Journal of The Mechanics and Physics of Solids最新文献

The foundation of a new concept, coined here as hyperinelasticity, is presented in this work for modelling the isothermal elastic and inelastic behaviours of polymers. This concept is based on the premise that both the elastic and inelastic behaviours of the subject specimen in the primary loading path may be characterised by a single constitutive law derived from a comprehensive deformation energy $W$, akin to hyperelasticity, whose constitutive parameters determine and capture both the elastic and inelastic behaviours without the need for additional flow/yield/damage parameters. This core hyperinelastic model captures the elastic and inelastic behaviours in the primary loading path. It is then further specialised, by augmenting the embedded constitutive parameters in the core model, for capturing the inelasticity of the unloading behaviour and the rate of deformation effects. The former is done by devising and incorporating a discontinuous inelasticity variable into the core function, and the latter is achieved by considering that the core model parameters can evolve with, i.e., be a function of, the deformation rate. Examples of the application of the core and augmented hyperinelastic models to a wide range of extant experimental datasets will be presented, ranging from foams, glassy and semi-crystalline polymers to hydrogels and liquid crystal elastomers. The loading modes encompass both tensile and compressive deformations. With a reduced set of number of model parameters (compared with the existing models in the literature), simplicity of implementation (as essentially a straightforward extension to hyperelasticity), and encouraging accuracy in the modelling results, the concept of hyperinelasticity together with the presented hyperinelastic model are proposed as a unified modelling means for capturing the elastic and inelastic behaviours of polymers.

Laboratory description of clay normally distinguishes the scale of atoms from the scale of clay particles and aggregates. Contemporary constitutive models for clay tend to ignore this scale separation, and rather focus on phenomenology. By considering scale separation, this paper introduces a robust physics-based phenomenological constitutive model for clay that qualitatively captures their broad spectrum of rate-dependent mechanical features. The model is derived using the thoroughly rigorous hydrodynamic procedure. While some imagine that by considering rigour and physics, their models would get complicated, the resulting set of equations reveal a surprising degree of simplicity. The derivation strongly benefits from the principle of two-stage irreversibility, which describes energy flow within the material from the continuum scale down to the atomistic micro-scale, through the meso-scale of clay aggregates. While thermal and meso-related temperatures capture atomistic and clay aggregate fluctuating motions, a sink term from the latter to the former underpins the direction of the energy flow. The model’s standout feature is in pinpointing new transport coefficients that drive both volumetric and shear plastic flows in a thermodynamically coupled manner. A novel scheme is then proposed to calibrate these coefficients from conventional steady-state observations. Thanks to the formulation the model shows a remarkable level of predictiveness, despite being relatively simple mathematically. In particular, the model readily explains the broad spectrum of rate-dependent phenomena during transient loading, along with creep and relaxation processes. Given the generality of hydrodynamics, it is anticipated that the new model could be expanded to capture fluid-solid transitions between liquid-like soft mud and plastic-like stiff clay responses, contingent on water content variations.

Light serves a pivotal function in polymer systems, creating a dynamic interplay with the materials. It initiates various photochemical processes such as polymerization, phase transitions, photo-isomerization, photo-ionization, etc, endowing the polymers with diverse functionalities. Concurrently, as these materials undergo the changes, their shape and optical properties evolve, which also change the light behaviors in terms of reflection, refraction, and propagation. This mutual interaction is intricate and can lead to novel phenomena. Understanding this complex coupling is crucial for generating new insights and paves the way for innovative design possibilities. In this study, we combine principles of geometrical optics with a nonlinear chemomechanical theory to investigate the interdependent effects of light direction and polymer behavior, including reactions and deformations. We apply this framework to a photo-responsive hydrogel, comparing simulation with experimental results to extract necessary material properties and using the calibrated model to propose a new design of an optical fiber actuator through simulations. This example highlights how the interaction between light direction and the hydrogel’s photo-induced swelling governs actuation, and we discuss strategies to leverage this understanding for enhanced control and functionality of such devices. Additionally, we employ the model to analyze the growth morphology of the photo-responsive hydrogel, offering a detailed examination of how these interactive forces contribute to the gel’s photo-induced morphological evolution.

