Showing papers in "Journal of The Mechanics and Physics of Solids in 2023"
TL;DR: In this article , the authors proposed a new micro-macro transition for the microstructural hyperelasticity modeling, which is further integrated into the full network framework and achieved remarkable success in capturing the stress responses in multi-axial deformation modes for soft materials with an absence of strain stiffening effect.
Abstract: Many classic hyperelastic models fail to predict the stress responses of soft materials in complex loading conditions with parameters calibrated through one simple test. To address this fundamental issue, we propose a new micro–macro transition for the microstructural hyperelasticity modeling, which is further integrated into the full network framework. With a Gaussian chain distribution, this new mapping scheme yields an explicit one-parameter hyperelastic model in terms of principal stretches. This new linear model achieves remarkable success in capturing the stress responses in multi-axial deformation modes for soft materials with an absence of strain stiffening effect, which is beyond the capability of the widely used neo-Hookean model. A new two-parameter hyperelastic model is further developed by combining the new micro–macro transition and non-Gaussian Langevin chain distribution. Compared with other two-parameter hyperelastic models based on Langevin statistics, such as the eight-chain model, affine full network model, and equilibrated microsphere model, our new model exhibits greatly improved predictive ability for complex loading types. The new model is also implemented for finite element analysis, which shows the ability to capture the responses of soft materials with heterogeneous strain distribution. In all cases, the parameters in our models can be determined through the data of uniaxial loading tests, along with the behaviors in other loading modes being well forecast, which is a challenge for various other existing hyperelastic models. This novel micro–macro transition is shown to properly capture the inherent correlations between different deformation modes, which may advance fundamentally modeling hyperelasticity and other constitutive behaviors for soft materials.
7 citations
TL;DR: In this paper , the authors embed physical principles into machine learning (ML) architectures to evaluate and compare ML frameworks against benchmark datasets, and to test their broader extensibility, which enables ML models with a wide range of architectures to be compared, compared, evaluated, and extended to broader experimental and computational frameworks.
Abstract: Experimental solid mechanics is at a pivotal point where machine learning (ML) approaches are rapidly proliferating into the discovery process due to significant advances in data storage and processing capabilities. Much of the ML that is being adopted by the mechanics community was initially developed for application outside of science and engineering, and has the potential to produce results of questionable physical validity. To ensure that these data-driven approaches are trustworthy, there is a clear need to embed physical principles into their architectures, to evaluate and compare ML frameworks against benchmark datasets, and to test their broader extensibility. Frameworks must be grounded in a clear objective, quantifiable error, and a well-defined scope of extensibility. These principles enable ML models with a wide range of architectures to be meaningfully categorized, compared, evaluated, and extended to broader experimental and computational frameworks. Application of these principles are demonstrated through an investigation of ML models in two different use cases, acoustic emission and resonant ultrasound spectroscopy, along with a discussion of outlooks for the future of trustworthy ML in experimental mechanics.
6 citations
5 citations
TL;DR: Wang et al. as discussed by the authors proposed a wrinkling-assisted strategy to substantially facilitate the delamination at desired regions of the bilayer film/substrate system, which can enable the assembly of highly flexible 3D mesostructures and those with large areas attached to the substrate in the initial configuration, which are particularly challenging to achieve by using previous strategies.
Abstract: Mechanically-guided three-dimensional (3D) assembly is a recently established method for the fabrication of 3D structures and devices at micro/nanoscale. Such assembly methods typically involve a process of compressive buckling in a patterned high-modulus thin film integrated with a low-modulus elastomer substrate at selective regions. A successful assembly requires, simultaneously, a sufficiently strong interface in selective regions to stay undelaminated, and a sufficiently weak interface in remaining regions to be fully separated. However, such requirements are very challenging to meet for highly flexible 3D mesostructures or those with large-area suspended features. Here, we propose a wrinkling-assisted strategy to substantially facilitate the delamination at desired regions of the film/substrate system. An additional assisting layer is introduced such that a weaker film/assisting-layer interface replaces the original film/substrate interface, and the wrinkles formed in the assisting layer induce additional driving forces to separate the film/assisting-layer interface. An analytical model is developed to capture the delamination of the thin film from the wrinkled assisting layer, which is validated by both experiments and finite element analyses (FEA). The model shows that a combined material/geometry parameter governs the process of delamination in the bilayer film/substrate system, offering a useful design reference for the mechanically-guided 3D assembly. Furthermore, our experiments and FEA demonstrate that the wrinkling-assisted strategy can enable the assembly of highly flexible 3D mesostructures and those with large areas attached to the substrate in the initial configuration, which are particularly challenging to achieve by using previous strategies.
