Macroscopic Mechanical Response Research Articles

Liquefaction characteristics in triaxial tests under various gravity environments – DEM analyses

Liquefaction of sands occurs when the effective stress becomes zero during undrained loading, and the state of liquefaction is often considered that individual particles do not transmit contact forces. In shaking table model tests, seepage flows towards the surface occur during liquefaction; this potentially maintains individual particles floated as the gravitational forces can be cancelled out by the upward seepage forces. In laboratory element tests, however, undrained conditions induce no seepage flows during liquefaction. This raises a key question of how the individual particles behave during liquefaction in element tests, and how the macroscopic mechanical response is affected due to gravity. To answer these questions, this contribution conducts a series of triaxial loading simulations using the discrete element method (DEM) considering the effect of gravity on the mechanical response of spherical particle assemblies. The results reveal that the presence of gravity affects both packing properties and liquefaction characteristics. Inter-particle contacts are maintained during liquefaction under non-zero gravity conditions. Although the liquefaction resistance is merely affected due to gravity, the stress–strain relation and stress path are measurably altered. This contribution highlights the importance of considering the potential effect of gravity when laboratory or DEM results on liquefaction phenomena are interpreted.

Computational Modeling of Intergranular Crack Propagation in燼n營ntermetallic Compound Layer

A micromechanical model is presented to study the initiation and propagation of microcracks of intermetallic compounds (IMCs) in solder joints. The effects of the grain aggregate morphology, the grain boundary defects and the sensitivity of the various cohesive zone parameters in predicting the overall mechanical response are investigated. The overall strength is predominantly determined by the weak grain interfaces; both the grain aggregate morphology and the weak grain interfaces control the crack configuration; the different normal and tangential strengths of grain interfaces result in different intergranular cracking behaviors and play a critical role in determining the macroscopic mechanical response of the system.

The effective shear modulus of a random isotropic suspension of monodisperse liquid n-spheres: from the dilute limit to the percolation threshold.

A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid n-spherical inclusions (n = 2, 3), each having identical initial radius A, in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension γ. For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus n in terms of the shear modulus μ of the elastomer, the initial elasto-capillary number eCa = γ/2μA, the volume fraction c of inclusions, and the space dimension n. This paper presents numerical solutions-generated by means of a recently introduced finite-element scheme-for n over a wide range of elasto-capillary numbers eCa and volume fractions of inclusions c. Complementary to these, a formula is also introduced for n that is in quantitative agreement with all the numerical solutions, as well as with the asymptotic results for n in the limit of dilute volume fraction of inclusions and at percolation . The proposed formula has the added theoretical merit of being an iterated-homogenization solution.

Simplified modelling of self-piercing riveted joints and application in crashworthiness analysis for steel-aluminium hybrid beams

In this paper, an equivalent simplified model of self-piercing riveting (SPR-ESM) validated by tests is constructed to characterize the macroscopic mechanical responses of SPR joints under quasi-static and dynamic loading conditions. The application of SPR-ESM in the crashworthiness analysis of steel-aluminium hybrid beam is investigated. The results reveal that the failure of the riveting point in the test specimen is accurately simulated by the numerical model connected by SPR-ESM, and relative errors of mechanical responses between simulation and test are controlled within 7 %. Parametric study is performed to explore the effect of the riveting point failure on the mechanical performance of steel-aluminium hybrid beam under different loading angles. The results indicate that: (1) a severe instability deformation mode of steel-aluminium hybrid beam is easily to happen when the loading angles increases; (2) the effect of riveting point failure on the mechanical performance of steel-aluminium hybrid beam is limited when the beam has a stable folding deformation; and (3) a significant decrease in the ability of resisting deformation and energy absorption is easily to happen when the steel-aluminium hybrid beam has a severe instability deformation mode.

On deformation and fracture of PBX simulant employing modified three-body potential peridynamics model with deformation-based failure criteria

The modified three-body potential peridynamics (PD) model is used to study the macroscopic mechanical responses of polymer bonded explosive (PBX) mock materials. Combined with PD functions, under small deformation conditions, bond shear form of the PD model is derived from the micro-potential incorporating modified three-body interaction potential, giving some attention to the applicable condition for its two expression forms, i.e., general form and bond shear form. Subsequently, an improved mode Ⅱ failure criterion considering collective shear deformation of family members is proposed to enhance the deformation-based failure criteria adopted in the present study. A series of PBX simulants associated with elastic deformation and brittle fracture behaviors are carried out by the proposed numerical method. And the numerical results are verified by experimental and other numerical ones published previously, which show that the proposed numerical method is suitable for modeling PBX mock materials.