Mechanical metastructures have been prevailing recently owing to their unusual mechanical responses. Despite notable progress in designing periodic metastructures, creating irregular and stochastic metastructures with optimized performance remains challenging because of the enlarged design space. In this study, we introduce a novel approach to realize the unstructured growth of irregular architectures for optimized metastructures. A “growth”-like design scheme is proposed to facilitate random yet controllable growth of predefined building blocks on an unstructured graph toward desired bulk properties. We also formulate a topology optimization framework that simultaneously optimizes building block selection and transformation (scaling, skew, and rotation) to generate metastructures with various optimized mechanical functionalities. These functionalities are achieved by harnessing the diverse homogenized material properties spanned by various frequency combinations of building blocks and the microstructure’s transformations. We discover metastructures that ensure geometric integrity and exhibit explicitly controllable and globally uniform feature sizes beneficial for fabrication. Moreover, the transformation-based topology optimization ensures these metastructures naturally conform to the boundaries of the design domain and can serve as mechanical infills. The proposed approach holds promise for uncovering optimized metastructures applicable across a wide array of engineering applications.

Ice, a quasi-brittle material with a complex crystal organization and found ubiquitously in nature, undergoes an impact fragmentation process that implies a rich physical mechanism, yet remains not thoroughly elucidated. We develop a highly robust and efficient meshless method for fluid–solid coupling, specifically designed to elucidate the mechanisms of crack propagation in S2 columnar ice subjected to high-speed water jet impacts. This method couples a low-dissipation Riemann smooth particle hydrodynamics approach with a non-ordinary state-based peridynamics model,¹ enabling detailed exploration of fracture process. Our theoretical advancements enhance numerical stability at the fluid–solid interface and establish a precise ice constitutive model by capturing the unique hydrostatic pressure-dependent and rate-dependent plasticity within the peridynamics framework, effectively addressing challenges in both fluid and solid phases. Combined with high-velocity water jet impact experiments, this study successfully delineates the initiation and expansion of circumferential and radial cracks in ice plates. We demonstrate that these cracks, both circumferential and radial, originate from tensile failure induced by circular elastic–plastic stress waves initiated by point source shocks. Specifically, circumferential cracks emerge and propagate from the upper to the lower surface driven by radial tensile stress, while radial cracks, motivated by circumferential tensile stress, develop from the lower to the upper surface. This investigation not only provides a foundational understanding of ice impact fracturing but also establishes a versatile theoretical framework applicable to a wide range of quasi-brittle materials.

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

The strength-toughness tradeoff in biological materials such as nacre and bone is essentially due to their stacked microstructures formed by hard and soft phases. In some of these materials, purely soft phase acts as interface layers linking hard phases (platelets), while in some others, hard-phase bridges exist in the soft phase to form a hybrid interface. In order to disclose the selection mechanism of such different interface structures in biological materials, a novel shear-lag model with an interface consisting of alternatively distributed elasto-plastic (soft) and brittle-elastic (hard) segments is proposed. Using this model, solutions of tensile stress and tensile displacement in hard platelets and shear stresses in soft and hard interfacial segments are analytically achieved. Effects of the hybrid interface on the effective mechanical performances of the composite are analyzed, the results of which are well consistent with the existing experimental observations in biocomposites and bio-inspired composites. The most important finding is that the fracture strain of the soft phase has a decisive effect on the selection of a purely soft-phase interface or a hybrid interface of hard and soft phases in stacked biological materials in order to realize a tradeoff between strength and toughness. When the failure strain of the soft phase is relatively small, such as nacre, the purely soft-phase interface is too weak to transfer enough load to the platelet, and hard bridges are necessarily required to reinforce the interface and guarantee an efficient load transfer. When the soft phase has a sufficiently large failure strain, such as bone, the purely soft-phase interface is tough enough to sustain a large shear deformation, realizing an efficient load transfer and adequate utilization of all constituents, while an additional hard bridge is not conducive to the composite toughness due to its reducing effect on the interfacial shear deformation. The results not only help people gain a deeper understanding of the secrets behind the construction of different interfaces in biological materials, but also provide useful guidance for interface optimization design in strong and tough artificial materials.

