Journal of The Mechanics and Physics of Solids最新文献

In this work a generalized phase-field cohesive zone model ($\mu$ PF-CZM) is proposed within the framework of the unified phase-field theory for brittle and cohesive fracture. With the introduction of an extra dissipation function for the crack driving force, in addition to the geometric function for the phase-field regularization and the degradation function for the constitutive relation, theoretical and application scopes of the original PF-CZM are broadened greatly. These characteristic functions are analytically determined from the conditions for the length scale insensitivity and a non-shrinking crack band in a universal, optimal and rationalized manner, for almost any specific traction–separation law. In particular, with an optimal geometric function, the crack irreversibility can be considered without affecting the target traction–separation softening law. Not only concave softening behavior but also high-order cohesive traction, both being limitations of the previous works, can be properly dealt with. The global fracture responses are insensitive not only to the phase-field length scale but also to the traction order parameter, though the crack bandwidth might be affected by both. Despite the loss of variational consistency in general cases, the resulting $\mu$ PF-CZM is still thermodynamically consistent. Moreover, the existing numerical implementation can be adopted straightforwardly with minor modifications. Representative numerical examples are presented to validate the proposed $\mu$ PF-CZM and to demonstrate its capabilities in capturing brittle and cohesive fracture with general softening behavior. The insensitivity to both the phase-field length scale and the traction order parameter is also sufficiently verified.

Shear wave elastography (SWE) is an innovative method that allows for the nondestructive and quantitative characterization of muscular mechanical properties. This method finds extensive utility in fields such as sports medicine, sports rehabilitation, and the diagnosis of muscle-related ailments. Existing studies have demonstrated the promise of SWE in probing intramuscular pressure (IMP), a factor intimately tied to muscular physiological functions and the onset of certain diseases. Nonetheless, there remains a lack of a SWE method grounded in an appropriate biomechanical model capable of effectively imaging IMP in vivo. Addressing this issue, we propose a shear wave imaging method relaying on a porohyperelastic model encompassing well-defined parameters for both muscular active behavior and intramuscular pressure. Drawing upon wave motion analysis, we establish a correlation between shear wave velocities and IMP in analytical form. This theoretical solution on one hand help understand the interplay between IMP and muscle active stress and the impact of muscle contraction on IMP. On the other hand, it enables us to develop an elastography method to assess IMP in vivo. We conducted a series of experiments to underscore the applicability of our theory and elastography method. Ex vivo experiments were performed on porcine muscles, while in vivo tests were carried out on human skeletal muscles. The results from the ex vivo tests validate the efficacy of our method. Meanwhile, the in vivo outcomes suggest that our approach holds potential to assess the variation of IMP with muscle fatigue and injuries, inspect intramuscular injections, and diagnose acute and chronic compartment syndrome.

Creep poses a significant threat to the integrity and longevity of structural components at high-temperature. The most current understanding of creep mainly focuses on the coupled dynamics of point defects and dislocation, which may well describe the first and second stage of creep. However, the behavior of the three stages of creep is jointly controlled by point defect (vacancy) diffusion, dislocation glide, dislocation climb, grain boundary (GB) sliding, and void evolution. A critical knowledge gap still exists regarding how these different creep mechanisms are simultaneously coupled during the three stages of creep. In this work, a multi-physical mechanisms-based crystal plasticity model is proposed to consider the concurrent evolution of point defect, dislocation, GB, and void based on a unified thermodynamic framework. In-situ scanning electron microscope creep experiments and macroscopic creep experiments of Ti-6Al-4V were conducted to validate our model. The in-situ creep experiment directly revealed the GB sliding creep failure behavior of Ti-6Al-4V for the first time. The proposed model well predicts both the microscopic and macroscopic experimental behavior of creep. The contribution of different microstructure evolutions is discussed, and a phase diagram of the dominated creep mechanism is obtained. An in-depth analysis was conducted on the coupling effects and microstructure characteristics of different creep mechanisms. This work not only deepens our understanding of the micro creep mechanism but also offers valuable insights for designing materials with specific microstructures to enhance their creep resistance.

Modeling of subcutaneous injections in soft adipose tissue – a common way to administer pharmaceutical medication – is a challenging multiphysics problem which has recently attracted the attention of the engineering community, as it could help optimize medical devices and treatments. The underlying continuum mechanics of this process is complex and involves finite strain poro-mechanics – where a viscous fluid, containing different charged species, is injected into a porous viscoelastic matrix and absorbed by blood and lymph vessels – as well as electrochemistry, that generates osmotic pressure due to electrical charges attached to the tissue. In this paper, we present a chemo-mechanical model of subcutaneous injections that accounts for the diffusion of electrically charged chemical species – contained in the interstitial fluid – into the tissue, blood and lymph vessels. This work provides the methodology to derive a general theory accounting for the electro-chemo-poro-mechanical couplings in a thermodynamically consistent framework, avoiding phenomenological biases or inconsistencies likely to arise in the derivation of nonlinear theories with many couplings. To motivate its use for the modeling of subcutaneous injections, it is complemented by a simplified, linearized boundary value problem that illustrates the importance of considering these couplings for the prediction of subcutaneous injections key performance indicators.

Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and the supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation mechanics (FDM) theory. The energy density function in our model encodes accepted and simple physical facts related to rocks and granular materials under compression. We work within a 2-dimensional ansatz of FDM where the rupture front is allowed to move only in a horizontal fault layer sandwiched between elastic blocks. Damage via the degradation of elastic modulus is allowed to occur only in the fault layer, characterized by the amount of plastic slip. The theory dictates the evolution equation of the plastic shear strain to be a Hamilton–Jacobi (H-J) equation, resulting in the representation of a propagating rupture front. A Central-Upwind scheme is used to solve the H-J equation. The rupture propagation is fully coupled to elastodynamics in the whole domain, and our simulations recover static friction laws as emergent features of our continuum model, without putting in by hand any such discontinuous criteria in the formulation. Estimates of material parameters of cohesion and friction angle are deduced. Short-slip and slip-weakening (crack-like) behaviors are also reproduced as a function of the degree of damage behind the rupture front. The long-time behavior of a moving rupture front is probed, and it is deduced that equilibrium profiles under no shear stress are not traveling wave profiles under non-zero shear load in our model. However, it is shown that a traveling wave structure is likely attained in the limit of long times. Finally, a crack-like damage front is driven by an initial impact loading, and it is observed in our numerical simulations that an upper bound to the crack speed is the dilatational wave speed of the material unless the material is put under pre-stressed conditions, in which case supersonic motion can be obtained. Without pre-stress, intersonic (supershear) motion is recovered under appropriate conditions.

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

We investigate the role of polycrystalline disorder on the effective ferro-electro-elastic behavior of perovskite ferroelectric ceramics under electro-mechanical loading. Assuming random initial grain orientations, we use high-resolution phase-field simulations and periodic homogenization of two-dimensional model polycrystals to study the evolution of the domain microstructure within and across grains as well as the resulting effective, macroscopic polarization and strain fields under loading. The number of randomly-oriented grains in simulations, at fixed grain size and fixed numerical resolution per grain, is used to control the polycrystalline disorder. Results indicate that, when the polycrystalline samples are sufficiently disordered (i.e., when sufficiently many randomly-oriented grains are considered), their effective electromechanical response under uniaxial compression is stable, and the concomitant polarization and deformation are always aligned with the mechanical load. Thus, the present study supports the viewpoint that polycrystalline disorder in bulk perovskite ceramics stabilizes the overall ferro-electro-elastic response despite the underlying nonconvex polarization energy landscape.

The advent of additive manufacturing technology empowers precise control of multi-material components or specific defects in lightweight lattice metamaterials, however, fracture mechanics and toughening design strategies in such metamaterials remain enigmatic. By incorporating theoretical analysis, numerical simulation, and experimental investigation, our study reveals that stretch-bend synergistic strut deformations caused by bi-material components or topology defects contribute notably tougher lattice structures surpassing its ideal single-material lattices. A peak fracture energy at a critical modulus ratio was found in a designed bi-material lattice composed of triangular soft struts and hexagonal stiff struts, which originates from the shift of fracture modes at crack tip from strut bending to stretching dominated failure modes as the modulus of soft struts increases, where the compromise in competition between bending-enhanced and stretching-weakened energy dissipations of struts deformations results in the maximized fracture energy. A parametric design protocol was proposed to optimize fracture energy of bi-material lattices through tuning the modulus ratio and relative density. Furthermore, the concept of stretch-bend synergistic toughening can also be applied to make tougher single-material lattices with specific topological defects. Our findings not only provide physical insights into directing crack propagation but also provide quantitative guidance to optimize fracture resistance within low-density tough lattice metamaterials.

Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope (AFM) probe. Classical solutions assuming a point load and a fixed edge, which are referred to as Schwerin-type solutions, are commonly used to estimate Young’s modulus of the membrane material out of load–deflection measurements. However, given the widespread experimental evidence for adhesive and frictional contacts between the probe tip and the membrane, as well as sliding between the membrane and its supporting substrate, quantitative investigations of the effects of these interactions are required. In this paper, we formulate a boundary value problem to rigorously model such effects, ensuring relevance to experimental operations. Our numerical analyses reveal that the adhesive effect at the tip-membrane interface diminishes as the indentation depth increases or the tip size decreases. Furthermore, frictional interactions at this interface shift the maximum membrane stress from the center to the tip-membrane contact line with increasing indentation depth and interfacial shear stress. At large indentation depths, the size of the indenter tip and the sliding of the membrane-substrate are found to have a large effect on the indentation load–deflection relationship. Thus, we propose a new approximate formula for this relationship assuming a non-adhesive and frictionless spherical tip of a finite radius and a slippery contact with the supporting substrate. This formula is more accurate than the widely used Schwerin-type solution. It can be used to simultaneously extract the in-plane stiffness of the membrane and the shear strength at the membrane-substrate interface.

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.