Large Deformation Regime Research Articles

Effects of a nonlocal microstructure on peeling of thin films

In this work, starting from an approach previously proposed by the Authors, we put forward an extension to the large deformation regime of the dimensionally-reduced formulation for peridynamic thin plates, including both hyperelasticity and fracture. In particular, the model, validated against numerical simulations, addresses the problem of the peeling in nonlocal thin films, which when attached to a soft substrate highlights how nonlocality of the peeled-off layer might greatly influence the whole structural response and induce some unforeseen mechanical behaviours that could be useful for engineering applications. Through a key benchmark example, we in fact demonstrate that de-localization of damage and less destructive failure modes take place, these effects suggesting the possibility of ad hoc conceiving specific networks of nonlocal interactions between material particles, corresponding to lattice-equivalent structure of the nonlocal model treated, of interest in designing new material systems and interfaces with enhanced toughness and adhesive properties.

On the theory of mechanically induced chemiluminescence in multiple network elastomers

Mechanophores, force-sensitive molecules, can be covalently linked into polymer networks to reveal the damage properties of polymeric materials under deformation. Recent works have introduced bis-adamantyl dioxetane (Ad) into multiple network elastomers. These mechanoluminescent cross-linking molecules can emit luminescence as they break. The experimental results can directly visualize the damage behaviors of multiple network elastomers and reveal the damage mechanism of these materials during deformation. In this work, we develop a constitutive model to describe the complex mechanical behaviors of multiple network elastomers based on observations from mechano-chemiluminescent experiments. The free energy density consists of the contributions from the filler network, the matrix network, and the entangled network. A new type of single-chain model is developed for the filler network, while the classic eight-chain mapping is adopted for the micro–macro transition. The chains in the filler network are progressively damaged under deformation to explain the stress-softening behaviors observed in the small and median strain regions of multiple network elastomers. The entangled network is rooted in individual fragments of the damaged filler network, which can be further damaged in the large deformation regime. The model can comprehensively capture the complex mechanical responses of multiple network elastomers with different values of the prestretching ratio of the filler network, including linear response, necking instability, and re-hardening phenomena in quadruple networks. By assuming that the luminescence intensity of the materials is proportional to the total percentage of damage from both filler and entangled networks, we quantify the relationship between damage and the luminescence intensity from mechanophores, which is further validated in quantifying luminescence intensity against different sets of experimental data on the uniaxial tension of multiple network elastomers. The model is further implemented for finite element analysis, demonstrating the ability to visualize and characterize the damage behaviors around a crack.

Experimental investigation of yield and hysteresis behaviour of an epoxy resin under cyclic compression in the large deformation regime

Experimental investigation of yield and hysteresis behaviour of an epoxy resin under cyclic compression in the large deformation regime

Computational study of a homogenized nonlinear generalization of Timoshenko beam proposed by Turco et al.

<p>Mechanical metamaterials are most often assemblies of stocky beam elements connected through rigid connections, hinges, or flexural joints. The description of these materials through classical beam theories is challenging because of the wide variety of complex phenomena observed in the severe deformation regime mechanical metamaterials must undergo and because most classical beam theories can only be applied to elements with sufficiently high slenderness. In the spirit of Hencky, Turco et al. (2020) has recently formulated an intrinsically discrete nonlinear elastic model suitable for the design of mechanical metamaterials. The objective of this contribution was to present a numerical study of the nonlinear generalization of the Timoshenko beam that results from the asymptotic homogenization of the discrete model introduced by Turco et al. The present numerical study took into account several loading cases and elucidated the sensitivity of the homogenized continuum with respect to axial, bending, and shear stiffness parameters, as well as to load imperfections, in terms of mechanical behavior, including buckling onset and post-critical behavior. It was found that the predictions obtained with the homogenized model in the large deformation regime matched excellently with those of the discrete model proposed by Turco et al.</p>

Gastropod Slime-Based Gel as an Adjustable Synthetic Model for Human Airway Mucus.

