Journal of The Mechanics and Physics of Solids最新文献

Multicellular tubes are fundamental tissues for transporting and distributing liquids and gases in living organisms. Although the molecular, cellular and mechanical aspects in tube formation have been addressed experimentally, how these factors are coupled to control tube patterning and dynamics at the tissue level remains incompletely understood. Here, we propose a three-dimensional (3D) vertex model that incorporates a mechanochemical feedback loop correlating cell deformation and actomyosin signaling pathway to probe the morphodynamics of multicellular tubes. We show that diverse patterns, including ring, helix, double helix, and labyrinth, are generated in tubes through pitchfork bifurcation, where spatial fluctuations of both biochemical signaling and 3D cell deformation are remarkably involved. The mechanochemical feedback loop enables cell oscillations via Hopf bifurcation, which induces the mechanical and chemical patterns to propagate successively as either traveling or pulse waves while their spatial configurations are maintained, strikingly distinct from the classical Turing instability. Our simulations, together with stability analysis of a minimal model, uncover the essential role of mechanochemical principles in sculpting biological tubes.

Mode II fracture toughness of interfaces in laminated structures is usually assessed through standardized tests. Standards are based on samples featuring regular shapes and uniform cross-sections, in which mode II propagation happens to be unstable. We explore here, via a semi-analytical approach, the potential of more complex geometry and shapes for stabilizing the crack propagation. Results demonstrate that an end-notch flexure (ENF) sample with increasing width along the propagation direction possesses a more stable fracture compared to the classical configuration. This leads to the conceptualization of a width-tapered ENF (WTENF) that can address the instability issue encountered by the classical ENF samples. The closed-form solution of WTENF is derived, including the compliance and energy release rate of the system, based on which, the stability status diagram of WTENF has been provided. A systematic validation is performed by numerical and physical experiments, confirming the validity and the accuracy of the associated data reduction model. The WTENF can be a robust method with enhanced stability for measuring the mode II delamination toughness. Beyond solving the WTENF, the derived equations hold significant potential for other applications, such as probing the length-scale effect for delamination of fiber-reinforced composites and guiding the design of toughening strategies for interfaces.

The solid-solid contact interface is crucial for the reliability of solid-state energy storage systems. The contact condition becomes more complicated when lithium (Li) metal is used as the anode. The contact between solid electrolyte (SE) and Li metal is inferior compared to the liquid/solid interface in conventional Li-ion batteries. Experimental evidence has shown that improper operating conditions of solid-state batteries can lead to electro-chemo-mechanical failures at the Li/SE interface, including the formation of voids and the penetration of Li. In this study, a unified phase-field model is developed to investigate these two mechanisms. The model considers the coupled electro-chemo-mechanical processes including void diffusion, lattice annihilation, stripping and plating reactions, and plastic deformation of Li metal. The study begins with a revisit of the deformation-mechanism map for Li metal under a wide range of temperatures, stress, and deformation rates. This map serves as the basis for the mechanical characterization in the phase-field model. The large inelastic deformation of Li is considered by introducing an advection term into the Allen-Cahn equation, which is used to describe the dynamic evolution of the Li and void phases. The effects of current density and stack pressure on void evolution and Li penetration are studied based on the model predictions. By combining the simulation results with the experimental data from publications, we obtain the stable operation zone of stack pressure and applied current density. In this zone, the Li/SE interface can enable stable stripping and plating of Li metal. The same phase-field modeling framework is transferred to investigate the Li-Mg alloy/SE interface considering Li-Mg alloy is also used as the anode. The fundamental difference between Li/SE and Li-Mg/SE is analyzed accordingly. This study provides a useful tool for the design, manufacturing, and management of next-generation batteries by providing important scientific insights into the electro-chemo-mechanical processes of different anode materials under various operational conditions.

Ferroelectric materials are widely used in energy applications due to their field-driven multiferroic properties. The stress-induced phase transformation plays an important role in the functionality over repeated and consecutive operation cycles, especially at the micro/nanoscales. Here we report a systematic in-situ uniaxial compression tests on cuboidal Barium titanate (BaTiO${}_3$) nanopillars with size varying from 100 nm to 3000 nm, by which we explore the stress-induced transformation and its interplay with plastic deformation. We confirm the superelasticity achieved in pillars by martensitic phase transformation from tetragonal to orthorhombic. There exists a critical size, 330 nm, for the yield stress. Above 330 nm, martensitic phase transformation aids slip along the plane with a low Schmid factor, in turn, the pseudo-compatible twins form within the shear band. The scaling exponent of size-dependent yield strength is found to be exactly 1. For nanopillars smaller than 330 nm, no twins form, only slips with large Schmid factors are activated, and size effect vanishes. All pillars with sizes from 100 nm to 300 nm achieve the theoretical yield limit around 9 GPa. Our experimental results uncover the interplay between twins and slips in BaTiO${}_3$ nanopillars, which pave the way for the optimization of microstructure design of ferroelectric materials for microelectronic applications at small scales.

Disordered biopolymer gels, such as those synthesized from polysaccharide and gelatin, play an important role in biomedical applications, particularly in tissue engineering. During the gelation process of these gels, polymer chains associate in the presence of gelling agents, forming physical cross-links known as the junction zones. In contrast to rubber-like networks, the resulting network comprises two main regions: the ordered region due to the junction zones and the amorphous region due to the unassociated chains. Under thermal fluctuations and/or external loading, the number and locations of junction zones can change leading to “zipping” (lengthening, i.e., expansion of the junction zones) and “unzipping” (shortening, i.e., shrinkage of the junction zones). This gives rise to intriguing features in biopolymer gels such as healing and damage-like energy dissipation. Despite the recognition of zipping and unzipping in such gels, the development of mathematical models that incorporate the microscopic mechanisms into the material’s macroscopic mechanical properties is still in its early stages. In this paper, we provide a systematic framework for such multiscale modeling. Several critical steps are taken to equip the eight-chain network model with a previously developed micromechanics model for a coil–rod structure, where the coil represents an unassociated chain and the rod represents a junction zone. Most importantly, for a network of coil–rod structures under zero stress, the rigidity induced by the rod leads to an end-to-end distance ($r_0$) for the coil–rod which is different from a classical result for a Gaussian coil: $\sqrt{n}b$ where $b$ is the Kuhn length and $n$ is the number of Kuhn segments in the coil. By relaxing the incompressible assumption in the original eight-chain model, $r_0$ is determined for the gel network, which depends on the length of the junction zone. Consequently, as the junction zone extends/shrinks following zipping/unzipping under an external load, an irreversible deformation can occur after unloading, consistent with experimentally observed “permanent set”. The extension/shrinkage of the junction zone is captured by statistical mechanics analysis in the grand canonical ensemble, which allows the exchange of segments between the coil and the rod, driven by the binding energy of polymer chain association. The model also includes explicit consideration of swelling and the influence of solvent molecules as a result of their mixing with the polymer chains in the gel network. With physically reasonable parameters, the proposed model is shown to provide good matching with experimental data on the uniaxial testing