Uniaxial Extension Research Articles

Flow-induced crystallization of polylactides

In this work, the flow-induced crystallization of two polylactides (PLAs) with different microstructures (different l-lactic acid contents) is studied using simple shear, uniaxial extension and capillary flow experiments. In a simple shear and capillary flow, an increase in shear rate and a decrease in temperature were found to enhance the crystallization kinetics particularly for Weissenberg numbers (based on the reptation relaxation time, Wi) greater than 1 (strong flow causing chain stretching). On the other hand, in a uniaxial extensional flow, once a critical Hencky strain is achieved, crystallization starts independently of strain rate and temperature. The amount of mechanical work per unit volume imposed/dissipated onto the polymers during flow to initialize crystallization was also calculated in the simple shear, capillary, and extensional flow. The critical mechanical work for the onset of flow-induced crystallization was found to be independent of temperature and degree of molecular chain stretch (Wi) as Wi becomes greater than 1. The critical mechanical work for the onset of flow-induced crystallization in an extensional flow was found to be much smaller than that in a shear flow. The PLA sample with higher content of PLLA showed slightly higher zero-shear viscosity and a smaller thermodynamic barrier for the onset of crystallization. Finally, the degree of crystallinity increases linearly from 0% at the start of the flow-induced crystallization region and reaches a plateau at Wi equals to around 1.

Parameter-free strain-energy function which automatically and accurately matches benchmark test data for soft elastic solids

PurposeA new and explicit form of the elastic strain-energy function for modeling large strain elastic responses of soft solids is constructed based on Hencky's logarithmic strain tensor.Design/methodology/approachWell-designed invariants of the Hencky strain are introduced for characterizing deformation modes and, furthermore, a new interpolating technique is proposed for combining piecewise splines into a single smooth function.FindingsWith this new form and this new technique, objectives in three respects may be achieved for the first time.Originality/valueFirst, no adjustable parameters need to be treated. Second, large strain responses for three benchmark modes are derivable in a decoupled sense without involving strongly nonlinear coupling effects. Finally, large strain data may be automatically and accurately matched for three benchmark modes, including uniaxial, equi-biaxial and plane-strain extension. Numerical examples are presented and compared with usual approaches.

Evolution of the Surface Structure and Functional Properties of the Electroconducting Polymer Coatings onto Porous Films

Composite systems containing electroconducting polymer coatings (polyaniline and polypyrrole) applied to porous films of semicrystalline polymers (polyethylene, polypropylene, and polyvinylidene fluoride) have been prepared. Porous supports were obtained in the process based on polymer melt extrusion with subsequent annealing, uniaxial extensions, and thermal stabilization. Conducting coatings were formed by the oxidative polymerization of the monomers directly onto the porous supports. The structure (overall porosity, permeability, pore sizes, factor of orientation) and morphology (specific surface and character of the film surface) of the supports were characterized by sorptometry, filtration porosimetry, atomic force microscopy (AFM), and X-ray scattering techniques. It was observed that the porous supports have a strongly developed relief surface which is formed in the pore formation process. It was proven by scanning electron microscopy (SEM) that the porous supports have an oriented structure, and the surface of the composites is defined by the morphology inherent in the conducting component. It was shown that these composites (porous support/conducting coating) demonstrate electric conductivity both along the surface and between surfaces. It was demonstrated that the deposition of conducting coatings leads to an increase in the water wettability of the composites compared with pronounced hydrophobic supports. The composites are characterized by good adhesion between components due to a relief film surface as well as high mechanical strength and elasticity provided by the oriented character of the supports.

Structure formation and depolarization relaxation processes in porous piezoactive polyvinylidene fluoride films

Piezoactive porous polyvinylidene fluoride films prepared in the process based on melt extrusion with subsequent isometric annealing, uniaxial extension and thermal fixation have been studied. It was shown that two competing orientation processes -polymorphous transition of non-polar α-phase into polar piezoactive β-phase and formation of porous structure - occur during the uniaxial extension of annealed films. It has been established that orientation degree of extruded films is the key factor determining the efficiency of both processes. Thermally stimulated depolarization method was used to investigate the dipole relaxation in oriented films, and activation energy of these processes was found. The films were polarized using corona discharge and high-voltage contact methods, both, and the dependence of piezoelectric modulus on the polarization conditions has been obtained. The maximum value of piezoelectric modulus d31=30.1 pC/N was achieved by polarization of films in corona discharge method. Keywords: polyvinylidene fluoride, porous films, supramolecular structure, piezoelectric properties, polarization, relaxation processes.