5 citations
TL;DR: In this paper , the authors presented integrated electromigration (EM) studies through experiment, theory, and simulation, where extensive EM tests were performed using Blech and standard wafer-level electromigration acceleration test (SWEAT)-like structures, which were fabricated on four-inch wafers.
Abstract: This paper presented integrated electromigration (EM) studies through experiment, theory, and simulation. First, extensive EM tests were performed using Blech and standard wafer-level electromigration acceleration test (SWEAT)-like structures, which were fabricated on four-inch wafers. Second, a molecular dynamics (MD) simulation-based diffusion-induced strain was incorporated into the existing coupled theory. Third, one-dimensional (1D) governing equations in terms of atomic concentration for un-passivated and passivated configurations were derived for void formation and growth, using a modified Eshelby's solution to consider the effect of passivation. Fourth, a systematic approach was established, including theoretical formulations and experimental methods, to obtain key material properties, i.e., critical atomic concentration and diffusivity. We then determined the material's properties from a specific set of experimental data, using aluminium (Al) as a carrier for demonstration. These properties were then used to predict the time to failure and void growth under various conditions. The theoretical results agreed well with the experimental data. Moreover, we theoretically determined the critical threshold products of current density and conductor length for the un-passivated and passivated configurations, respectively. Both experiment and theory showed that, in the absence of mechanical stress in un-passivated configurations, the atomic self-diffusion, which was opposite to electron wind, was significant in resisting EM development. However, when mechanical stress was present, such as in passivated configurations, stress migration played a dominant role in resisting EM development. Our numerical results showed that the current density exponent n in Black's law remained as 2 in the range of the current density greater than 0.2 MA/cm2 and rapidly approached infinity at a low level of current density.
5 citations
TL;DR: In this article , the authors formulated a time-dependent damage theory for rocks subjected to mechanical deformation and solid dissolution, which is inspired by the transition state theory, which states that the rate of dissolution is a function of the reactive surface area measured through the crack density in the volume.
Abstract: We formulate a time-dependent damage theory for rocks subjected to mechanical deformation and solid dissolution. The constitutive description is inspired by the transition state theory, which states that the rate of dissolution is a function of the reactive surface area measured through the crack density in the volume. We use a gradient-enhanced damage framework in which damage depends on the deformation of the material as well as on the amount of solid mass dissolved over time. The gradient-enhanced formulation is characterized by a three-field variational formulation with the solid displacement, nonlocal equivalent strain, and nonlocal rate of solid dissolution as the basic state variables. Traditionally, time-independent damage theories have only allowed damage to increase with increasing external load. In the proposed framework, the degree of damage may increase due to solid dissolution even when the external load is held fixed. In this way, solid dissolution is viewed as a process that is responsible for bringing about rate-dependent effects such as creep and stress-relaxation, which are two common features of geomaterial behavior.
4 citations
TL;DR: In this paper , a micromechanical model was developed to quantify the evolution of visco-hyperelastic responses with water content of polyacrylamide (PAAm) hydrogels.
Abstract: Hydrogels without special treatment would lose water dramatically, which significantly alters their properties. No physically-based constitutive models have been developed so far to quantify the evolution of visco-hyperelastic responses with water content of hydrogels. In this work, systematical experiments are performed on polyacrylamide (PAAm) hydrogels with varied water content. The results reveal that the increase of modulus caused by deswelling is much more pronounced than the decrease of modulus caused by swelling. A more significant strain-softening phenomenon and a transition from almost pure hyperelastic behaviors to apparent viscoelastic behaviors are observed as the water content decreases. To fully capture the experimental observations, a micromechanical model is developed. In this model, the rate-independent hyperelastic response comes from the contributions of both cross-linked networks and entanglements, while the rate-dependent viscoelastic response arises from the reptation of free chains. The relations between model parameters (e.g., cross-linked shear modulus, entangled shear modulus, and relaxation time) and water content are further derived using the scaling law in polymer physics. The developed visco-hyperelastic model exhibits remarkable prediction ability for PAAm hydrogels with a wide water content distribution. The finite element analysis also verifies that the model can describe the mechanical responses of hydrogels in complex loading conditions. The current work deepens our fundamental understanding on the effect of water content on mechanical behaviors of hydrogels. It also provides an efficient theoretical framework to predict the performance of hydrogels in practical applications.
