Strain Regime Research Articles

Mechanical resilience of the sessile tunicate Botryllus schlosseri.

We demonstrate that the sessile tunicate Botryllus schlosseri is remarkably resilient to applied loads by attaching the animals to an extensile substrate subjected to quasistatic equiradial loads. Animals can withstand radial extension of the substrate to strain values as high as 20% before they spontaneously detach. In the small to moderate strain regime, we found no relationship between the dynamic size of the external vascular bed and the magnitude of applied stretch, despite known force sensitivities of the vascular tissue at the cellular level. We attribute this resilience to the presence and mechanical properties of the tunic, the cellulose-enriched gel-like substance that encases the animal bodies and surrounding vasculature.

The synergy between texture evolution and grain refinement in a BCC steel

ABSTRACT This work investigates the synergy between texture evolution and grain refinement in ultra-low carbon body-centred cubic (BCC) ferritic steel. In this regard, experiments and polycrystal plasticity for ambient compressive deformation in low (up to ϵ≈0.22) and moderate (ϵ≈0.22−0.69) strain regimes were carried out. The tests were interrupted at intermediate strains for microstructure and texture characterisation. It was observed that the change in texture to γ -fibre ( { 111 } ∥ Compression direction ( CD ) ) and the formation of θ -fibre ( { 100 } ∥ CD ) up to ϵ ≈ 0.22 contributes towards lattice bending, resulting in grain size reduction from ∼ 104 ( 23 ) μ m to ∼ 23 ( 6 ) μ m . Simultaneously, crystallite size decreases, and statistically stored dislocations (SSD) and geometrically necessary boundaries (GNB) increase rapidly. Thus, resulting in an abrupt decrease in strain hardening rate (SHR). From ϵ ≈ 0.22 − 0.69 , the γ and θ -fibre broadens and θ -fibre intensity increases. The low GNB density increase indicates insignificant deformation-induced lattice curvature formation within grains, resulting in SSD intensification. Thus, leading to elongated grains with sluggish grain size decrease to ∼ 17 ( 4 ) μ m and a lesser decrease in SHR. The α -fibre could not evolve due to the dispersion of 110 axes along the axisymmetric radial direction due to axial deformation. The polycrystal model could appropriately simulate strain-hardening behaviour and texture evolution.

Dynamic finite element modelling of the macaque mandible during a complete mastication gape cycle.

Three-dimensional finite element models (FEMs) are powerful tools for studying the mechanical behaviour of the feeding system. Using validated, static FEMs we have previously shown that in rhesus macaques the largest food-related differences in strain magnitudes during unilateral postcanine chewing extend from the lingual symphysis to the endocondylar ridge of the balancing-side ramus. However, static FEMs only model a single time point during the gape cycle and probably do not fully capture the mechanical behaviour of the jaw during mastication. Bone strain patterns and moments applied to the mandible are known to vary during the gape cycle owing to variation in the activation peaks of the jaw-elevator muscles, suggesting that dynamic models are superior to static ones in studying feeding biomechanics. To test this hypothesis, we built dynamic FEMs of a complete gape cycle using muscle force data from in vivo experiments to elucidate the impact of relative timing of muscle force on mandible biomechanics. Results show that loading and strain regimes vary across the chewing cycle in subtly different ways for different foods, something which was not apparent in static FEMs. These results indicate that dynamic three-dimensional FEMs are more informative than static three-dimensional FEMs in capturing the mechanical behaviour of the jaw during feeding by reflecting the asymmetry in jaw-adductor muscle activations during a gape cycle. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

Chronic diastolic stretch unmasks conduction defects in an in vitro model of arrhythmogenic cardiomyopathy.

