrical, rectangular, and slit-like confinements, the chains’ free energy and extension adhere to a scaling law consistent with the Odijk theory. While this scaling law may not apply to tubes with different cross-sectional geometries, there is a lack of research examining the behavior of stiff chains in tubes with intricate cross-sectional shapes. In this study, we investigate the partition function of a stiff chain confined within an elliptic tube using the path integral approach, deriving a deflection length in a concise closed form through dimensional analysis. This length scale facilitates straightforward expressions for the chain's free energy and extension. Notably, we discover a shape-independent property of these expressions applicable to tubes with a wide variety of cross-sectional geometries. Extensive numerical simulations are conducted using a biased chain-growth Monte Carlo method, incorporating the Pruned and Enriched Rosenbluth algorithm, to validate the theoretical predictions on the confinement free energy and extension of chains in tubes with differing shapes.

We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of freedom, but exhibits linear-elastic fracture mechanics scaling and therefore no size effect. To higher order, the overall energetics of the metastructure can be characterized explicitly in terms of the solution of the zeroth-order continuum problem by the method of $\Gamma$-expansion. We present explicit expressions of the second-order correction for octet frames. As an application, we evaluate the compliance of double-cantilever octet specimens to second order and use the result to elucidate the dependence of the apparent toughness of the specimen on cell size. The analysis predicts the discreteness of the metamaterial lattice to effectively shield the crack-tip, a mechanism that we term lattice shielding. The theory specifically predicts anti-shielding, i. e., coarser is weaker, in agreement with recent experimental observations.

Peeling of thin films has been widely used in adhesion measurement, film transfer and bio-inspired design. Most previous studies focused on the peeling of thin films from rigid substrates, but soft substrates are common in practical applications. Herein, we propose a two-dimensional model based on the bilinear cohesive law to characterize the 90-degree peeling of elastic thin films from elastic soft substrates, and obtain theoretical solutions expressed in terms of the Chebyshev series. The theoretical solutions match well with the finite element method results, including the load-displacement curves and the bulging deformation of soft substrates. We find that with decreasing substrate modulus, the maximum peeling force ($P_{\text{max}}$) decreases but the steady-state peeling force remains unchanged. With the present solutions, the interfacial strength and fracture energy can be extracted simultaneously from the 90-degree peeling experiments of thin film/soft substrate systems, and then the experimentally measured $P_{\text{max}}$ for different film thicknesses can be well predicted. Furthermore, we obtain a new power scaling law of $P_{\text{max}}$, where the scaling exponent depends on substrate elasticity. These results can help us measure the interfacial properties of thin film/soft substrate systems via peel tests, and regulate their peeling behaviors by interface design.

A semiconductor device integrates dissimilar materials of small sizes and complex geometries. During fabrication, the materials are deposited at various temperatures. Both deposition and change in temperature cause stresses in the materials. Under the stresses, ductile materials may deform plastically, and brittle materials may crack. Here we focus on how plastic deformation in the ductile materials affects cracking in nearby brittle materials. We study a model structure in which a metal line is encased by a silicon substrate and a brittle oxide layer. In the triaxially constrained metal, the stresses readily exceed the yield strength of the metal. Such high stresses in the metal elevate the stresses in the oxide. The degree of triaxial constraint varies with the aspect ratio of the metal. We compute the stress in the oxide, as well as the energy release rate of an edge crack and a long channel crack. We discuss strategies to avert cracking in the oxide.

The quantized Frank–Bilby equation can be used to identify interfacial line defect array configurations which relax the misorientation and/or misfit of a coherent crystalline interface. These line defect arrays may be comprised of dislocations and/or disconnections, which are interfacial steps with dislocation character. When an interface contains disconnections, solution of the quantized Frank–Bilby equation is complicated by the fact that the habit plane orientation is not known in advance because it depends on the unknown spacing of the disconnection array. We present a root-finding-based method for addressing this issue, enabling a self-consistent solution for arbitrary defect content. Our method has been implemented in an open-source code which enumerates all possible solutions given a list of candidate line defects. Two cases are presented employing the code: a misoriented FCC twin boundary and an FCC/BCC phase boundary with the Nishiyama-Wasserman orientation relationship. Both cases exhibit more than 10,000 solutions to the Frank–Bilby equation, with several hundred solutions categorized as “low energy” and thus plausible configurations for the actual interface. The resulting set of solutions can be utilized to predict and understand the properties of a given interface.