Airway mucus works as a protective barrier in the human body, as it entraps pathogens that will be later cleared from the airways by ciliary transport or by coughing, thus featuring the rheological properties of a highly stretchable gel. Nonetheless, the study of these physical barrier as well as transport properties remains limited due to the restricted and invasive access to lungs and bronchi to retrieve mucus and to the poor repeatability inherent to native mucus samples. To overcome these limits, we report on a biobased synthetic mucus prepared from snail slime and multibranched thiol cross-linker, which are able to establish disulfide bonds, in analogy with the disulfide bonding of mucins, and therefore build viscoelastoplastic hydrogels. The gel macroscopic properties are tuned by modifying the cross-linker and slime concentrations and can quantitatively match those of native sputum from donors with cystic fibrosis (CF) or non-cystic fibrosis bronchiectasis (NCFB) both in the small- and large-deformation regimes. Heterogeneous regimes were locally found in the mucus model by passive microrheology, in which both diffusive and non-diffusive motion are present, similar to what is observed in sputa. The biobased synthetic approach proposed in the present study thus allows to produce, with commercially available components, a promising model to native respiratory mucus regarding both mechanical and, to a lesser extent, physicochemical aspects.

Droplet absorption and spreading into thin layers of polymer hydrogels

From biological tissues to microactuators and absorption of solvents into layers of paint, macroscopically non-porous materials with the capacity to swell when in contact with a solvent are ubiquitous. In these systems, owing to strong solid–fluid interactions, chemically driven flows can yield large geometric changes. We study experimentally and theoretically the canonical problem of the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental set-up, we observe fast absorption leading to a radially spreading axisymmetric blister. We use a fully three-dimensional linear poroelastic framework with nonlinear kinematic equations to obtain governing equations, which we then reduce with thin-layer scalings to a one-dimensional nonlinear diffusion equation for the evolution of the blister geometry. In the limits of large and small deformations, the evolution of the blister characteristic height and radius are self-similar, following power laws in time. Our experimental measurements show that the evolution of the blister is broadly within the theoretical predictions in the large and small deformation regimes. In the general intermediate deformation regime, the measurements are well captured by our reduced one-dimensional diffusion model, which does not require the sophisticated and computationally expensive numerical approaches necessary for the original two-dimensional nonlinear coupled transport problem. By adapting modelling techniques from the fluid dynamics of thin porous elastic layers to a polymer swelling problem, our modelling framework extends the range of polymer swelling problems that can be treated with semi-analytical methods. Moreover, our detailed experimental data can serve as a test case for future nonlinear poroelastic frameworks of swelling polymer materials.

An improved semi-implicit material point method for simulating large deformation problems in saturated geomaterials

This study presents an improved semi-implicit MPM formulation for coupled large deformation problems in geotechnics based on the fractional step method. The main objective of this study is to make the choice of the time step size independent of the permeability and to reduce the pressure oscillations by applying the special splitting procedure and the stabilized technique. The proposed coupled MPM is validated by comparing numerical results with analytical solutions of the one-dimensional consolidation problem in both small and large deformation regimes. Three numerical tests are performed to further evaluate the performance of the proposed method, including a self-weight slumping block, 2D consolidation test, and the stability of a saturated elasto-plastic slope. The numerical results indicate that the proposed method is suitable for simulating fluid-saturated porous media involving large deformation.

Simulation of soil-tool interaction using smoothed particle hydrodynamics (SPH)

Numerical techniques in soil-tool interaction play a critical role in the applications of optimal design and optimal control of soil-engaging components. However, one of the greatest challenges in the simulation of soil-tool interaction is the complex dynamic behaviors of the soil in the regime of large deformations, and the analysis and evaluation of forces at the soil-tool interface. Recently smoothed particle hydrodynamics (SPH) has shown its advantages in modeling large deformation problems with deformable boundaries and moving interfaces. In this paper, an SPH model of soil-tool interaction based on the elastoplastic constitutive is established. Firstly, the cutting process and soil-tool interaction for both non-cohesive and cohesive soil are simulated based on a shear failure model and a contact algorithm. The simulation results for non-cohesive soil and cohesive soil in different operating conditions are discussed separately, and the results for different operating conditions are compared. In addition, interactions between soil and inclined short flat blades are also simulated to estimate the cutting force during the tillage process. The predicted soil configuration and cutting force are in good agreement with our experiments and with the results in published literature. The cutting forces for non-cohesive soil exhibit similar trends and average values throughout the process. For cohesive soil, the cutting force curve has a wavy trend and the average value in a stable state is greater than for non-cohesive soil. In order to further validate the feasibility and precision of the presented model, different tillage conditions (cutting angles and depths), internal friction angles for non-cohesive soil, different cohesion for cohesive soil, and different friction coefficient of the cutting blade are all discussed. This work has demonstrated that the proposed model is accurate in soil-tool interaction simulations and can also provide an accurate description of the shear fragmentation of cohesive soil. It helps to contribute to a better understanding of the tillage process that is fundamental and essential for the optimal design of the soil-engaging components.