We seek to elucidate the precise nature of mechanical loading that precipitates conduction deficits in a concealed-phase model of arrhythmogenic cardiomyopathy (ACM). ACM is a progressive disorder often resulting from mutations in desmosomal proteins. Exercise has been shown to worsen disease progression and unmask arrhythmia vulnerability, yet the underlying pathomechanisms may depend on the type and intensity of exercise. Because exercise causes myriad changes to multiple inter-dependent hemodynamic parameters, it is difficult to isolate its effects to specific changes in mechanical load. Here, we use engineered heart tissues (EHTs) with iPSC-derived cardiomyocytes expressing R451G desmoplakin, an ACM-linked mutation, which results in a functionally null model of desmoplakin (DSP). We also use a novel bioreactor to independently perturb tissue strain at different time points during the cardiac cycle. We culture EHTs under three strain regimes: normal physiological shortening; increased diastolic stretch, simulating high preload; and isometric culture, simulating high afterload. DSPR451G EHTs that have been cultured isometrically undergo adaptation, with no change in action potential parameters, conduction velocity, or contractile function, a phenotype confirmed by global proteomic analysis. However, when DSPR451G EHTs are subjected to increased diastolic stretch, they exhibit concomitant reductions in conduction velocity and the expression of connexin-43. These effects are rescued by inhibition of both lysosome activity and ERK signaling. Our results indicate that the response of DSPR451G EHTs to mechanical stimuli depends on the strain and the timing of the applied stimulus, with increased diastolic stretch unmasking conduction deficits in a concealed-phase model of ACM.

A constitutive modeling approach to simulate time‐dependent phenomena in rubber‐like materials

AbstractIndustrial rubber materials and similar rubber‐like materials exhibit complex mechanical behavior including nonlinear stress‐strain behavior up to large strains, hysteresis, Mullins effect, permanent set, as well as time‐dependent effects, like relaxation and rate dependency. The modeling of all these phenomena is a challenging task. One constitutive model that is capable to capture many effects in the large strain regime is the so‐called model of rubber phenomenology (MORPH). However, it is not able to capture any of the mentioned time‐dependent phenomena. Thus, this contribution deals with the extension of this model to simulate relaxation and rate dependency of rubber‐like materials. Thereby, a basic modeling approach is proposed, where only a slight change in the original system of tensorial equations is necessary. This approach is further extended by applying not only a constant relaxation time, but also loading history‐depended relaxation properties. For numerical simulations, a time discretization has to be applied to the constitutive equations, which is briefly shown. Finally, the extended MORPH model is applied to two different materials: an industrial rubber material and a polyurethane based adhesive. In both cases, the extended MORPH model is adjusted to uniaxial tension test data by parameter identification procedures. It will be shown that basic time‐dependent phenomena of rubber‐like materials can be captured well with the proposed extensions.

Empirical Interscale Finite Element Method (EIFEM) for modeling heterogeneous structures via localized hyperreduction

This work proposes a special type of Finite Element (FE) technology – the Empirical Interscale FE method – for modeling heterogeneous structures in the small strain regime, for both dynamic and static analyses. The method combines a domain decomposition framework, where interface conditions are established through “fictitious” frames, with dimensional hyperreduction at subdomain level. Similar to other multiscale FE methods, the structure is assumed to be partitioned into coarse-scale elements, each of these elements is equipped with a fine-scale subgrid, and the displacements of the boundaries of the coarse-scale elements are described by standard polynomial FE shape functions. The distinguishing feature of the proposed method is the employed “interscale” variational formulation, which directly relates coarse-scale nodal internal forces with fine-scale stresses, thereby avoiding the typical nested local/global problems that appear, in the nonlinear regime, in other multiscale methods. This distinctive feature, along with hyperreduction schemes for nodal internal and external body forces , greatly facilitate the implementation of the proposed formulation in existing FE codes for solid elements. Indeed, one only has to change the location and weights of the integration points, and to replace a few polynomial-based FE matrices with “empirical” operators, i.e., derived from the information obtained in appropriately chosen computational experiments. We demonstrate that the elements resulting from this formulation are not afflicted by volumetric locking when dealing with nearly-incompressible materials, and that they can handle non-matching fine-scale grids as well as curved structures. Last but not least, we show that, for periodic structures, this method converges upon mesh refinement to the solution delivered by classical first-order computational homogenization. Thus, although the method does not presuppose scale separation, it can represent solutions in this limiting case by taking sufficiently small coarse-scale elements.