4 citations
3 citations
3 citations
TL;DR: In this paper , second-order mechanical topological insulators (SMTIs) implemented by mechanical metamaterials are systematically investigated in the rectangular lattice, the kagome lattice and the square lattice.
Abstract: Recently, higher-order topological insulators (HOTIs) as a novel frontier of topological phases of matter have been induced in mechanical systems, opening new routes to manipulate the propagation of elastic waves. Here, second-order mechanical topological insulators (SMTIs) implemented by mechanical metamaterials are systematically investigated in the rectangular lattice, the kagome lattice, the square lattice and the hexagonal lattice. The mechanical metamaterials are constructed from the generalized 2D Su–Schrieffer–Heeger (SSH) models. The topological mechanical metamaterials are characterized by the theories of topological indices and Wannier centers. With simulations and experiments, the corner states and edge states are observed in the topological mechanical metamaterials. Interestingly, the numbers of corner, edge and bulk states are respectively equal to the number of sites located at the corners, edges and bulk. This work offers an inspiring and unified model to study the higher-order topology in mechanical systems, and provides a new way for designing functional and integrated topological devices.
2 citations
TL;DR: In this article , the impact of hard magnetics on the fracture behavior of ultra-soft magnetorheological elastomers (MREs) was investigated and it was shown that MREs with remanent magnetisation have up to a 50 % higher fracture toughness than non pre-magnetised samples.
Abstract: Pre-existing flaws in highly stretchable elastomers trigger fracture under large deformations. For multifunctional materials, fracture mechanics may be influenced by additional physical phenomena. This work studies the implications of hard magnetics on the fracture behaviour of ultra-soft magnetorheological elastomers (MREs). We experimentally demonstrate that MREs with remanent magnetisation have up to a 50 % higher fracture toughness than non pre-magnetised samples. Moreover, we report crack closure due to the magnetic field as a mechanism that delays the opening of cracks in pre-magnetised MREs. To overcome experimental limitations and provide further understanding, a phase-field model for the fracture of MREs is conceptualised. The numerical model incorporates magneto-mechanical coupling to demonstrate that the stress concentration at the crack tip is smaller when the MRE is pre-magnetised. Overall, this work unveils intriguing applications for functional actuators, with better fracture behaviour and potential better performance under cyclic loading.
TL;DR: In this article , a light-gas gun is used to fire a conical nosed cylindrical projectile that impacts axially on a thin-walled tube fabricated by 3D printing.
Abstract: In this paper, we have developed and demonstrated a novel high-velocity impact experiment to study dynamic fragmentation of additively-manufactured metals. The experiment consists of a light-gas gun that fires a conical nosed cylindrical projectile, that impacts axially on a thin-walled cylindrical tube fabricated by 3D printing. The diameter of the cylindrical part of the projectile is approximately twice greater than the inner diameter of the cylindrical target, which is expanded as the projectile moves forward, and eventually breaks into fragments. The experiments have been performed for impact velocities ranging from ≈180m/s to ≈390m/s, leading to strain rates in the cylindrical target that vary between ≈9000s-1 and ≈23500s−1. The cylindrical samples tested are printed by Selective Laser Melting out of aluminum alloy AlSi10Mg, using two printing qualities, with two different outer diameters, 12 mm and 14 mm, and two different wall thicknesses, 1 mm and 2 mm. A salient feature of this work is that we have characterized by X-ray tomography the porous microstructure of selected specimens before testing. Three-dimensional analysis of the tomograms has shown that the initial void volume fraction of the printed cylinders varies between 1.9% and 6.1%, and the maximum equivalent diameter of the 10 largest pores ranges from 143μm to 216μm, for the two different printing conditions. Two high-speed cameras have been used to film the experiments and thus to obtain time-resolved information on the mechanics of formation and propagation of fractures. Moreover, fragments ejected from the samples have been recovered, sized, weighted and analyzed using X-ray tomography, so that we have obtained indications on the effect of porous microstructure, specimen dimensions and loading velocity on the number and distribution of fragment sizes. To the authors’ knowledge, this is the first paper (i) providing a systematic experimental study (34 impact tests) on the fragmentation behavior of printed specimens, and (ii) including 3D reconstructions of dynamic cracks in porous additively-manufactured materials.
