Phase field methods and sharp interface models are commonly used to predict the motion of a phase boundary in a phase transforming solid. Yet there remains a lack of clarity on the relationship between these competing methods, and whether they can be brought into alignment through a suitable choice of material parameters. The essential underlying features of the sharp interface model and the phase field models of Cahn-Hilliard and Allen-Cahn are highlighted by limiting attention to a 1D problem; this is relevant to (de)lithiation of certain classes of Li ion battery materials. The Onsager variational framework is employed in order to match the rate of loss of free energy within the system to dissipative processes at the interface and in the bulk. Asymptotic analysis is used to obtain the jump conditions across the diffuse interface of the phase field models, and thereby calibrate the jump conditions in the sharp interface version. The Allen-Cahn model gives the possibility of continuity of chemical potential across a moving interface in contrast to the Cahn-Hilliard model. A 1D numerical simulation is used to explore the degree to which phase field models and their sharp interface limits can be brought into alignment.
Granular crystals combine the mechanics of granular materials with the structural performance of architectured materials. In this report we explore the dynamic behavior of fully dense cohesive FCC granular crystals and compare their response with cohesive randomly distributed spheres (RDS). The specimens were tested from quasi-static to impact strain rates, using standard mechanical testing, a modified Dropkinson bar configuration, high-speed imaging, digital image correlation, and grain-tracking analysis. Under quasi-static loading, the FCC crystals deformed by sliding along the densest-packed {111} planes in a mechanism akin to traditional crystal plasticity. At higher loading rates we observed elastic waves, and increasing the strain rate led to an increase in elastic wave speed which we attributed to the viscoelastic characteristics of the adhesive. The FCC crystals were 3–5 times stronger than RDS. Both RDS and FCC samples showed rate-dependent strengthening under high strain loading, which we attributed to the viscous response of the adhesive interfaces. At the highest impact speed, we observed a plastic wave in the FCC crystals, which forced a more homogeneous, but more difficult to activate type of inelastic deformation. Finally, while FCC crystals suffered from embrittlement at higher rates, their energy absorption capability was still greater than RDS at very slow and very fast deformation rates because of their superior strength and mechanical stability. These results provide new insights into the mechanics and performance of granular crystals under high rates of deformation. The experiments and models presented here can also be used to guide the design of future cohesive granular crystals for impact-resistant and energy-absorbing structures.
Supercontracting muscles generate active tension under extreme shortening, far beyond the operating range predicted by classical sliding-filament models. The mechanical principles that allow such large deformation while avoiding uncontrolled force amplification remain unclear. Here, we develop a multi-sarcomere model that couples Z-disc perforation with load-dependent thick-filament mechano-sensing. Z-disc perforation enables thick filaments to penetrate adjacent sarcomeres and form additional cross-bridges at short lengths, thereby extending the geometric range of force generation. In contrast, thick-filament mechano-sensing regulates myosin availability through the axial load borne by the thick filament backbone, providing a load-sensitive brake on motor recruitment. The model shows that these two mechanisms act antagonistically to shape short-length force-length relations. Perforation alone produces enhanced short-length force and a secondary force peak, whereas mechano-sensing suppresses excessive recruitment and transforms the response from double-peaked to plateau-like or monotonic profiles. The same framework preserves the classical Hill-type force-velocity behavior under isotonic contraction, indicating compatibility with canonical muscle mechanics. We further find that the coupling between structural penetration and mechanosensitive recruitment generates history-dependent contractility: the force attainable at a given short length depends on prior activation and contraction path, and transient loss of activation can switch the system into a low-force state. These results identify structural permissiveness and load-sensitive motor recruitment as competing design principles governing supercontracting muscle mechanics, with implications for high-strain bioinspired actuators.