Inelastic response of thermo-oxidatively aged carbon black filled polychloroprene rubber. Part I: Viscoelasticity

The first part of a two parts study focuses on the inelastic response of carbon black-filled polychloroprene rubber undergoing thermo-oxidative aging. More precisely, the prominence of the present work is laid on the attempt to provide a better understanding of the network modification due to thermo-oxidative aging and its consequences on the macroscopic mechanical responses including viscoelasticity (in Part I) and Mullins effect (in Part II). For this purpose, the polychloroprene rubber specimens are exposed to a temperature of 120 °C for a duration of 2, 3, and 4 days to induce three different aging levels before undergoing various tests. Results indicated that during thermo-oxidative aging, crosslinking dominates chain scission, and the strain-induced crystallization becomes more pronounced. Furthermore, it is observed that the inelastic responses such as stress relaxation and strain-induced crystallization are strongly affected by this thermo-oxidative aging-induced network alteration.

Multi-modal Dataset of a Polycrystalline Metallic Material: 3D Microstructure and Deformation Fields

The development of high-fidelity mechanical property prediction models for the design of polycrystalline materials relies on large volumes of microstructural feature data. Concurrently, at these same scales, the deformation fields that develop during mechanical loading can be highly heterogeneous. Spatially correlated measurements of 3D microstructure and the ensuing deformation fields at the micro-scale would provide highly valuable insight into the relationship between microstructure and macroscopic mechanical response. They would also provide direct validation for numerical simulations that can guide and speed up the design of new materials and microstructures. However, to date, such data have been rare. Here, a one-of-a-kind, multi-modal dataset is presented that combines recent state-of-the-art experimental developments in 3D tomography and high-resolution deformation field measurements.

Coupled quantitative modeling of microstructural evolution and plastic flow during continuous dynamic recrystallization

Continuous dynamic recrystallization (cDRX) dominates microstructural evolution during the hot working of metallic materials with high stacking fault energy (SFE), such as aluminum alloys. However, in reality, a lack of quantitative and visual modeling of the process hinders its widespread application in the hot working process. In this study, using a recently developed multilevel cellular automaton (MCA) that integrates the newly established cell switching rules and topology deformation technique, a novel mesoscale MCA-cDRX model was constructed to investigate the evolution of both microstructures and macroscopic mechanical response in the hot working of AA7075 aluminum alloy. By considering the evolution of dislocation density and the orientation angle of the local cells as the primary clues, the plastic flow, recrystallization kinetics, features of subgrain size and high-angle grain boundaries, and influence of initial matrix characteristics on the cDRX mechanism were analyzed. The model predictions are consistent with the experimental data. Quantitative analysis confirms that the incubation time for the initiation of subgrain formation is significantly short. The fine-grain matrix and high initial volume fraction of low-angle grain boundaries can significantly accelerate the progress of cDRX owing to a stronger accumulation of dislocations in the dislocation cell walls through the climb and cross-slip mechanisms in the deformed aluminum alloy. The subgrain size is dependent on the Zener-Hollomon parameter. The developed simulation framework offers an effective means to allow the visualization of the cDRX.

Structural modelling and quantitative analysis of mechanical gradient in CNT/Al composites

Carbon nanotube-reinforced aluminium normally considered to be composed of Carbon nanotube (CNT) free grain interior (GI) and CNT containing grain boundary affected zone (GBAZ). Research works showed that the property of GI varies with the distance from the boundary. To better understand the influence of this mechanical heterogeneity, we introduced a transition zone (TZ) to emphasise the mechanical heterogeneity of the GI. A dislocation-based plastic strain constitutive model was used to analyse the mechanical response, and the simulation results fit well with the experimental result. Moreover, the TZ thickness with a large simulation influence was found, and its strengthening mechanism, the influence of TZ thickness on the macroscopic mechanical response, geometrically necessary dislocation distribution were discussed in this study.

A comprehensive study on the mechanical behavior, deformation mechanism and texture evolution of Mg alloys with multi texture components

In this study, the deformation behaviors of Mg-3Al-1Zn alloy with multi texture components have been investigated using a combined experimental measurement and crystal plasticity modeling. Six types of multi textured samples were successfully prepared by an easily operated processing containing cold rolling, compression loadings, and subsequent annealing. The corresponding processing parameters to control multi texture components were also proposed. The effect of multi texture distribution on macroscopic mechanical response, activation of deformation modes, texture evolution, as well as the 101̅2 and 101̅1 twin fractions were systematically investigated. It’s a challenge work to model several texture components and random textures using EVPSC-TDT model for the first time. The simulation results generally match well with the experimental data. It has been found that the mechanical performance are strongly dependent on the multi texture components distribution and it was revealed by detailing the quantitative contribution of different deformation mechanisms to the plastic deformation. It’s the more disperse (0002) distribution of hard orientations that matters in enhancing the yield strength and ductility of samples with a given fraction of soft orientations. The findings in the present study are crucial for enriching the texture engineering for Mg alloys and could assist in designing better materials in term of mechanical properties and material performance.