TL;DR: In this paper , a temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature.
Abstract: The motion of dislocations governs the plastic deformation of crystalline materials, which in turn determines the mechanical properties. The complex thermal history, large temperature gradients and high cooling rates during the process of additive manufacturing (AM) can induce high dislocation density and unique dislocation structures in the material. The origin of these dislocation structures and their stability during mechanical loading are debated. A novel temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature. The CDD model is fully coupled with a crystal plasticity solver, which captures the plastic deformation induced by the dislocation motion. A hybrid continuous and discontinuous Galerkin formulation is developed to accurately reproduce the dynamics of highly discontinuous dislocation density fields that are typical of dislocation structures. A multiscale modeling approach is used, in which the thermally induced deformation in specific grains of a polycrystal is extracted from larger scale crystal plasticity simulations of the laser powder-bed fusion process, and is then used for single crystal scale dislocation dynamics simulations. Simulation results reveal the dynamics of dislocation structure formation in grains at different positions during laser scanning and cooling stages. The effect of the cyclic thermal stress during multi-layer AM fabrication is also investigated. The simulations provide a new perspective on the specific conditions that should be satisfied during AM process for the formation of stable dislocation structures.
TL;DR: In this paper , the authors take advantage of texture engineering with incorporation of grain boundary (GB) strengthening and gradient microstructure design to achieve a more desirable strength-ductility synergy.
Abstract: The strength–ductility trade-off has been a long-standing dilemma for polycrystalline metals. Though many strategies such as introduction of gradient and twinned microstructure have been proposed to overcome the strength–ductility trade-off of nanocrystalline (NC) metals, a higher strength–ductility synergy is always called for. Here schemes taking advantage of texture engineering with incorporation of grain boundary (GB) strengthening and gradient microstructure design are proposed to achieve a more desirable strength–ductility synergy. Taking into account the size-dependent storage of dislocations in grains, GB sliding, and evolution of the void volume fraction, crystal plasticity finite element simulations incorporating the Gurson-type model are performed to reveal the mechanisms underlying the low ductility and strength–ductility trade-off of NC metals. Low GB strength and nonmonotonic variation of dislocation storage ability with respect to the grain size are revealed as the dominant factors responsible for the low ductility and the strength–ductility trade-off in NC metals. The speculation that there exists a most brittle grain size for NC metals is confirmed. It is also found that the ductility of NC metals is governed by the GB damage and the ability of intragranular dislocation storage at high GB strength. Moreover, it is shown that the failure tensile strain for cube-textured NC copper at a certain grain size could be more than twice the failure tensile strain for untextured one at high GB strength.
TL;DR: In this article , a model based on the formation of a dislocation dipole across the precipitate thickness was developed to explain the observed strengthening. But the model is restricted to Orowan looping with parallel plate-like precipitates rather than a single critical dislocation geometry.
Abstract: Many common engineering alloys are strengthened by precipitates with plate-like geometries. The mechanics of precipitation strengthening, while well resolved with spherical precipitates, are less well understood for plate-like geometries. In this work, we employ discrete dislocation dynamics simulations to study precipitation strengthening by θ′ precipitates in AlCu. We show that Orowan looping with parallel plate-like precipitates can be fundamentally different from spheres because it is governed by a steady-state glide process rather than a single critical dislocation geometry. We develop a model based on the formation of a dislocation dipole across the precipitate thickness to explain the observed strengthening. Finally, we show that while the precipitate misfit field can lead to both strengthening and weakening, strengthening is more common because of the steady-state process by which Orowan loops form.