Many classes of flexible and stretchable bio-integrated electronic systems rely on mechanically sensitive electromagnetic components, such as various forms of antennas for wireless communication and for harvesting energy through coupling with external power sources. This efficient wireless functionality can be important for body area network technologies and can enable operation without the weight and bulky size of batteries for power supply. Recently, antenna designs have received increased attention because their mechanical and electromagnetic properties significantly influence the wireless performance of bio-integrated electronics, particularly under excessive mechanical loads. These mechanical factors are critical for skin-integrated electronics during human motion, as complex skin deformations can damage the conductive traces of antennas, such as those used for near-field communication (NFC), leading to yield or fracture and affecting their electromagnetic stability. Serpentine interconnects have been proposed as a geometric alternative to in-plane circular or rectangular spiral antenna designs to improve the elastic stretchability of the metallic traces in NFC antennas and prevent mechanical fractures. Despite the use of serpentine interconnects within the physiologically relevant strain range for skin (<20 %), the electromagnetic stability of the antennas decreases. This instability, reflected by shifts in resonance frequency and scattering parameters due to inductance changes, reduces the antennas' wireless power transfer efficiency and readout range. Therefore, maintaining the electromagnetic stability of antennas, specifically NFC antennas, under various mechanical deformations has become a critical challenge in practical wireless skin-integrated applications, such as sensing and physiological monitoring. Here, we establish a new mechanics and electromagnetic scaling law that quantifies the inductance changes under strain in a rectangular-loop serpentine structure typically used for NFC wireless communication in stretchable electronics. We present a systematic analysis of the antenna's geometric parameters, material properties of the antenna and substrate, and the applied strain on the inductance change. Our findings demonstrate that the relative change of inductance is solely influenced by the serpentine structure's width-radius ratio, arc angle, aspect ratio of the NFC antennas, and the applied strain. Additionally, under physiological strain conditions for the skin, the relative change of inductance can be minimized to preserve the NFC antenna's performance and prevent mechanical fracture and electromagnetic stability loss.

Displacement-controlled cyclic compressive responses of polycrystalline superelastic NiTi shape memory alloys (SMAs) are investigated at a maximum strain ε_max of 4.2 % and over frequencies ranging from 0.0007 Hz to 50 Hz in stagnant air. Our focus was on understanding the interactions among phase transition (PT), heat transfer and plastic flow of austenite phase during cyclic operation. We monitored temperature oscillations along with stress-strain relations and observed a critical frequency $f_{cri}^{AY}$, below which the responses were primarily influenced by the frequency-dependent coupling between PT and heat transfer, and above which macroscopic plastic deformation of the austenite phase played an important role in the cycling process, interacting with PT and heat transfer. Such interactions at high frequencies ($f>f_{cri}^{AY}$) led to reductions in temperature magnitude, transition strain, latent heat, and hysteresis heat in subsequent cycles, eventually leading to stabilized responses without plastic deformation. Theoretical analysis considering the interactions among PT, heat transfer, and plastic deformation was conducted to interpret and quantify the experimental findings. We find that the initiation and saturation of macroscopic plastic deformation of SMAs due to heat accumulation acted as a negative feedback mechanism in the cyclic responses, preventing the materials from overheating and potential damage in applications.

Living tissues can remarkably adapt to their mechanical and biochemical environments through growth and remodelling mechanisms. Over the years, extensive research has been dedicated to understanding and modelling the complexities of growth. However, the majority of growth laws are based on phenomenological, ad hoc, proposed evolution equations. This work aims to describe a general bulk growth model that developed in the framework of generalised continuum mechanics. This new model of growth is based on a continuum description of the growth process and is an extension of the work of DiCarlo and Quiligotti of the early 2000s. This model builds on the virtual power principle, and the constitutive theory is thermodynamically consistent. The proposed framework allows the inclusion of different constitutive theories linking the elastic strain and stresses, together with accommodating different non-mechanical mechanisms. Moreover, the framework supports anisotropy of both the material and growth, allowing the exploration of complex growth processes further. The descriptive capabilities of the model are demonstrated through numerical benchmarks and simulations describing real-life scenarios, such as the growth of the spine and an artery. The simulation results indicate that the developed thermodynamic consistent growth model is versatile and holds the potential to capture the complexities of living tissue growth, offering valuable insights into biological phenomena and pathologies.