A coarse-grained molecular dynamics investigation of the role of mineral arrangement on the mechanical properties of mineralized collagen fibrils.

Mineralized collagen fibrils (MCFs) comprise collagen molecules and hydroxyapatite (HAp) crystals and are considered universal building blocks of bone tissue, across different bone types and species. In this study, we developed a coarse-grained molecular dynamics (CGMD) framework to investigate the role of mineral arrangement on the load-deformation behaviour of MCFs. Despite the common belief that the collagen molecules are responsible for flexibility and HAp minerals are responsible for stiffness, our results showed that the mineral phase was responsible for limiting collagen sliding in the large deformation regime, which helped the collagen molecules themselves undergo high tensile loading, providing a substantial contribution to the ultimate tensile strength of MCFs. This study also highlights different roles for the mineralized and non-mineralized protofibrils within the MCF, with the mineralized groups being primarily responsible for load carrying due to the presence of the mineral phase, while the non-mineralized groups are responsible for crack deflection. These results provide novel insight into the load-deformation behaviour of MCFs and highlight the intricate role that both collagen and mineral components have in dictating higher scale bone biomechanics.

A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure

AbstractThis study presents a novel transition scheme that can trace an actual crack path as closely as possible and stably update its explicit crack tip even in a large deformation regime. The crack initiation and propagation processes are determined from an energy minimization problem with respect to the displacement field and crack phase‐field, and the predicted path represented by a diffuse crack topology is replaced by a discrete path by applying the finite cover method. By developing a technique for determining explicit crack tips, the crack topology is updated from diffusive to discrete intermittently during the course of the staggered iterative procedure. Therefore, even a curved crack path that evolves significantly within a single time increment can be explicitly captured. Additionally, to stably update an explicit crack tip within the finite strain framework, we introduce a stabilization technique. Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. After describing the individual techniques devised in the proposed scheme for achieving these features based on their algorithmic aspects, we present several representative numerical examples to demonstrate the performance and capability of the developed approach.

Experimental analysis, discrete modeling and parameter optimization of SLS-printed bi-pantographic structures

Making use of experimental data for bias extension, shearing, and point-load tests in large deformation regime for rectangular and square bi-pantographic specimens, we perform a numerical identification to fit the a priori parameters of a planar discrete spring model. The main objective of the work is to develop an automatized optimization process based on the Nelder–Mead simplex algorithm for identifying the constitutive parameters of discrete modeling of bi-pantographic structures, as well as assessing its descriptiveness and predictive capacity. The analysis allows to conclude that there exists a single set of parameters for the adopted discrete modeling such that it is descriptive and predictive for several different tests and for a wide range of deformations.

Sandwich structures with repairable cores based on truncated cube cells

With dramatic increase in 3D printing applications in industry, sandwich panels with 3D printed cores have gained a lot of attention recently. In harmony with global movement towards sustainability and low-carbon emission industries, sandwich panels with easy-to-repair and cost-effective cores would be very attractive structures. In this regard, implementing separated cells for constructing lattice structures instead of using back-to-back lattice structures makes repairing local damages in the core easier and more cost-effective. Ideally, a damaged cell can be replaced with an intact new cell without the need to change the whole core structure. In this study, mechanical responses of a single truncated cube unit cell, a well-known geometry for constructing regular lattices has been studied analytically, numerically, and experimentally. Analytical relationships were derived for stiffness, yield stress, and Poisson's ratio of a single unit cell. Samples were 3D printed and tested mechanically in large deformation regime. A good agreement between results from analytical derivations, numerical simulations, and experiments was observed. It was shown that an equilateral truncated cube structure has a yield stress at least twice of that for a simple cube structure. Three types of repairable sandwich panels with different uniform core densities as well as four graded cores were studied as well. The functionally graded sandwich panels presented the best performance while considering both energy absorption capacity and mass. The best functionally graded sandwich panels (Type 4) showed an increase in specific energy absorption (SEA) by almost 21% and a decrease in maximum displacement by 2.5% with respect to the second-ranking best option.

