Journal of The Mechanics and Physics of Solids最新文献

We present a multiphysics phase-field fracture model for thermo-elasto-plastic solids in the context of finite deformation and apply it to simulate the hot cracking phenomenon during metal additive manufacturing. The model is derived in a thermodynamically consistent manner, with the intercoupling mechanisms among elastoplasticity, phase-field crack and heat transfer comprehensively considered. It involves particularly coupled parameters among these materials physics, e.g. plasticity-dependent degradation function and fracture toughness, damage-dependent yield surface and thermal properties, and temperature-dependent elastoplastic properties and fracture strength. The finite element implementation of the coupled phase-field model is benchmarked with simulation results of a tensile test of an I-shape specimen, encompassing elastoplasticity, hardening, necking, crack initiation and propagation, in contrast to the related experimental results. The validated model is further employed to simulate the multiphysics hot cracking phenomenon in additive manufacturing in the context of both the effective powder-bed model and the powder-resolved model thanks to prior non-isothermal phase-field powder-bed-fusion simulations. Simulation results reveal certain key features of the hot crack and its dependency on process parameters like beam power and scan speed, which are helpful for the fundamental understanding of crack formation mechanisms and process optimization.

We numerically and experimentally investigate the propagation of mechanical waves in two-dimensional periodic and spatially graded elastic beam lattices. Experiments on metallic lattices admit the characterization of the linear elastic wave dispersion over a wide range of frequencies, resulting in complete, experimentally-constructed dispersion surfaces in excellent agreement with predictions obtained from finite element-based Bloch wave analysis. While Timoshenko beam theory is shown to be sufficiently accurate for predicting the lowest modes, experiments prove that solid finite elements are required to capture the dispersion relations at higher frequencies as well as when mode coupling occurs. Based on an improved numerical procedure, group velocity maps further highlight the directionality of wave dispersion and allow for the simple identification of bandgaps. In addition to classically studied periodic trusses, we extend the framework to spatially graded structures and demonstrate acoustic rainbow trapping in beam lattices undergoing out-of-plane vibrations. Our experiments confirm broadband vibration attenuation of the typical meta-wedge type previously observed only in optics and few mechanical studies. Results further show convincing agreement between Bloch theory-based predictions, finite element simulations, and experimental measurements. Such spatially-variant architected lattices show great promise for steering the motion of elastic waves in applications from wave guiding and wave shielding to energy harvesting.

Recent studies on magnetically hard, particle-filled magnetorheological elastomers ($h$-MREs) have revealed their stretch-independent magnetization response after full pre-magnetization. We discuss this phenomenon, focusing on incompressible, isotropic, particle-filled $h$-MREs. We demonstrate that the fully dissipative model of Mukherjee et al. (2021) for arbitrary loads can be reduced, under physically consistent assumptions, to the energetic model of Yan et al. (2023), but not that of Zhao et al. (2019). The latter two are valid for small magnetic fields around an already known pre-magnetized state. When the pre-magnetized $h-$MRE undergoes non-negligible stretching, the Zhao et al. (2019) model yields predictions that disagree with experiments due to its inherent stretch-dependent magnetization response. In contrast, the Mukherjee et al. (2021) and Yan et al. (2023) models are able to accurately capture this important feature present in pre-stretched $h$-MREs. However, for inextensible slender structures under bending deformation, where stretching is negligible, the Zhao et al. (2019) model provides satisfactory predictions despite its underlying assumptions. Our analysis reveals that, in the fully dissipative model, magnetization can be related to an internal variable but cannot be formally used as one, except for ideal magnets, and is subject to constitutive assumptions. Furthermore, the magnetization vector alone is insufficient to describe the magnetic response of an MRE solid; the introduction of one of the original Maxwell fields is necessary for a complete representation.

Micro-organisms propel themselves in viscous environments by the periodic, nonreciprocal beating of slender appendages known as flagella. Active materials have been widely exploited to mimic this form of locomotion. However, the realization of such coordinated beating in biomimetic flagella requires complex actuation modulated in space and time. We prove through experiments on polyelectrolyte hydrogel samples that directed undulatory locomotion of a soft robotic swimmer can be achieved by untethered actuation from a uniform and static electric field. A minimal mathematical model is sufficient to reproduce, and thus explain, the observed behavior. The periodic beating of the swimming hydrogel robot emerges from flutter instability thanks to the interplay between its active and passive reconfigurations in the viscous environment. Interestingly, the flutter-driven soft robot exhibits a form of electrotaxis whereby its swimming trajectory can be controlled by simply reorienting the electric field. Our findings trace the route for the embodiment of mechanical intelligence in soft robotic systems by the exploitation of flutter instability to achieve complex functional responses to simple stimuli. While the experimental study is conducted on millimeter-scale hydrogel swimmers, the design principle we introduce requires simple geometry and is hence amenable for miniaturization via micro-fabrication techniques. We believe it may also be transferred to a wider class of soft active materials.