TL;DR: In this paper , the anisotropic cryogenic ductile and cleavage fracture properties of a body-centered cubic (bcc) steel at −196°C have been investigated under a broad spectrum of loading conditions, crossing stress triaxiality range from −1/3 to 1.5, and along three loading directions.
Abstract: The anisotropic cryogenic ductile and cleavage fracture properties of a body-centered cubic (bcc) steel at −196°C have been investigated under a broad spectrum of loading conditions, crossing stress triaxiality range from −1/3 to 1.5, and along three loading directions. Fracture is completely impeded in uniaxial compression tests. Conventional brittle behavior is only observed in high triaxiality conditions for the investigated bcc steel, and on the contrary ductile fracture with shear and void coalescence as underlying mechanisms takes place in low (simple shear) and moderate triaxiality (uniaxial tension) at −196°C. Cleavage fracture occurs after significant plasticity at −196°C under moderate triaxiality conditions during tensile tests using flat-notched specimens under plane-strain tension. For all the stress states, anisotropy has shown a profound influence in ductile fracture, brittle fracture, and, particularly in the transition region mixed with two failure types. It is concluded that the reason for the anisotropic transition of activated failure mechanisms crossing stress states at −196°C is because strain hardening capacity, Lankford coefficients, fracture initiation strain as well as cleavage fracture strength are all dependent on loading orientations. Based on the collected local critical stress and strain variables from finite element simulations using an evolving anisotropic plasticity model, an anisotropic unified fracture criterion revealing the underlying failure mechanisms is developed and demonstrates distinguished predictive capability in describing cryogenic ductile and cleavage fracture properties under different stress states and loading directions.
TL;DR: In this paper , the authors investigated whether a more accurate calibration of a material model could be obtained by considering not only the global behaviour of the specimen, but also the local strain-time response calculated from full-field displacement information obtained using digital image correlation.
Abstract: Tensile tests are often used as part of material characterisation strategies; however, the observed deformation is often complex, and it can be difficult to distinguish the underlying material behaviour from the structural response of the specimen. The objective of the research in this paper was to investigate whether a more accurate calibration of a material model could be obtained by considering not just the global behaviour of the specimen, but also the local strain-time response calculated from full-field displacement information obtained using digital image correlation. Tensile experiments were performed using ISO standard, flat, dog bone specimens. Optical and infra-red imaging were used to calculate full field displacement and temperature maps, and a finite element model of the experiment was produced. These were combined with compression test data from the same material to calibrate a constitutive model, which was shown to describe well the deformation and temperature rise in the specimen. The research demonstrates that it is insufficient to use force-displacement information from tensile experiments to calibrate, or validate, constitutive models of polymers. Further, it demonstrates a more applicable method, which could be further automated in the future.
TL;DR: In this article , a simple, intuitive assumption for how the network locally rotates relative to applied loading (e.g. stresses, external fields) is proposed. And the new assumption is then shown to make more intuitive predictions (than prior models) for stimuli-responsive networks with orientational energies (e.,g. electroactive polymers), which is significant for shape morphing and designing high degree of freedom actuators (e,g. for soft robotics).
Abstract: Polymer network models construct the constitutive relationships of a broader polymer network from the behavior of a single polymer chain (e.g. viscoelastic response to applied forces, applied electromagnetic fields, etc.). Network models have been used for multiscale phenomena in a variety of contexts such as rubber elasticity, soft multifunctional materials, biological materials, and even the curing of polymers. For decades, a myriad of polymer network models have been developed with differing numbers of chains, arranged in different ways, and with differing symmetries. To complicate matters further, there are also competing assumptions for how macroscopic variables (e.g. deformation) are related to individual chains within the network model. In this work, we propose a simple, intuitive assumption for how the network locally rotates relative to applied loading (e.g. stresses, external fields) and show that this assumption unifies many of the disparate polymer network models--while also recovering one of the most successful models for rubber elasticity, the Arruda-Boyce $8$-chain model. The new assumption is then shown to make more intuitive predictions (than prior models) for stimuli-responsive networks with orientational energies (e.g. electroactive polymers), which is significant for shape morphing and designing high degree of freedom actuators (e.g. for soft robotics). Lastly, we unveil some surprising consequences of the new model for the phases of multistable biopolymer and semi-crystalline networks.
