Journal of The Mechanics and Physics of Solids最新文献

The mitotic spindle, crucial for precise chromosome segregation and cytoplasmic partitioning during cell division, demands stability against forces arising from chromosomal movements and thermal fluctuations. Despite its central role, the mechanical properties of spindles remain largely elusive. In this study, we delve into the mechanical properties of spindles through a comprehensive model encompassing interactions among centrosomes, microtubules, chromosomes, and molecular motors. Our model successfully reproduces the 3D self–assembly of spindles and their responses to mechanical forces. We find that the spindle exhibits viscoelastic properties, responding distinctively to stretch and compression. Rapid stretch induces transient softening of the spindle, while compression leads to temporary hardening. Based on the viscoelastic responses of spindles under constant–force and constant–displacement loadings, we propose a minimal constitutive model for the spindle structure. This constitutive model can not only accurately recapture the viscoelastic responses of spindles under stretch and compression but also predict the mechanical behaviors of spindles under constant–rate loadings and cyclic loadings, which are further verified by simulations. Therefore, our validated constitutive model can replace complex simulations, providing more interesting predictions and guidance for future experiments.

Magnetostrictive alloys are usually brittle materials with micromagnetic structures. Their structural reliability and durability depend on the complex micromagnetic-mechanical coupling at smaller length scales encompassing the evolution of micromagnetic structures. Herein we propose a micromagnetic-mechanically coupled phase-field model for fracture and fatigue behavior of magnetostrictive alloys with evolution of the micromagnetic structure. The thermodynamically-consistent model is derived from microforce theory, laws of thermodynamics, and Coleman–Noll analysis. The evolution of crack phase-field and magnetization-vector order parameters that are fully coupled is governed by history field dependent Allen–Cahn and Landau–Lifshitz–Gilbert equations, respectively. The model is extended to fatigue by introducing a degradation prefactor for the fracture energy as a function of positive elastic energy. One-dimensional analyses are then presented to anatomize the crack driving forces in terms of fully coupled micromagnetic-mechanical and pure mechanical driving force. We demonstrate the model capabilities by finite-element numerical studies on the micromagnetic domain evolution during the crack propagation and the influence of external magnetic field for type-I, type-II, and three-point bending fracture, as well as for the fracture of a single-edge notched specimen with an elliptical inclusion. The simulation result shows that depending on how micromagnetic domains are switched under micromagnetic-mechanical coupling, the magnetic field can enhance or decrease the critical load. In the presence of inclusion with larger fracture toughness, a crack is found to nucleate in the tri-junction of multi-domain micromagnetic structure owing to the high elastic strain around the tri-junction point. It is further found that a suitable magnetic field promoting magnetization-vector rotation around the crack tip could remarkably improve the fracturing load and fatigue life. The results demonstrate the model promising for the study of micromagnetic-mechanically coupled fracture and fatigue in magnetostrictive alloys.

During collective invasion in 3D, cohesive cellular tissues migrate within a fibrous extracellular matrix (ECM). This process requires significant remodeling of the ECM by cells, notably proteolysis at the cell–ECM interface by specialized molecules. Motivated by this problem, we develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition. To account for the active nature of this process, we develop a continuum theory based on irreversible thermodynamics, leading to a kinetic relation for the degradation front that locally resembles the force–velocity relation of a molecular motor. We further study the effect of mechanotransduction on the stability of the cell–ECM interface, finding a variety of self-organized dynamical patterns of collective invasion. Our work identifies ECM proteolysis as an active process possibly driving the self-organization of cellular tissues.

Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials by combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implementing it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetically-driven smart structures, such as soft robots.

We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotic method. Biological materials may exhibit remarkable compressibility when under large deformations, and we take this factor into account for accurate predictions of their morphoelastic changes. The morphoelastic shell model combines the growth model of Rodriguez et al. and a novel shell model developed by us. We start from the three-dimensional (3D) morphoelastic model and construct the optimal shell energy based on a series expansion around the middle surface. A two-step variational method is applied that retains the leading-order expansion coefficient while eliminating the higher-order ones. The main outcome is a two-dimensional (2D) shell energy depending on the stretching and bending strains of the middle surface. The derived morphoelastic shell model is asymptotically consistent with three-dimensional morphoelasticity and can recover various shell models in literature. Several examples are shown for the verification and illustration.

Impacts in granular materials occur over a velocity range of a few hundred m/s in manufacturing processes to several km/s during asteroid impacts. Different energy dissipation mechanisms are activated during impacts based on the kinetic energy of the impactor and the properties of the granular material. Material response during impact can be classified into two broad regimes – quasi-static and dynamic – characterized by the nature of grain and pore deformation and the deformation morphology of grain interfaces. In the quasi-static regime, all energy from the impactor is utilized in pore (or void) collapse, while in the dynamic regime, excess energy after pore closure leads to material melting or jetting and often to non-planar grain interfaces. To understand the transition between the quasi-static and dynamic regimes, in-situ measurements of temperature, local stresses, and porosity at the grain scale are critical but often not possible due to short timescales and inherent heterogeneity of granular materials. In this work, we use X-ray phase contrast imaging (XPCI) to visualize grain-scale deformation during rapid granular compaction and observe phenomena such as plastic flow-induced pore collapse, compaction wave propagation, and the morphology of the grain-grain interfaces. Alongside these experiments, we develop and validate a mesoscale numerical model that incorporates each sample’s microstructure and captures realistic plasticity and thermal effects. Using this validated model, we quantify the temperatures, pressures, and porosity as granular materials are compacted in both quasi-static and dynamic deformation regimes. By comparing our results with existing theoretical models, we find that the continuum definitions of quasi-static and dynamic regimes needs to be updated for a realistic heterogeneous granular media. Specifically, the two regimes can coexist in the same assembly of grains at different time instants due to spatial heterogeneity and rapid dissipation of impact energy away from the point of impact. Finally, we quantify the energies associated with different dissipation mechanisms for individual grains using coupled numerical and analytical techniques. Our methodology allows us to obtain full 3D kinematics and kinetics of rapidly compacted granular materials at both the mesoscale and the grain scale.