Mesoscopic damage mechanism and a constitutive model of shale using in-situ X-ray CT device

With the continuous development of shale gas engineering in China, an accurate and adequate understanding of shale damage mechanism has become a critical scientific problem addressed by rock mechanics. So far, many researchers have studied the fracturing process and mechanism of shale in multi-scales. The mesoscopic structural characteristics of shale during loading can be obtained using the in-situ X-ray computed tomography (CT) technology. Some scholars have observed the structure evolution of shale under in-situ uniaxial compression conditions, but the quantitative investigation of damage evolution and constitutive model of shale still requires further studies. Given this, the in-situ micro-CT device was adopted to study the macroscopic mechanical response and the mesoscopic structural evolution of Longmaxi shale under uniaxial compression conditions. The evolution law of the damage variable with the axial strain was analysed according to the characterisation of the damage variable based on the CT image grey variance. In combination with the macroscopic stress-strain curve shape, evolution stage of the mesoscopic void, evolution of the damage variable, mesoscopic mechanism of the macroscopic mechanical response was investigated, and a damage constitutive model of shale under the uniaxial compression test was proposed. The conclusion of this study can provide a foundation for further research into the multi-scale failure mechanism of shale and exert theoretical guidance significance on shale gas fracturing engineering practice.

Elastomers filled with liquid inclusions: Theory, numerical implementation, and some basic results

Experimental and theoretical results of late have pointed to elastomers filled with various types of liquid inclusions as a promising new class of materials with unprecedented properties. Motivated by these findings, the first of two objectives of this paper is to formulate the homogenization problem that describes the macroscopic mechanical response of elastomers filled with liquid inclusions under finite quasistatic deformations. The focus is on the non-dissipative case when the elastomer is a hyperelastic solid, the liquid making up the inclusions is a hyperelastic fluid, the interfaces separating the solid elastomer from the liquid inclusions feature their own hyperelastic behavior (which includes surface tension as a special case), and the inclusions are initially spherical in shape. The macroscopic behavior of such filled elastomers turns out to be that of a hyperelastic solid, albeit one that depends directly on the size of the inclusions and the constitutive behavior of the interfaces. It is hence characterized by an effective stored-energy function W¯(F¯) of the macroscopic deformation gradient F¯. Strikingly, in spite of the fact that there are local residual stresses within the inclusions (due to the presence of initial interfacial forces), the resulting macroscopic behavior is free of residual stresses, that is, ∂W¯(I)/∂F¯=0. What is more, in spite of the fact that the local moduli of elasticity in the bulk and the interfaces in the small-deformation limit do not possess minor symmetries (due to the presence of residual stresses and initial interfacial forces), the resulting effective modulus of elasticity does possess the standard minor symmetries, that is, L¯ijkl=L¯jikl=L¯ijlk, where L¯ijkl≔∂2W¯(I)/∂F¯ij∂F¯kl. The second objective of this paper is to implement and deploy a finite-element scheme to numerically generate solutions for the macroscopic response of a basic class of elastomers filled with liquid inclusions, that of isotropic suspensions of incompressible liquid inclusions of monodisperse size embedded in incompressible Neo-Hookean elastomers wherein the interfaces feature a constant surface tension. With guidance from the numerical solutions, the last part of this paper is devoted to proposing a simple explicit approximation for the effective stored-energy function W¯(F¯).

Controllable photomechanical bending of metal-organic rotaxane crystals facilitated by regioselective confined-space photodimerization

Molecular machines based on mechanically-interlocked molecules (MIMs) such as (pseudo) rotaxanes or catenates are known for their molecular-level dynamics, but promoting macro-mechanical response of these molecular machines or related materials is still challenging. Herein, by employing macrocyclic cucurbit[8]uril (CB[8])-based pseudorotaxane with a pair of styrene-derived photoactive guest molecules as linking structs of uranyl node, we describe a metal-organic rotaxane compound, U-CB[8]-MPyVB, that is capable of delivering controllable macroscopic mechanical responses. Under light irradiation, the ladder-shape structural unit of metal-organic rotaxane chain in U-CB[8]-MPyVB undergoes a regioselective solid-state [2 + 2] photodimerization, and facilitates a photo-triggered single-crystal-to-single-crystal (SCSC) transformation, which even induces macroscopic photomechanical bending of individual rod-like bulk crystals. The fabrication of rotaxane-based crystalline materials with both photoresponsive microscopic and macroscopic dynamic behaviors in solid state can be promising photoactuator devices, and will have implications in emerging fields such as optomechanical microdevices and smart microrobotics.