Graphite holds significant values in the energy and electronics industries due to its unique properties. As a quintessential example of highly anisotropic materials, the shear strength measures one of its most fundamental mechanical properties. However, the lack of ideal materials and testing methods has led to a wide dispersion in the reported values. To address this issue, we utilized epitaxially grown single-crystal graphite and developed a high-throughput sample preparation method, along with a novel loading technique in this work. The intrinsic shear strength of AB-stacked graphite was determined to be τ_s = 62 MPa, by excluding the size effect in measurements. The results are further compared to highly oriented pyrolytic graphite specimens processed down to nanoscale thickness, highlighting the adverse impact of twisted single-crystalline interfaces between the graphitic layers. Additionally, we observed a distinctive failure mechanism with continuous and uniform cascade plastic slips across the thickness of graphite samples, which corresponds to an interlayer shear strength approaching τ_s. The intrinsic shear strength characterized in our work sets an upper limit for the interlayer shear resistance of graphite. The experimental procedure for measuring shear strength can be applied to other van der Waals materials.

The contact between a rigid Hertzian indenter and an adhesive broad-band viscoelastic substrate is considered. The material behavior is described by a modified power law model, which is characterized by only four parameters, the glassy and rubbery elastic moduli, a characteristic exponent $n$ and a timescale ${\tau }_0$. The maximum adherence force that can be reached while unloading the rigid indenter from a relaxed viscoelastic half-space is studied by means of a numerical implementation based on the boundary element method, as a function of the unloading velocity, preload and by varying the broadness of the viscoelastic material spectrum. Through a comprehensive numerical analysis we have determined the minimum contact radius that is needed to achieve the maximum amplification of the pull-off force at a specified unloading rate and for different material exponents $n$. The numerical results are then compared with the prediction of Persson and Brener viscoelastic crack propagation theory, providing excellent agreement. However, comparison against experimental tests for a glass lens indenting a PDMS substrate shows data can be fitted with the linear theory only up to an unloading rate of about $100\mu \mathrm{m/s}$ showing the fracture process zone rate-dependent contribution to the energy enhancement is of the same order of the bulk dissipation contribution. Hence, the limitations of the current numerical and theoretical models for viscoelastic adhesion are discussed in light of the most recent literature results.

Predicting stress fluctuations in granular media under steady-state shear loading is crucial for applications ranging from geophysical processes to construction engineering. Stress fluctuations emerge from particle rearrangement, usually enabled by frictional slip and force-chain buckling. Existing models used to predict stress fluctuations are largely phenomenological, often accounting for the force chain phenomena implicitly through the introduction of internal variables, or explicitly through assumptions of force chain mechanics. Improper consideration of particle mechanics or mesoscale effects can lead to inaccurate predictions of shear strength and instability, making it difficult to predict the onset of yielding, shear band formation, and other instabilities. Furthermore, while recent advancements in machine learning methods have established links between microscale behavior and macroscopic stress drops in granular fault gouges, their predictive capabilities are limited due to their black-box nature. To gain a deeper understanding of stress fluctuations, and ultimately predict them in a physics-informed manner, it is necessary to examine how system energetics change with stress fluctuations. In this paper, we analyze stress fluctuations in a 2D granular fault gouge loaded under quasistatic, steady-state shear. We track the flow of potential energy between force networks and understand how energy and force networks vary with stress rises and drops. We derive an analytical, dynamic force chain model from first principles to illustrate how interactions between force networks lead to the emergence of localized instability phenomena. Finally, we offer insights into how these localized instabilities ultimately enable shear stress fluctuations at the continuum scale.

Extremal elastic materials here refer to a specific class of elastic materials whose elastic matrices exhibit one or more zero eigenvalues, resulting in soft deformation modes that, in principle, cost no energy. They can be approximated through artificially designed solid microstructures. Extremal elastic materials have exotic bulk wave properties unavailable with conventional solids due to the soft modes, offering unprecedented opportunities for manipulating bulk waves, e.g., acting as phonon polarizers for elastic waves or invisibility cloaks for underwater acoustic waves. Despite their potential, Rayleigh surface waves, crucially linked to bulk wave behaviors of such extremal elastic materials, have largely remained unexplored so far. In this paper, we theoretically investigate the propagation of Rayleigh waves in extremal elastic materials based on continuum theory and verify our findings with designed microstructure metamaterials based on pantographic structures. Dispersion relations and polarizations of Rayleigh waves in extremal elastic materials are derived, and the impact of higher order gradient effects is also investigated by using strain gradient theory. This study provides a continuum model for exploring surface waves in extremal elastic materials and may stimulate applications of extremal elastic materials for controlling surface waves.