Temperature dependent large strain cavitation in ultra high molecular weight polyethylene during tensile deformation

The large strain cavitation stemmed from the fragmentation of the highly oriented amorphous network in the quenched ultra high molecular weight polyethylene was investigated as a function of deformation temperature. The critical stress for initiating such cavitation was found to be dependent on the deformation temperature (Td) in a way being constant below Td of 90 °C but increased with Td above 90 °C. This peculiar deformation temperature dependency of critical stress for the large strain cavitation stress was found to be associated with the activation of the αⅡ-relaxation in the deformed samples. The αⅡ-relaxation temperature increased with the increase of Td, which was attributed to the increase of the stability of the fibrils formed at large strain. The difference between αⅡ-relaxation temperature and deformation temperature showed a one-to-one correspondence to the critical stress of large strain cavitation indicating a stress was required to activate the αⅡ-relaxation at a selected Td to initiate failure of the oriented network so that cavitation in the large strain regime.

A modified neo-Hookean model for semi-crystalline thermoplastics assessed by relaxation and zero-stress creep tests of recycled polypropylene and polyoxymethylene

The mechanical behavior of thermoplastics is strongly rate-dependent, and oftentimes it is difficult to find constitutive models that can accurately describe their behavior in the small to moderate strain regime. In this paper, a hyperelastic network model (modified neo-Hookean) and a set of experiments are presented. The testing consists of monotonic tensile loading as well as stress relaxation and zero stress creep. Two materials were tested, polyoxymethylene (POM) and recycled polypropylene (rPP), representing one more rigid and brittle and one softer and more ductile semi-crystalline polymer. The model contains two main novelties. The first novelty is that the stiffness is allowed to vary with the elastic deformation (in contrast to a standard neo-Hookean model). The second novelty is that the exponent governing viscous relaxation is allowed to vary with the viscous deformation. The basic features of the new model are illustrated, and the model was fitted to the experimental data. The model proved to be able to describe the experimental results well.

Second-order multi-scale modelling of natural and architected materials in the presence of voids: Formulation and numerical implementation

This contribution proposes a second-order computational homogenisation formulation for natural and architected materials in the presence of voids. The macro-scale is described by a second gradient continuum theory in the finite strain regime, and the micro-scale is modelled by the concept of representative volume element (RVE) within the classical first-order continuum mechanics. The Method of Multi-scale Virtual Power is employed to link the two scales, ensuring a variationally consistent scale transition. Unlike the multi-scale model proposed by Rodrigues Lopes and Andrade Pires (2022), the developed formulation allows the consideration of voids in the RVE domain and boundary, which is critical for modelling cellular materials, lattice structures, and metamaterials, among others. This is achieved by defining the kinematical quantities only in the solid domain of the RVE and postulating a new homogenisation relation for the second-order gradient. The kinematic constraints are imposed on the RVE by the Lagrange multiplier method and particularised for minimal (lower bound), periodic and direct (upper bound) conditions. It is demonstrated that the homogenised macroscopic stress tensors can be expressed in terms of the Lagrange multipliers. The finite element method is adopted for the numerical solution of the micro and macro equilibrium. The Newton–Raphson scheme is employed to solve the non-linear systems of equations at both scales and the consistent macroscopic tangents required for the FE2 framework are derived. Several numerical examples of porous solids, lattice structures and metamaterials illustrate the consistency and applicability of the formulation for two and three-dimensional problems.

A mixed integration point (MIP) formulation for hyperelastic Kirchhoff–Love shells for nonlinear static and dynamic analysis

We present a mixed integration point (MIP) formulation for hyperelastic isogeometric Kirchhoff–Love shells. While previous works have proposed mixed integration point schemes for different structural formulations in the context of geometric nonlinearity, we extend this concept to the large strain regime in this paper. The non-trivial extension to the nonlinear dynamic analysis for these materials based on the one-step energy-conserving method is also proposed. We present a general, consistent derivation of the formulation, which is not restricted to Kirchhoff–Love shells, hyperelastic materials, or isogeometric analysis, but can be applied to any structural problem involving geometric and material nonlinearities. Several numerical benchmark examples demonstrate the applicability and efficiency of the method.