Mechanical and histological characteristics of aortic dissection tissues

Aims: This study investigated the association between the macroscopic mechanical response of aortic dissection (AoD) flap, its fibre features, and patient physiological features and clinical presentations.Methods: Uniaxial test was performed with tissue strips in both circumferential and longitudinal directions from 35 patients with (AoD:CC) and without (AoD:w/oCC) cerebral/coronary complications, and 19 patients with rheumatic or valve-related heart diseases (RH). A Bayesian inference framework was used to estimate the expectation of material constants (C1, D1, and D2) of the modified Mooney-Rivlin strain energy density function. Histological examination was used to visualise the elastin and collagen in the tissue strips and image processing was performed to quantify their area percentages, fibre misalignment and waviness.Results: The elastin area percentage was negatively associated with age (p = 0.008), while collagen increased about 6% from age 40 to 70 (p = 0.03). Elastin fibre was less dispersed and wavier in old patients and no significant association was found between patient age and collagen fibre dispersion or waviness. Features of fibrous microstructures, either elastin or collagen, were comparable between AoD:CC and AoD:w/oCC group. Elastin and collagen area percentages were positively correlated with C1 and D2, respectively, while the elastin and collagen waviness were negatively correlated with C1 and D2, respectively. Elastin dispersion was negatively correlated to D2. Multivariate analysis showed that D2 was an effective parameter which could differentiate patient groups with different age and clinical presentations, as well as the direction of tissue strip.Conclusion: Fibre dispersion and waviness in the aortic dissection flap changed with patient age and clinical presentations, and these can be captured by the material constants in the strain energy density function. Statement of significanceAortic dissection (AoD) is a severe cardiovascular disease. Understanding the mechanical property of intimal flap is essential for its risk evaluation. In this study, mechanical testing and histology examination were combined to quantify the relationship between mechanical presentations and microstructure features. A Bayesian inference framework was employed to estimate the expectation of the material constants in the modified Mooney-Rivlin constitutive equation. It was found that fibre dispersion and waviness in the AoD flap changed with patient age and clinical presentations, and these could be captured by the material constants. This study firstly demonstrated that the expectation of material constants can be used to characterise tissue microstructures and differentiate patients with different clinical presentations.

Damage-augmented nonlocal lattice particle method for fracture simulation of solids

Fracture of solids, particularly for ductile metallic materials, typically involves elastoplastic deformation and associated damaging processes. This paper proposes a general damage-augmented nonlocal lattice particle method (LPM) to model this coupled behavior. The concept of interchangeability between particle-wise and bond-wise properties in LPM is first introduced and validated. It is shown that tensors can naturally represent material state variables, which is rarely seen in most lattice methods. A tensor-based return-mapping algorithm based on implicit integration is thus implemented to simulate J2 plasticity. Next, the damage-augmented LPM is proposed to properly simulate the material deterioration by combining LPM with a nonlocal damage evolution rule. The proposed method can handle the brittle fracture and pure elastoplastic deformation and simulate ductile fracture phenomena with moderately large time steps. The particle-size/lattice dependency issues of macroscopic mechanical responses are reduced under the proposed framework. Numerical examples of predicting the elastoplastic behavior of engineering structures with/without damage and fracture are provided. Several conclusions and limitations of the proposed method are also discussed.

Analyzing effects of microscopic material parameters on macroscopic mechanical responses in underwater mixing using discrete element method

Mixing processes are commonly used to handle powders and grains in several industrial fields, and their performance has been subjected to extensive study. However, research is limited on underwater mixing in novel deep-sea mining applications. Consequently, we adopt a discrete element method (DEM) enhanced by a lubrication model to investigate the underwater mixing process. We focus on the effect of microscopic material parameters on macroscopic mechanical responses in this study. Variations in macroscopic responses are small among DEM samples with a well-controlled initial density; the largest coefficient of variation (cv) is less than 1.4% in normalized forces on the sidewall, and the values of cv are less than 1.0% for other macroscopic responses. A comprehensive parametric study is conducted for elastic moduli and for dissipative parameters. Elastic moduli exhibited a negligible influence, and the effects of dissipative parameters ranged from most significant to most negligible in the order of coefficient of rolling friction, coefficient of friction, coefficient of restitution, and fluid viscosity. We further discuss the network connectivity of force chains and shear-induced size segregation; it was found that an increase in rolling friction increases the connectivity of particles in principal stress chains, which increases the mixing resistance. Size segregation is monitored for DEM samples with particles that initially follow a uniform size distribution: an increase in friction is observed to enhance the segregation and an increase in fluid viscosity to alleviate it. The findings in this paper can advance the understanding of the dynamics of underwater mixing and offer insights for designing mixing systems for granular materials with large variations in material properties.