TL;DR: In this article , three kinds of postbuckling paths, including continuous buckling, snap-through, and snap-back, are discovered, and two phase diagrams of the critical stretch for the onset of buckling are presented.
Abstract: While the buckling of tubes under axial compression has been extensively studied, the postbuckling behavior of thick tubes remains elusive. In this paper, we conduct three-dimensional buckling and postbuckling analysis for thick hyperelastic tubes subjected to axial compression under finite deformation by the asymptotic expansion method. Our theoretical results successfully predict the deformation and stress-strain curves of buckled tubes near the critical loading, which are well validated by finite element analysis. Depending on the geometry, three kinds of postbuckling paths, including continuous buckling, snap-through and snap-back, are discovered. We summarize our results in two phase diagrams of the critical stretch for the onset of buckling and postbuckling paths with respect to the geometric parameters. In particular, we have observed that the postbuckling response can undergo a complex transition among different types of postbuckling paths, including continuous buckling, snap-through and snap-back, which is attributed to the competition between two modes of deformation, i.e., global deformation and local distortion. When a tube is long and thick, it prefers global deformation, and its cross section remains almost a plane after buckling, whereas when a tube is relatively short and relatively thin, it prefers local distortion and its cross section does not remain a plane any more after buckling. Our work provides understanding and insights into the buckling and postbuckling of thick tubes, and bridges the knowledge gap between postbuckling of thick columns and tubes.
TL;DR: In this paper , a finite-deformation theory for magneto-viscoelasticity of hard-magnetic soft-elastomeric materials is proposed and numerically implemented in a finite element program.
Abstract: Hard-magnetic soft-elastomeric materials show great potential for use in applications where the ability of remote actuation, together with high-flexibility and low-weight are important. One promising type of magnetic-actuator made from such a material is a bistable arch which can can harness snap-through instabilities for short response times and high actuation forces. In this paper we formulate a continuum finite-deformation theory for magneto-viscoelasticity of hard-magnetic soft-elastomeric materials. We have numerically implemented the theory in a finite element program. We show that our theory, when suitably calibrated, can reproduce the results from several magnetically-induced snap-through experiments on a bistable arch reported recently by Tan et al. (2022). Finally, we demonstrate the broader usefulness of our theory and its numerical implementation by successfully simulating the complex and reversible magnetically-induced snap-through eversion of a hemispherical shell.
TL;DR: In this paper , the authors reported the first in-operando spectro-mechanical characterization of elastomeric polymers (polyurea is used as a representative material) loaded at high strain rate using bulk terahertz spectroscopy synchronized in real-time with laser-induced shock wave setup.
Abstract: Temporary and permanent macromolecular conformational changes can accompany the deformation of elastomers under high strain rate loading. Mechanical failure can occur as spallation, volumetric cracking, subsurface morphological changes, and plastic deformations. While high strain rate loading has been extensively reported using various loading mechanisms, where the current state-of-the-art relies on cascading failure and spectroscopic analyses after mechanical loading. In recent years, in-situ spectro-mechanical characterization, entailing concurrent spectroscopic interrogation and mechanical loading, has interested the scientific community in avoiding destructive evaluations in favor of noninvasive characterization, preferably during loading. To overcome the current limitations, this paper reported the first in-operando spectro-mechanical characterization of elastomeric polymers (polyurea is used as a representative material) loaded at high strain rate using bulk terahertz spectroscopy synchronized in real-time with laser-induced shock wave setup. Spectroscopic terahertz signals were collected concurrently with the imposition of shock waves based on the exfoliation of a sacrificial metallic layer using a high-energy laser pulse with nanosecond duration. The shock-loaded samples were also characterized using the scanning electron microscope, revealing signs of plastic deformations and morphological failure throughout the cross-section, including evidence of crazing and vitrification separately. Multifaceted time and frequency domain analyses elucidated the conformational changes, including spectral peak shifting, enhancement, manifestation, and concealment. The time domain analysis leveraged the dynamic time wrapping approach to quantify the temporal disparity between terahertz signals collected from unloaded, during shock, and loaded samples by calculating the Euclidean distances among signal pairs. Microscopy revealed morphological changes that corroborated the terahertz spectral differences at several energy fluences. Finite element analysis was performed to assess the levels of stresses and strains as a function of the energy fluence from focusing the high-energy laser illumination onto the sacrificial energy layer. The stresses at the depths of failure determined using electron microscopy, corresponded to the tensile strength of the material. The present results demonstrate the viability of the spectro-mechanical characterization of polymers using terahertz-based spectroscopy and laser-induced shock wave, contributing to a new experimental paradigm in polymer mechanics under shock loading.