A brittle glassy polymer can be made ductile by forming a nanocomposite with a rubbery polymer. This paper investigates a nanocomposite of poly(methyl methacrylate) (PMMA) and poly(ethyl acrylate) (PEA). Pure PMMA is a brittle glass, pure PEA is a rubber, and a PEA-PMMA nanocomposite is ductile. We fabricate the nanocomposite by swelling PEA with MMA monomer, followed by polymerizing MMA. We prepare nanocomposites of various weight fractions of PMMA and measure their properties, including modulus, yield strength, fracture strain, fracture strength, work of fracture, and toughness. Whereas bulk PMMA fractures at a strain of ∼0.05 by localizing inelastic deformation in crazes, the PEA-PMMA nanocomposite can be stretched several times its original length with homogeneous deformation. The nanocomposite separates into a glassy phase and a rubbery phase. For a nanocomposite of 45 % weight fraction of PMMA, atomic force microscopy shows that the two phases are bicontinuous and the phase size is at ∼20 nm. For the nanocomposite to undergo large deformation, the continuous glassy phase must accommodate. Our experiments exclude the mechanism that the glassy phase in the nanocomposite breaks into small pieces. Rather, the glassy phase in the nanocomposite is itself ductile. We discuss the molecular picture of this ductility.

We introduce a multiscale mechanics model for analyzing the elastic properties of super-strong densified wood (DW). Our model incorporates microstructural features such as microfibril angle and densification ratio, along with chemical parameters including degree of polymerization, crystallinity, and density of hydrogen bonds. At the nanoscale and microscale, the elastic properties of cellulose nanofibril and cell wall layers are derived analytically using the mechanics of composite materials. Finite element simulations based on representative volume elements are conducted at the mesoscale to obtain homogenized effective elastic properties at the macroscale. Our quantitative investigations validate that microstructural changes and alterations in chemical components significantly enhance DW's mechanical performance. Densification and chemical changes, especially increased cellulose content and reduced lignin, emerge as vital mechanisms for strengthening DW. The model's insights offer valuable guidance for optimizing the two-step preparation process of DW to achieve superior mechanical performance. Additionally, the versatility of the model allows for exploring the influence of cell dimensions and potential applications in designing bioinspired materials.

With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids not just under monotonic but under general loading conditions, this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary non-monotonic quasistatic loading conditions, which include monotonic and cyclic loadings as special cases. Centered around experimental observations, the idea consists in: ($i$) viewing the critical energy release rate $G_c$ not as a material constant but rather as a material function of both space $X$ and time $t$, ($ii$) one that decreases in value as the loading progresses, this solely within a small region ${\Omega }_{\ell }\left(t\right)$ around crack fronts, with the characteristic size $\ell$ of such a region being material specific, and ($iii$) with the decrease in value of $G_c$ being dependent on the history of the elastic fields in ${\Omega }_{\ell }\left(t\right)$. By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.

When subjected to mechanical, thermal, or other loads, film–substrate systems may undergo complex cracking behaviors, which encompass film and substrate cracking, interfacial debonding, and their combinations, exhibiting rich fracture patterns, such as three-dimensional helical cracks. Identifying the mechanisms underlying these fracture phenomena may lead to more advanced strategies for technologically significant applications. In this paper, we develop an interfacial cohesive peridynamic method for fracture analysis of multiple-phase materials. Particularly, we focus on the modeling of coupled film cracking and interfacial debonding in film–substrate systems. By introducing cohesive interfacial bonds to describe the mechanical properties of the interfaces and adopting a displacement-based cohesive failure criterion, the model is able to predict the critical condition and path of interfacial crack propagation. The robustness of the interfacial cohesive peridynamic method is validated through a series of representative examples. We also demonstrate its efficacy in simulating three-dimensional cracks and identify the essential role of the interfacial energy release rate in controlling the cracking mode transition from a restricted pattern to a helical pattern. The numerical predictions of cracking paths and stress distributions agree well with the previous experimental results. This study provides a valuable tool for analyzing different cracking patterns in film–substrate systems and composite materials.

This paper presents a fully coupled thermo-mechanical peridynamic model for simulating interactive thermo-mechanical material responses and thermally induced fracturing of solids. A temperature-dependent constitutive model and a deformation-dependent heat conduction model are derived for state-based peridynamic formulation. The dispersion relation and truncation error of the state-based peridynamic heat equation are analyzed for the first time. It is found that as non-locality becoming more pronounced, the dissipative rate of heat is reduced, and the truncation error becomes larger. A small horizon can effectively mitigate oscillation while reducing the error in the temperature field. For coupled thermo-mechanical modeling, a novel multi-horizon scheme is introduced where the thermal field is solved with a different horizon than that of the mechanical field. The multi-horizon scheme allows for the implementation of a distinct degree of non-locality for different physical field. Comparing with the constant-horizon scheme, we demonstrate through numerical examples that the multi-horizon scheme offers smoother and more accurate solutions and serves a promising option for peridynamics-based multi-physics simulations.

A contemporary semiconductor device often contains multiple chips. Corners of the chips concentrate stress, and are principal sites to initiate failure. Here we propose to characterize the corners using a double cantilever beam, in which two silicon beams sandwich a row of chips. As the two beams are pulled open, a crack initiates at the corner of a chip, and runs unstably on the interface between the chip and a beam. The crack may or may not arrest, depending on various experimental conditions. We calculate energy release rate as a function of crack length by using a combination of finite element method and an analytical solution of the singular field around a corner. At a fixed applied displacement, the energy release rate is low for a short crack, peaks for a crack of intermediate length, and drops for a long crack. This non-monotonic behavior explains how a crack initiates, grows unstably, and possibly arrests. If the crack does arrest, as the two beams open further, the crack grows stably. We relate the initiation and arrest of the crack to machine compliance, specimen geometry, and flaw size. The force at which the crack initiates can be used to characterize the manufacturing process, whereas the stable growth of the crack can be used to measure interfacial toughness. It is hoped that this work will aid the development of multi-chip semiconductor devices.