Reflectance anisotropies of polycrystalline Ce[formula omitted] Gd[formula omitted] O[formula omitted]/ Si[formula omitted] interfaces

Ce1−xGdxO2−x/2 thin films were deposited by spin coating on oxidized Si(001) substrates. Two strain regimes are observed by μ− Raman spectroscopy: for x< 0.1 the films are tensile strained, whereas a strain component of the wave number shift of −71.2x cm−1 compensates with a 32.6x cm−1 bond component for x> 0.1. Reflectance anisotropy spectroscopy (RAS) measurements were carried out on these films in which interface-related optical anisotropies signatures appearing in the 1.5 eV to 3.6 eV photon energy range are found dependent on the incorporation of Gd in the lattice. To explain the observed RAS signatures with a complex reflectance three-phase model, we resorted to spectroscopic ellipsometry (SE) to retrieve the interface optical anisotropies (IOA) related to the changes in refractive index, <Δn>, between interface formed by both the oxidized Si(001) and polycrystalline CeO2:Gd films, and to assess the CeO2 energy gap variation from 3.2 to 2.8 eV in the 0 <x< 0.4 composition range. This study renders the combination of RAS, Raman, and SE versatile tools to optimize the growth parameters during the fabrication of devices based on polycrystalline CeO2 on a quantitative basis.

Strain-tuned optical conductivity of monolayer PbBiI

In this paper, we investigate the optical response of the PbBiI single-layer by developing a strain-induced Kane–Mele model from Peierls substitution and by employing the Kubo formula at low temperatures. We address three different regimes of uniform and non-uniform classes created by tuning the strength of the strain. From a detailed analysis of the electronic band structure, we find that the Rashba spin splitting gap is destroyed with strain, while the bulk gap slightly changes. We also find that interband optical transitions exhibit a blueshift spectrum with strain. Interestingly, all these findings are independent of the regime and class of strain. However, our simulations show that only the non-uniform class of strain leads to anisotropic optical conductivity. These results enhance optoelectronic applications of low-dimensional materials.

Fabricating of a custom 3D-printed setup for evaluating gel-based strain sensors

Health monitoring systems that incorporate stretchable sensors can provide real-time feedback on a person's physical activity, stress levels, and overall well-being. For instance, stretchable sensors based on conductive hydrogels have emerged as a promising technology for monitoring physiological signals such as heart rate, respiration, and muscle activity. For developing such systems, a strain machine is accounted as the first requirement for laboratories focusing on developing conductive hydrogels as strain sensors. In this article, we present a programmable, user-friendly, and versatile 3D-printed setup designed and fabricated for measuring the strain and strain sensitivity of soft electronic materials. The setup comprises a computer (or mobile), an impedance analyzer, and the strain machine that are required for developing stretchable strain sensors in scientific laboratories. We provide a very detailed build manual on how to manufacture and use the strain machine, using an ionic conductive hydrogel based on polyacrylic acid and polyvinyl alcohol as a model system. The results demonstrated the excellent performance of the strain machine in applying programmable strain regimes to the material of interest. By offering clear instructions and a build manual, our work enables scientific researchers to construct an affordable and user-friendly strain machine to boost their research progress.

The biomechanics of chewing and suckling in the infant: A potential mechanism for physiologic metopic suture closure.