Toward Measuring the Mechanical Stresses Exerted by Branching Embryonic Airway Epithelial Explants in 3D Matrices of Matrigel.

Numerous organs in the bodies of animals, including the lung, kidney, and mammary gland, contain ramified networks of epithelial tubes. These structures arise during development via a process known as branching morphogenesis. Previous studies have shown that mechanical forces directly impact this process, but the patterns of mechanical stress exerted by branching embryonic epithelia are not well understood. This is, in part, owing to a lack of experimental tools. Traditional traction force microscopy assays rely on the use of compliant hydrogels with well-defined mechanical properties. Isolated embryonic epithelial explants, however, have only been shown to branch in three-dimensional matrices of reconstituted basement membrane protein, or Matrigel, a biomaterial with poorly characterized mechanical behavior, especially in the regime of large deformations. Here, to compute the traction stresses generated by branching epithelial explants, we quantified the finite-deformation constitutive behavior of gels of reconstituted basement membrane protein subjected to multi-axial mechanical loads. We then modified the mesenchyme-free assay for the ex vivo culture of isolated embryonic airway epithelial explants by suspending fluorescent microspheres within the surrounding gel and tracking their motion during culture. Surprisingly, the tracked bead motion was non-zero in regions of the gel far away from the explants, suggestive of passive swelling deformations within the matrix. To compute accurate traction stresses, these swelling deformations must be decomposed from those generated by the branching explants. We thus tracked the motion of beads suspended within cell-free matrices and quantified spatiotemporal patterns of gel swelling. Taken together, these passive swelling data can be combined with the measured mechanical properties of the gel to compute the traction forces exerted by intact embryonic epithelial explants.

A novel enhanced anti-tetra-missing rib auxetic structure with tailorable in-plane mechanical properties

In analogy with the enhanced hexa-missing rib structure, a novel enhanced anti- tetra-missing rib structure was proposed in this work. Using a simple energy-based approach, mechanical modelling under infinitesimal deformation was proposed to provide guidelines for determining the geometries with targeted mechanical properties. It is shown that the proposed structure provides tunable Poisson’s ratios and elastic and shear moduli in wide ranges. The analytic solutions of the effective Poisson’s ratio, elastic and shear moduli from the mechanics model were validated by systematic finite element (FE) calculations on one unit-cell with considering periodic boundary conditions (PBCs). The underlying deformation mechanism accounting for the auxetic behavior on different geometric parameters of the proposed design was then investigated by elaborated FE analysis in a large deformation regime. The targeted NPR performance was also verified with a nonlinear base material. Uniaxial tensile experiments and the corresponding numerical simulations for lattice structures consisting of an array of proposed unit-cells were also performed to validate the theoretical and FE results obtained from one unit-cell analysis.

An Isogeometric analysis based method for frictional elastic contact problems with randomly rough surfaces

The problem addressed in this paper concerns the frictional contact between an elastomer and a rigid body with randomly rough surfaces. The work is accomplished on the basis of two crucial elements: a framework for generating random geometries and a robust frictional contact algorithm, both of which are realised in the approach of Isogeometric analysis (IGA) for its high accuracy and robustness. For the former, a new Isogeometric framework for random geometry modelling is proposed, which combines the random field generation based on Karhunen–Loève expansion theory with Non-Uniform Rational B-Spline (NURBS) interpolation method. For the latter, a mortar-based frictional contact algorithm in 2D large deformation regime is adopted incorporating a modified closest point projection method for detection of contact. Numerical experiments are conducted with several settings such as ‘rough–smooth’, ‘smooth–rough’ and ‘rough–rough’ contact, depending on which side of the contact pair the randomly rough surface belongs to. The ratio of the global coefficient of friction to the prescribed local one and the ratio of true contact area to the nominal contact area are characterised under these settings, and factors like the root mean square roughness and correlation length of the random surface and the external traction are discovered to have a significant influence on the two ratios.