On the choice of mathematical functions to model damage in anisotropic soft tissues

Soft tissues display highly non linear behaviour under various mechanical loads. Due to various diseases, injury or when exposed to supra physiological loads, soft tissues demonstrate a softening behaviour or damage. Continuum damage models coupled with continuum material models have been successful in mathematically predicting the damage in tissues. Continuum models also incorporate anisotropy to give better predictions of the response of tissues at higher stretch values. In this work, three different mathematical decaying functions (exponential, logarithmic and stretched exponential) have been adopted to propose continuum damage models for anisotropic soft tissues. The model predictions were compared with the experimental data of uniaxial extension from literature. The stretched exponential function with the least computed error demonstrated the most accurate performance for predicting the damage in soft tissues. A general algorithm for the procedure was also remarked upon.

Analisys of interlaminar stresses in composite laminates by finite difference method

In this work, full stress tensor components regarding stress state for a simmetrical composite laminate under uniform uniaxial extension have been determined. Off-plane stresses are specially meaningful due to the fact that they are responsible for failure mechanisms such as delamination and shear stress cracking. A finite difference scheme has been used to solve internal equilibrium equations subjected to stress-free boundary conditions along boundary lines; moreover symmetry considerations have been made. In such way, we get an improvement in solutions in contrast with results obtained following bidimensional reasoning and using laminate based elements. Off-plane stresses for differents ply-sequences have been evaluated and maximum and minimum values for different fibers orientations were explored.

Tensile strength of a compacted vegetated soil: Laboratory results and reinforcement interpretation

So far, root reinforcement on soil has been primarily evaluated through direct shear and roots pull-out tests, while the effect of other stress paths and the behaviour at the soil–root​ interface are still poorly investigated. In this regard, an apparatus with the facility to test soil and roots jointly under uniaxial extension is presented in the paper, together with its first results.Vegetated samples with Cynodon dactilon were tested after one and three months of growth. Soil exhibited a ductile response when close to saturation and a brittle one at drier states within the field capacity domain. The presence of roots increased the material’s tensile strength and enhanced its post-peak ductility. Measurements of matric suction and degree of saturation allowed interpreting the results in terms of constitutive stresses within a shear strength failure criterion for partially saturated soils. Even if plant roots critically impacted soil hydraulics, a positive strengthening effect was noticed on its mechanical behaviour.Roots mechanical and morphological features were characterised after tests. Two well-established root reinforcement models in the literature were used to interpret the results at the phenomenological scale while considering the hydro-mechanical behaviour at the soil–root interface, different root’s reinforcement mechanisms and the effect of soil’s hydro-mechanical states.

Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels

Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, full-fidelity simulation techniques such as Finite Element Analysis, while effective, can be prohibitively computationally expensive when they are used to explore the massive input parameter space of heterogeneous materials. Therefore, there has been significant recent interest in machine learning-based models that, once trained, can predict mechanical behavior at a fraction of the computational cost compared to full fidelity simulations. Over the past several years, research in this area has been focused mainly on predicting single Quantities of Interest (QoIs). However, there has recently been an increased interest in a more challenging problem: predicting full-field QoI (e.g., displacement/strain fields, damage fields) for mechanical problems. Due to the added complexity of full-field information, network architectures that perform well on single QoI problems may perform relatively poorly in the full-field QoI problem setting. This problem is also challenging because, even outside the Mechanics research community, deep learning approaches to image-to-image mapping and full-field image analysis remain poorly understood. The work presented in this paper is twofold. First, we made a significant extension to the Mechanical MNIST dataset designed to enable the investigation of full-field QoI prediction. Specifically, we added Finite Element simulation results of quasi-static brittle fracture in a heterogeneous material captured with the phase-field method. This problem was chosen as a broadly relevant ”challenge problem” for full-field QoI prediction. Second, we investigated multiple Deep Neural Network architectures and subsequently established strong baseline performance for predicting full-field QoI. We found that a MultiRes-WNet architecture with straightforward data augmentation achieves 0.80% and 0.34% Mean Absolute Percentage Error on full-field displacement prediction for Equibiaxial Extension and Uniaxial Extension datasets in the Mechanical MNIST Fashion dataset, respectively. In addition, we found that our MultiRes-WNet architecture combined with a basic Convolutional Autoencoder achieves a mean F1 score of 0.87 on the newly added Mechanical MNIST Crack Path dataset. In addition to presenting the results in this paper, we have released our model implementation and the Mechanical MNIST Crack Path dataset under open-source licenses. We anticipate that future researchers will directly use our model architecture on related datasets and potentially design models that exceed the baseline performance for predicting full-field QoI established in this paper.