TL;DR: In this article , a model for the geometry of arrays of needles and numerical simulations for two compound twinned variants of martensite in a plane stress setting are presented, where the main finding is the transparency effect, which characterizes the effect of needles on domain boundaries located in front of their tip.
Abstract: Shape-memory alloys exhibit a rich microstructure, characterized by large regions containing relatively regular laminates mixing different martensitic variants. Macrointerfaces separate these regions, and are often composed of arrays of needle-shaped martensitic domains. We formulate a model for the geometry of arrays of needles and present numerical simulations, appropriate for two compound twinned variants of martensite in a plane stress setting. One important ingredient is a new class of polyconvex energy densities with cubic symmetry, that is able to reproduce the austenitic elastic constants of the relevant materials. The energy-minimizing needle geometry is determined with tools from shape optimization. Our main finding is the “transparency effect”, which characterizes the effect of needles on domain boundaries located in front of their tip. Our numerical results are in good agreement with experimental observations.
TL;DR: In this paper , a double phase-field model for coupled spall and adiabatic shear banding, which are two kinds of typical dynamic ductile fracture, is realized with a unified phase field theory for two coupled fracture types.
Abstract: In this work, a unified phase field theory for two coupled fracture types is proposed. Compared with the existing unified phase field theory for single fracture type, it considers the coupling behavior between different fracture types and is consistent with the single fracture type theory when one type of fracture is suppressed. Based on a new form of energy decomposition, that is, the strain energy is decomposed into deviatoric, tensile volumetric and compressive volumetric parts, and specifying the driving energy for each fracture type, a double phase-field model for coupled spall and adiabatic shear banding, which are two kinds of typical dynamic ductile fracture, is realized with the proposed unified phase field theory for two coupled fracture types. This coupled model can be used to predict the potential spall and adiabatic shear banding failures in ductile metals under dynamic loading, revealing the corresponding fracture types under different loadings without any additional criteria. The entire damage and fracture evolution (that is, from damage evolution, through crack expansion, and to fragmentation) are captured with this unified phase-field modeling framework. In addition, as an advantage of the double phase-field model, the complex multicrack distributions of spall and adiabatic shear bands in ductile metals can be presented with the proposed model. Based on these features, the expanding characteristics of complex cracks in metallic expanding shells are numerically studied. It is found that, if multilayer spall occurs, the specimen tends to fracture into three layers, that is, a complete spall layer, fragmentations in multilayer areas, and the main body, which is consistent with the experimental observations under certain conditions and is not the regular multiple layers predicted by the multilayer spall theory with ideal material assumption. For multiple adiabatic shear bands (ASBs) in the shell, the spiral patterns of ASBs’ distributions, the initial positions, and the propagating path are clarified for the collapsed and expanding shells. The collapsed shell tends to form a single-direction spiral pattern whereas the expanding shell tends to form a double-direction spiral pattern. In addition to the inner surface, the intersection points of two ASBs can initiate cracks, and, as the intersection points have the chance of being distributed on the outer surface, the expanding shell has a greater potential to initiate a crack on the outer surface than the collapsed shell. The propagating path will be deflected after interactions of two ASBs, and the quantitative relationship between the deflection angle and the stress state before the interactions is given, which explains why the deflection angle is significantly larger in the collapsed shell compared with that in the expanding shell. Based on the above results and analysis, four typical stages of fractures in the expanding shell under internal explosive loading are identified.