Reduced kinematic multiscale model for tissue engineering electrospun scaffolds

To this day, there is still a need for a direct relationship between the microscopic material properties and network microstructure configuration with the macroscopic mechanical response in order to optimize the design loops of biomimetic electrospun grafts. Multiscale mechanical modeling arises as a useful alternative, which allows to represent the individual nanofibers mechanical response and how the interaction between fibers results in the final macroscopic behavior. In this work, a micromechanical model that accounts for fiber interaction, progressive straightening (i.e. progressive recruitment) and reorientation is presented. An RVE is generated by means of a virtual deposition algorithm that mimics the electrospinning process itself, thus obtaining geometries that resemble the observed electrospun microstructure. These geometries were then validated by comparison with analysis of SEM images, taking special interest in the diameter, orientation and tortuosity distributions. Then, an elastic–plastic constitutive law for the nanofibers is implemented along with a simplified kinematic description that results in a significant reduction of the number of Degrees of Freedom of the discretized mechanical equilibrium problem. Finally, the micromechanical model is validated against uniaxial tensile tests of electrospun PLLA bone-shaped samples, reproducing the experimentally observed behavior while employing realistic geometric and constitutive parameters to characterize the fibers.

Linking microscopic structural changes and macroscopic mechanical responses in a near-ideal bottlebrush elastomer under uniaxial deformation.

Bottlebrush (BB) elastomers, in which load-bearing network strands are densely grafted with side chains, are gaining much attention due to their unique mechanical properties. Herein, we used in situ small-angle X-ray scattering coupled with tensile tests to investigate the microscopic structural changes induced in a model BB elastomer with a controlled network structure under uniaxial deformation. The model BB elastomer was synthesized by end-linking a monodisperse star-shaped BB polymer, which ensured a controlled network structure. The BB elastomer exhibited both significant strain stiffening and backbone chain alignment under uniaxial loading, and these properties were not observed in an analogous side chain-free elastomer and gel. It was also found that the side chains in the BB elastomer did not show any sign of chain orientation even when the attached backbone chain was aligned in the stretching direction. These observations highlighted the roles of side chains: they were structurally disordered at the segment level but their steric repulsion made the backbone chain aligned and overstretched.

Tuning the mechanical impedance of disordered networks for impact mitigation.

Disordered-Network Mechanical Materials (DNMM), comprised of random arrangements of bonds and nodes, have emerged as mechanical metamaterials with the potential for achieving fine control over their mechanical properties. Recent computational studies have demonstrated this control whereby an extremely high degree of mechanical tunability can be achieved in disordered networks via a selective bond removal process called pruning. In this study, we experimentally demonstrate how pruning of a disordered network alters its macroscopic dynamic mechanical response and its capacity to mitigate impact. Impact studies with velocities ranging from 0.1 m s-1 to 1.5 m s-1 were performed, using a mechanical impactor and a drop tower, on 3D printed pruned and unpruned networks comprised of materials spanning a range of stiffness. High-speed videography was used to quantify the changes in Poisson's ratio for each of the network samples. Our results demonstrate that pruning is an efficient way to reduce the transmitted force and impulse from impact in the medium strain rate regime (101 s-1 to 102 s-1). This approach provides an interesting alternative route for designing materials with tailored impact mitigating properties compared to random material removal based on open cell foams.

Strength of fluid-filled soft composites across the elastofracture length.

Materials that utilize heterogeneous microstructures to control macroscopic mechanical response are ubiquitous in nature. Yet, translating nature's lessons to create synthetic soft solids has remained challenging. This is largely due to the limited synthetic routes available for creating soft composites, particularly with submicron features, as well as uncertainty surrounding the role of such a microstructured secondary phase in determining material behavior. This work leverages recent advances in the development of photocrosslinkable thermogelling nanoemulsions to produce composite hydrogels with a secondary phase assembled at well controlled length scales ranging from tens of nm to tens of μm. Through analysis of the mechanical response of these fluid-filled composite hydrogels, it is found that the size scale of the secondary phase has a profound impact on the strength when at or above the elastofracture length. Moreover, this work shows that mechanical integrity of fluid-filled soft solids can be sensitive to the size scale of the secondary phase.