Ionic Polymer Nanocomposites Subjected to Uniaxial Extension: A Nonequilibrium Molecular Dynamics Study.

We explore the behavior of coarse-grained ionic polymer nanocomposites (IPNCs) under uniaxial extension up to 800% strain by means of nonequilibrium molecular dynamics simulations. We observe a simultaneous increase of stiffness and toughness of the IPNCs upon increasing the engineering strain rate, in agreement with experimental observations. We reveal that the excellent toughness of the IPNCs originates from the electrostatic interaction between polymers and nanoparticles, and that it is not due to the mobility of the nanoparticles or the presence of polymer–polymer entanglements. During the extension, and depending on the nanoparticle volume fraction, polymer–nanoparticle ionic crosslinks are suppressed with the increase of strain rate and electrostatic strength, while the mean pore radius increases with strain rate and is altered by the nanoparticle volume fraction and electrostatic strength. At relatively low strain rates, IPNCs containing an entangled matrix exhibit self-strengthening behavior. We provide microscopic insight into the structural, conformational properties and crosslinks of IPNCs, also referred to as polymer nanocomposite electrolytes, accompanying their unusual mechanical behavior.

Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects.

Rheological Characterization of Chapatti (Roti) Enriched with Flour or Paste of House Crickets (Acheta domesticus).

Addition of edible insects to food products may improve the nutritional status but can also influence their techno-functional properties. This study investigates the impact of supplementing wheat flour by cricket flour or paste at different levels (5–15%) on the rheological and textural properties of flour, dough, and baked chapatti. Addition of freeze-dried cricket flour resulted in the highest water absorption. The storage modulus increased at higher level (10–15%) of supplementation to wheat flour indicating an increased dough consistency. Similarly, biaxial extension of the dough showed an increased resistance to extension and decreased extensibility at higher level of supplementation due to a reduced strength of the gluten network. Uniaxial extension of baked chapatti showed less extensible and harder chapatti with the addition of a higher amount of cricket flour or paste. At lower level (5%), incorporation of cricket flour resulted in chapatti with textural properties comparable to the reference. Oven dried cricket powder is suggested as the best option for incorporating in chapatti dough to improve food security in Asian Countries.

Synergistic ionic interactions in EMAA ionomer blends: A rheological and mechanical property investigation

The rheological and mechanical (tensile) properties of ethylene methacrylic acid (EMAA) ionomers neutralized by Na, Li, and Zn are investigated in binary combinations of two pure ionomers with different counterions. Molecular weight, methacrylic acid content, degree of neutralization, and ion type are tested as experimental parameters to investigate the composition that leads to the largest enhancement in rheological and mechanical properties. Binary cation blend components with low molecular weight and high neutralization reveal enhancement in rheological and mechanical properties beyond a linear mixing combination of material properties such as zero-shear viscosity, relaxation time, and Young’s modulus. The sticky reptation model is applied to EMAA ionomer blends of binary counterions to calculate the timescales of chain dynamics delayed by ionic associations. The ionic clusters of binary cations have longer-lasting ionic associations forming a reinforced reversible crosslink network. The experimental analysis consists of linear and nonlinear viscoelastic experiments, uniaxial extension, and dynamic mechanical analysis, which reveal the conditions and extent of synergism seen in binary EMAA ionomer blends.