TL;DR: In this paper , a thermodynamically-consistent full-field model integrated within a voxel-based elasto-viscoplastic fast Fourier transform framework is presented, which considers the coupling between the diffusion-mediated plasticity mechanisms.
Abstract: Below the yield strength and at moderate-to-high homologous temperatures, the inelastic deformation of metals is mostly governed/rate-controlled by vacancy diffusion-mediated processes. As a function of grain size, stress, temperature and dislocation content, vacancies (or atoms) can adopt preferential diffusion paths across grain interiors, along grain boundaries, or towards and along dislocations, resulting in climb and self-climb. In the steady state and under constant load, grain boundary and grain bulk vacancy diffusion-mediated plasticity have been described in seminal works by Coble and by Nabarro and Herring, respectively. Yet, the interplay between all aforementioned potential diffusion pathways has not been comprehensively mapped. This work presents a thermodynamically-consistent full-field model integrated within a voxel-based elasto-viscoplastic fast Fourier transform framework, which considers the coupling between the diffusion-mediated plasticity mechanisms. In the proposed approach, the kinetics and kinematics of plastic deformation due to vacancy diffusion along grain boundaries and grain bulk, as well as the exchange between grain boundaries and bulk are described explicitly. A homogenization approach at the voxel level is further introduced to simultaneously consider bulk and grain boundary diffusion in a numerically efficient fashion. The new formulation predicts the expected strain rate dependencies and the scaling of the steady-state creep rate with respect to grain size, temperature, and stress. The model predicts the transition from grain bulk to grain boundary-dominated diffusion with reduction in grain size, a significant step towards capturing transitions in deformation behavior without any phenomenological or ad-hoc adjustments.
TL;DR: In this paper , a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior.
Abstract: In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using different sets of invariants as inputs, a hyperelastic potential is formulated as a convex neural network, thus fulfilling symmetry of the stress tensor, objectivity, material symmetry, polyconvexity, and thermodynamic consistency. In addition, a physically sensible stress behavior of the model is ensured by using analytical growth terms, as well as normalization terms which ensure the undeformed state to be stress free and with zero energy. In particular, polyconvex, invariant-based stress normalization terms are formulated for both isotropic and transversely isotropic material behavior. By fulfilling all of these conditions in an exact way, the proposed physics-augmented model combines a sound mechanical basis with the extraordinary flexibility that neural networks offer. Thus, it harmonizes the theory of hyperelasticity developed in the last decades with the up-to-date techniques of machine learning. Furthermore, the non-negativity of the hyperelastic neural network-based potentials is numerically examined by sampling the space of admissible deformations states, which, to the best of the authors' knowledge, is the only possibility for the considered nonlinear compressible models. For the isotropic neural network model, the sampling space required for that is reduced by analytical considerations. In addition, a proof for the non-negativity of the compressible Neo-Hooke potential is presented. The applicability of the model is demonstrated by calibrating it on data generated with analytical potentials, which is followed by an application of the model to finite element simulations. In addition, an adaption of the model to noisy data is shown and its [...]
TL;DR: In this article , an inhomogeneous lattice-based polar medium for ideal elastic waveguide, whose microstructures are inversely determined by the discrete transformation elasticity (DTE), is proposed.
Abstract: The ability to precisely directing and controlling longitudinal (P) and transverse (S) waves in 2D solids along an arbitrary trajectory has attracted significant research interest and is crucial for practical applications such as imaging, cloaking, and wave focusing. Here, we report, design and examine an inhomogeneous lattice-based polar medium for ideal elastic waveguide, whose microstructures are inversely determined by the discrete transformation elasticity (DTE). Microstructures of the suggested medium, which are realized through global linear transformation and local affine transformation, enables arbitrary waveguides to transport elastic waves with minimal energy loss. Numerical simulation is then conducted to demonstrate that the lattice-based polar waveguide can efficiently steer both in-plane P and S wave modes over a broad frequency band. We also leverage the medium for Rayleigh wave control on curved surfaces. The constructed polar surface can break the conventional limit of the Rayleigh wave propagation on both concave and convex surfaces with extreme curvatures. This study is not only a concrete manifestation of the polar material, discrete transform elasticity, and their advantages but also provides a great potential in engineering applications such as signal detection, vibration control, and earthquake protection.