Craniosynostosis is a condition with neurologic and aesthetic sequelae requiring invasive surgery. Understanding its pathobiology requires familiarity with the processes underlying physiologic suture closure. Animal studies have shown that cyclical strain from chewing and suckling influences the closure of cranial vault sutures, especially the metopic, an important locus of craniosynostosis. However, there are no human data correlating strain patterns during chewing and suckling with the physiologically early closure pattern of the metopic suture. Furthermore, differences in craniofacial morphology make it challenging to directly extrapolate animal findings to humans. Eight finite-element analysis (FEA) models were built from craniofacial computer tomography (CT) scans at varying stages of metopic suture closure, including two with isolated non-syndromic metopic craniosynostosis. Muscle forces acting on the cranium during chewing and suckling were simulated using subject-specific jaw muscle cross-sectional areas. Chewing and suckling induced tension at the metopic and sagittal sutures, and compressed the coronal, lambdoid, and squamous sutures. Relative to other cranial vault sutures, the metopic suture experienced larger magnitudes of axial strain across the suture and a lower magnitude of shear strain. Strain across the metopic suture decreased during suture closure, but other sutures were unaffected. Strain patterns along the metopic suture mirrored the anterior to posterior sequence of closure: strain magnitudes were highest at the glabella and decreased posteriorly, with minima at the nasion and the anterior fontanelle. In models of physiologic suture closure, increased degree of metopic suture closure correlated with higher maximum principal strains across the frontal bone and mid-face, a strain regime not observed in models of severe metopic craniosynostosis. In summary, our work provides human evidence that bone strain patterns from chewing and suckling correlate with the physiologically early closure pattern of the metopic suture, and that deviations from physiologic strain regimes may contribute to clinically observed craniofacial dysmorphism.

Mechanical, Electronic, and Optical Properties of 8-16-4 Graphyne: A 2D Carbon Allotrope with Dirac Cones

Graphene’s success has led to the theoretical prediction and experimental synthesis of various 2D carbon-based allotropes. To explore the mechanical, structural, electronic, and optical properties of 8-16-4 graphyne, we employed density functional theory using the GGA/PBE approach, ab initio molecular dynamics (AIMD), and classical reactive molecular dynamics simulations. Our AIMD results indicate that this material demonstrates excellent dynamical and thermal stabilities. It has a formation energy of −8.57 eV/atom and an elastic moduli of 262.37 GPa. Regarding its band structure, this graphyne analogue is a semimetal with two Dirac cones. It also exhibits transparency and intense optical activity in the infrared region. Notably, the band structure of 8-16-4 graphyne remains practically unchanged at moderate strain regimes. To our knowledge, this is the first known 2D carbon allotrope to exhibit such behavior.

A new implicit gradient damage model based on energy limiter for brittle fracture: Theory and numerical investigation

We present a general form of the gradient-enhanced damage theory and its numerical implementation using finite element method (FEM) in modeling quasi-static brittle crack growth in one- (1D), two- (2D) and three-dimensional (3D) bodies. Coupled equations of the equilibrium and a new implicit gradient damage formulation are introduced to govern the deformation of the solid and evolution of the damage. The resulting nonlocal damage evolution equation featuring the growth of diffusive crack is integrated with a characteristic length scale to eliminate the common mesh-bias issue in FEM implementation. In contrast to the traditional gradient-enhanced damage approaches, the nonlocal damage field here is defined as the primary variable of the damage evolution equation without interpolation mismatch between the displacement and nonlocal damage fields. For derivation of the material constitutive law and local damage parameter, a novel strain energy density (SED) function based on the energy limiter theory for brittle crack growth problems under small strain regime is introduced. To further improve the performance of the developed model, an initial SED threshold, which is used for determining the critical point when damage starts to initiate in the material, is integrated into the novel energy limiter theory. For preventing nonphysical failure in compression domains, the spectral decomposition technique for the strain tensor is adopted to split the reference SED. With integrating the energy limiter into the developed theory, unlike the conventional nonlocal damage theories where the interpretation of the length scale is still ambiguous, the developed nonlocal damage model defines the length scale parameter as the problem-dependent factor. The performance and ability of the proposed model are demonstrated via a set of representative numerical examples in 1D, 2D and 3D fracture problems.

Physical Regime Sensitivity

This work presents a novel sensitivity approach that quantifies sensitivity to regimes of a model’s state variables rather than constitutive model parameters. This Physical Regime Sensitivity (PRS) determines which regimes of a model’s independent variables have the biggest influence on an experiment or application. PRS analysis is demonstrated on a strength model used in the simulation of a copper Taylor cylinder. In a series of simulations, the strength model was perturbed sequentially in local regimes of plastic strain, plastic strain rate, temperature and pressure, and then the prediction of cylinder shape was compared to unperturbed calculations. Results show, for example, that the deformed length of the cylinder was most sensitive to strength at a strain rate of 1.0 × 104/sec., but the deformed footprint radius was most sensitive to strength at a strain rate of about 4.0 × 104/sec. Compared to current histogram approaches, PRS can be used to design or interpret integrated experiments by identifying not just which regimes are accessed somewhere in the experiment but the causality question of which regimes actually affect the measured data. PRS should allow one to focus experimental and modeling efforts where they are most needed and to better interpret experiments.