Dynamics of a viscous drop under an oscillatory uniaxial extensional Stokes flow

We quantify the transient deformation and breakup of a neutrally-buoyant drop with viscosity λμ∗ immersed in another Newtonian fluid with viscosity μ∗ undergoing oscillatory uniaxial extension at zero Reynolds number. The interfacial tension acting between drop phase and medium phase is γ∗. The drop is initially a sphere of radius a∗. Since the external flow oscillates harmonically with a frequency ω∗, the strength of the imposed flow is characterized by an instantaneous capillary number, Ca=Ca0cos(Det), where Ca0=μ∗ε̇a∗/γ∗ and De=ω∗μ∗a∗/γ∗ is the dimensionless frequency, or Deborah number. Here, ε̇ is the rate of extension in the imposed flow. We utilize boundary-integral computations to calculate the evolution of drop interface as a function of Ca0 and De, focusing primarily on the case where the drop and surrounding fluid have equal viscosities. The computations suggest two families of behavior for the drop deformation. First, below a critical Deborah number (which we determine to be in the interval 0.375<De<1.0), the drop breaks up in a finite time at a critical capillary number that is a function of De. At sufficiently small De the critical capillary number increases linearly with De and the breakup mode is that of “center-pinching”. On increasing De the break-up mode switches to “end-pinching”, and on further increasing De it appears that the critical capillary number diverges at a critical Deborah number between 0.375 and 1.0. This divergence signals the transition to the second family of behavior where the drop attains a long-time periodic state, or alternance, regardless of Ca0. However, at large Ca0 the drop dynamics exhibits a two time-scale behavior: the drop deforms instantaneously at a fast capillary relaxation time-scale τ∗=μ∗a∗/γ∗, whereas the maximum deformation attained during a cycle of the imposed flow grows at the slow time-scale τ∗Ca0=ε̇(μ∗a∗/γ∗)2. As such, the state of alternance is approached exceedingly slowly at large Ca0. Lastly, we perform calculations for different viscosity ratios and find the drop dynamics to be in qualitative agreement with above observations.

Constitutive Modelling of Polylactic Acid at Large Deformation Using Multiaxial Strains.

Sheet specimens of a PLLA-based polymer have been extended at a temperature near to the glass transition in both uniaxial and planar tension, with stress relaxation observed for some time after reaching the final strain. Both axial and transverse stresses were recorded in the planar experiments. In all cases during loading, yielding at small strain was followed by a drop in true stress and then strain hardening. This was followed by stress relaxation at constant strain, during which stress dropped to reach an effectively constant level. Stresses were modelled as steady state and transient components. Steady-state components were identified with the long-term stress in stress relaxation and associated with an elastic component of the model. Transient stresses were modelled using Eyring mechanisms. The greater part of the stress during strain hardening was associated with dissipative Eyring processes. The model was successful in predicting stresses in both uniaxial and planar extension over a limited range of strain rate.

Harnessing shape optimization techniques to develop novel methods to determine shear properties in PMCs

Shape optimization techniques are utilized to develop an optimal shear specimen for polymer matrix composites (PMCs) in which shear stresses result from simple uniaxial extension. An expanding array of composite applications means certification and damage tolerance are critical design factors. This methodology improves the ease of characterization for classically challenging material properties, such as shear failure. Numerical simulations were conducted using IM7/977-3 unidirectional prepreg mechanical properties. Large shear strain concentrations in the region of interest led to predicted failure in the region of interest under conditions consistent with shear. The geometry generated by the shape optimization should continue to be explored due to its capability generating a geometry which can measure the shear modulus and shear strength of a laminate. The shape optimization method’s ability to tailor a sample geometry for a desired strain state and failure mode leads the authors to recommend exploration of additional optimized test geometries for other failure modes and materials, in addition to the experimental investigation of the geometry generated for shear.

Thermo-mechanical modeling of viscoelastic crystallizable shape memory polymers

Shape memory polymers (SMPs) are a class of soft active materials that have the ability to retain one or multiple temporary shapes and exhibit deformation as a response to stimuli. The temporary shapes involved can be very complex but SMPs can recover large amounts of strains as compared to other smart materials. They have a wide range of applications in fields as diverse as healthcare, transportation, energy generation, etc. and their mechanism can be easily altered. Hence, there is an increasing need to model their behavior. This paper discusses the behavior of a thermally activated subclass of SMPs in which the temporary shape is fixed by a crystalline phase and the return to original shape is due to the transition of this crystalline phase. We simulate its thermo-mechanical behavior using a framework based on the theory of multiple natural configurations. Viscoelastic effects have been incorporated using a rate type model along with the anisotropy of the crystalline phase. The model has been applied to boundary value problems of homogeneous deformations such as uniaxial extension of dual shape and triple shape memory polymers under controlled stress and strain conditions. The model has also been applied to boundary value problems related to inhomogeneous deformations such as circular shear, inflation, and extension of a hollow cylinder. The effects of parameters such as temperature, external stress, crystallinity, shear modulus and relaxation time on the nonlinear deformation have been studied. The results are found to be consistent with the experimental data and show how the complicated thermo-mechanical behavior and shape memory effect are influenced by these parameters.

Predictive Continuum Constitutive Modeling of Unfilled and Filled Rubbers

The general CSE model fits Treloar’s uniaxial extension test and predicts unfitted uniaxial compression, equibiaxial extension, biaxial extension, pure shear, and simple shear tests. As a newly proposed method, the general CSE model, along with the stress-softening ratio, the residualstretch ratio, and the weighted piecewise two-point interpolation function, fits the Cheng–Chen’s test and the Diani–Fayolle–Gilormini’s test in cyclic uniaxial extension at different pre-stretches and predicts corresponding responses at untested pre-stretches. Physical mechanisms of the Mullins effect have also been predicted based on the evolution of constitutive parameters.