Hyperelastic proportional damping for numerical non-conservative dynamic models of hard rubbers under large deformations

The paper deals with a new approach to modeling the non-conservative behavior of hard rubbers in damping structures operating under quasi-harmonic, low-frequency conditions and in the large deformation regime. In particular, a hyperelastic proportional damping (HPD) model is proposed based on experimental research of dynamic responses of cylindrical specimens to torsion excitation. The HPD model depends on two ingredients. First, it relies on the integration of the dissipated energy of an experimentally obtained steady hysteresis loop. And second, this hysteresis loop is employed to construct a so-called skeleton curve, which is utilized to obtain the parameters of a generalized Rivlin model of the hyperelastic material. In addition, attention is paid to the HPD model’s dependence on the frequency and amplitude of the torsional excitation. Finally, the problem of nonlinear transient vibration of a viscoelastic cylinder is formulated and numerically solved by the finite element method. The results obtained from finite element analyses are in accord with experimental data and validate the proposed HPD model for material damping evaluation.

Explicit meshfree {{varvec{u}}}-{{varvec{p}}}_mathbf{mathrm{w}} solution of the dynamic Biot formulation at large strain

In this paper, an efficient and robust methodology to simulate saturated soils subjected to low-medium frequency dynamic loadings under large deformation regime is presented. The coupling between solid and fluid phases is solved through the dynamic reduced formulation u-p_mathrm{w} (solid displacement – pore water pressure) of the Biot’s equations. The additional novelty lies in the employment of an explicit two-steps Newmark predictor-corrector time integration scheme that enables accurate solutions of related geomechanical problems at large strain without the usually high computational cost associated with the implicit counterparts. Shape functions based on the elegant Local Maximum Entropy approach, through the Optimal Transportation Meshfree framework, are considered to solve numerically different dynamic problems in fluid saturated porous media.

Bearing capacity and failure of footing on anisotropic soil: A multiscale perspective

Fabric anisotropy underpins the mechanical response of granular soils pertaining to a wide range of practical geotechnical applications. This paper presents a multiscale computational study on a strip footing resting on an anisotropic soil foundation. The focus of this study is placed on examining the cross-scale links of key grain-scale mechanisms in the soil that underscore interesting macroscopic observations of the footing problem over a full loading range from peak to large deformation regimes until its failure. We employ a hierarchical coupling of Material Point Method and Discrete Element Method (MPM-DEM). Mesoscale ensembles consisting of elliptical particles with specific alignments to represent bedding planes in anisotropic soils are generated. They are embedded into the material points of the MPM and serve as Representative Volumetric Elements (RVEs) with solutions by DEM to extract nonlinear material responses in solving the footing as a boundary value problem that may undergo large deformation to failure. The study confirms experimental observations that the bearing capacity of the strip footing decrease with the bedding angle α. It shows that ignoring fabric anisotropy for soil may lead to a significant overestimation or underestimation of the bearing capacity in extreme cases. The final failure patterns for all anisotropic cases feature general failure modes with two major slip surfaces, and they are predominantly in an asymmetric manner except the horizontal bedding case and the isotropic case. The degree of asymmetry in the failure pattern shows a correlation with the bedding angle. These observed features are further corroborated with microstructural analyses on the evolution of different sources of fabric anisotropy in slip surface.

A machine learning approach to estimate the strain energy absorption in expanded polystyrene foams

Traditional modeling of mechanical energy absorption due to compressive loadings in expanded polystyrene foams involves mathematical descriptions that are derived from stress/strain continuum mechanics models. Nevertheless, most of those models are either constrained using the strain as the only variable to work at large deformation regimes and usually neglect important parameters for energy absorption properties such as the material density or the rate of the applying load. This work presents a neural-network-based approach that produces models that are capable to map the compressive stress response and energy absorption parameters of an expanded polystyrene foam by considering its deformation, compressive loading rates, and different densities. The models are trained with ground-truth data obtained in compressive tests. Two methods to select neural network architectures are also presented, one of which is based on a Design of Experiments strategy. The results show that it is possible to obtain a single artificial neural networks model that can abstract stress and energy absorption solution spaces for the conditions studied in the material. Additionally, such a model is compared with a phenomenological model, and the results show than the neural network model outperforms it in terms of prediction capabilities, since errors around 2% of experimental data were obtained. In this sense, it is demonstrated that by following the presented approach is possible to obtain a model capable to reproduce compressive polystyrene foam stress/strain data, and consequently, to simulate its energy absorption parameters.

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.