Evaluating the influence of deformation variables on dynamic recrystallization behavior using a crystal plasticity model

The present study is an attempt to model dynamic recrystallization (DRX) in a single phase metal using a mean field crystal plasticity (MFCP) based approach. A new empirical equation is proposed to model nucleation, in which the nucleation rate is a function of microstructure and plasticity descriptors that are known to affect DRX behavior, such as the temperature, strain rate, grain fineness and stored energy. Grains undergo nucleation when their dislocation density exceeds a threshold value. Subsequently, new grains grow based on the difference in stored deformation energy with respect to the average value over all grains. The MFCP-DRX model is able to correctly predict trends for the flow stress, dislocation density evolution, grain size evolution and kinetics across a range of temperatures and strain rates for uniaxial compression. Transition of the flow stress from single to multiple peaks is observed with increasing temperature and decreasing strain rate, thus comparing well against known DRX trends. The evolutions of crystallographic texture during DRX in uniaxial compression and plane strain compression are compared against experimental observations. A sensitivity analysis is conducted to understand the effect of variables on nucleation and growth. The competition between nucleation and growth dominated deformation in different strain regimes is analyzed in detail across various temperatures and strain rates.

Dislocation mediated dynamic tension-compression asymmetry of a Ni2CoFeV0.5Mo0.2 medium entropy alloy

Although tension-compression (T-C) asymmetry in yield strength was rarely documented in coarse-grained face centered cubic (FCC) metals as critical resolved shear stress (CRSS) for dislocation slip differs little between tension and compression, the T-C asymmetry in strength, i.e., higher strength when loaded in compression than in tension, was reported in some FCC high entropy alloys (HEAs) due to twinning and phase transitions activated at high strain regimes in compression. In this paper, we demonstrate a reversed and atypical tension-compression asymmetry (tensile strength markedly exceeds compressive strength) in a non-equiatomic FCC Ni2CoFeV0.5Mo0.2 medium entropy alloy (MEA) under dynamic loading, wherein dislocation slip governs dynamic deformation without twins or phase transitions. The asymmetry can be primarily interpreted as higher CRSS and more hard slip modes (lower average Schmid factor) activated in grains under dynamic tension than compression. Besides, larger strain rate sensitivity in dynamic tension overwhelmingly contributes to the higher flow stress, thanks to the occurrence of more immobile Lomer-locks, narrower spacing of planar slip bands and higher dislocation density. This finding may provide some insights into designing MEAs/HEAs with desired properties under extreme conditions such as blast, impact and crash.

Effect of electric field on mechanical behavior of vertically-aligned carbon nanotube structures

Here, we summarize various reports on the mechanical response of vertically aligned carbon nanotubes forest (CNTF) structures under an applied electric field. Quasi-static compression tests on CNTF structures show a dramatic strengthening by application of the electric field both in low-strain (linear) and high strain (nonlinear) regimes. The CNTF structures also show a finite hysteresis, i.e., energy dissipation, in stress–strain behavior during a loading–unloading cycle. Tests demonstrate that the application of an electric field can tailor the energy absorption capacity of CNTF structures. In practice, the energy absorption capacity of CNTF structures increases by several folds when the loading and unloading (under quasi-static strain rates) are performed in the presence and the absence of the electric field, respectively. However, the improvement in the energy absorption capacity decreases drastically at higher strain rates. Additionally, applying an electric field improves the creep resistance of the CNTF structures. Overall, the summarized studies show promising electro-mechanical properties of CNTF structures which are helpful in developing the next generation of nano-and micro-electro-mechanical devices and sensors.