Mathematical modelling of uniaxial extension of a heterogeneous gas cell wall in bread dough: Stress fields and stress concentration analysis relating to the proving and baking steps

A mathematical model was developed to increase the understanding of stress concentrations within a gas cell wall (GCW) in bread dough during baking. The GCW was composed of a single A-type wheat starch granule surrounded by various proportions of gluten typical of GCWs when about to rupture. Finite element simulations were carried out in 2D using linear viscoelasticity and visco-hyperelasticity. Strain orders of magnitude and rates relevant to dough during baking were applied as boundary conditions for two plausible sets of mechanical properties before and after protein coagulation and starch gelatinization (T < 50–60 °C and T > 70–80 °C). The average stress within the GCW was found to be strongly dependent on the starch fraction. Gluten-starch interactions influenced average stress values considerably when the starch fraction was greater than 11% v/v. The locations within the GCW where rupture was most likely to be initiated were identified by mapping maximal stress points using stress field and triaxiality analysis and the findings were discussed. • A mathematical model has been developed to better understand Gas Cell Wall rupture at the scale of bread dough constituents. • Stress fields in an extending GCW composed of a single starch granule and gluten were mapped. • Locations for rupture initiation in GCWs at strain and strain rates relevant to bread baking were identified. • The effects of gluten-starch proportion and gluten-starch interactions on stress concentration were discussed. • Gluten-starch proportion influenced average stress when the proportion was greater than 11%.

A comparison of the brittle PMMA with the ductile PC on the elasticity and yielding from a molecular dynamics perspective

The microscopic stress origins of elasticity and yielding of the brittle poly-(methyl methacrylate) (PMMA) under uniaxial extension condition was studied using a previously proposed method, and compared with ductile polycarbonate (PC). For this brittle material, the same energetic terms, namely, the bond, angle, and van der Waals (vdW) stresses, were identified as the major contributors to the overall stress response before the occurrence of cavitation that precedes the brittle fracture, meaning that the stress is produced under the identical mechanism with the ductile PC. However, all terms for PMMA have larger values, that add up to the overall higher stress, because of the more remarkable bond stretching and angle bending, and the loss of repulsive vdW interaction at even shorter distances between homochain adjacent sidechains than PC. The bulky and dense sidechains of PMMA are responsible for a large portion of the total stress response, and causes the difficulty in their conformational relaxation, and thus can be identified as a key structural reason for the larger elastic modulus and a potential candidate for the causes of its brittleness. This provided an insight into the higher elastic modulus and brittleness of PMMA.

Total finite element tearing and interconnection method for computationally efficient micromechanical analysis

Micromechanical analysis of a representative volume element (RVE) is commonly performed to estimate the material’s effective/homogenized properties in a multiscale analysis of deformation of materials. Typically numerical analysis techniques such as the finite element (FE) method are used for such an analysis. A highly refined FE mesh is required to capture microstructure features accurately for the analysis of RVE. However, this increases the number of degrees of freedom and affects computational time adversely. In this contribution a total finite element tearing and interconnection (TFETI) domain decomposition method based approach is presented for a computationally efficient micromechanical analysis. Two critical aspects of the micromechanical analysis, namely, a) computationally efficient solution of the boundary value problem and b) ease of computation of effective properties, are addressed in this work. This work focuses on the displacement driven micromechanical analysis where the boundary conditions are available in terms of displacements over the entire boundary. Two types of displacement boundary conditions, viz uniform or proportional displacements and periodic displacements corresponding to the state of uniaxial extension and simple shear are considered. The performance of the adapted TFETI with commonly used preconditioners, namely Dirichlet and lumped, for such displacement driven analysis is investigated. An efficient algorithm that exploits the structure of the TFETI method is proposed to calculate the effective properties. The proposed method’s efficacy is demonstrated by analyzing some representative model problems of composite materials. It is observed that the method’s performance depends on various problem parameters such as volume fraction, the shape of inclusion, the distance between the inclusions, and the contrast between the material properties of matrix and inclusion. The performance also depends on the numerical method parameters, such as the number of subdomains, shape of subdomains, and preconditioners. Therefore, a systematic study is carried out to study the influence of these parameters on the method’s performance.