Effects Of Nonlinear Deformation Research Articles

Measuring the viscoelastic relaxation function of cells with a time-dependent interpretation of the Hertz-Sneddon indentation model

The Hertz-Sneddon elastic indentation model is widely adopted in the biomechanical investigation of living cells and other soft materials using atomic force microscopy despite the explicit viscoelastic nature of these materials. In this work, we demonstrate that an exact analytical viscoelastic force model for power-law materials, can be interpreted as a time-dependent Hertz-Sneddon-like model. Characterizing fibroblasts (L929) and osteoblasts (OFCOLII) demonstrates the model's accuracy. Our results show that the difference between Young's modulus EY obtained by fitting force curves with the Hertz-Sneddon model and the effective Young's modulus derived from the viscoelastic force model is less than 3%, even when cells are probed at large forces where nonlinear deformation effects become significant. We also propose a measurement protocol that involves probing samples at different indentation speeds and forces, enabling the construction of the average viscoelastic relaxation function of samples by conveniently fitting the force curves with the Hertz-Sneddon model.

In-situ quantification of microscopic contributions of individual cells to macroscopic wood deformation with synchrotron computed tomography

Wood-based composites hold the promise of sustainable construction. Understanding the influence on wood cellular microstructure in the macroscopic mechanical behavior is key for engineering high-performance composites. In this work, we report a novel Individual Cell Tracking (ICT) approach for in-situ quantification of nanometer-scale deformations of individual wood cells during mechanical loading of macroscopic millimeter-scale wood samples. Softwood samples containing > 104 cells were subjected to controlled radial tensile and longitudinal compressive load in a synchrotron radiation micro-computed tomography (SRµCT) setup. Tracheid and wood ray cells were automatically segmented, and their geometric variations were tracked during load. Finally, interactions between microstructure deformations (lumen geometry, cell wall thickness), cellular arrangement (annual growth rings, anisotropy, wood ray presence) with the macroscopic deformation response were investigated. The results provide cellular insight into macroscopic relations, such as anisotropic Poisson effects, and allow direct observation of previously suspected wood ray reinforcing effects. The method is also appropriate for investigation of non-linear deformation effects, such as buckling and deformation recovery after failure, and gives insight into less studied aspects, such as changes in lumen diameter and cell wall thickness during uniaxial load. ICT provides an experimental tool for direct validation of hierarchical mechanical models on real biological composites.

A new workflow for the effective distinction between necking induced spilts and direct fracture phenomena

The predominant mode of failure in stamping applications is still splitting due to localized necking. This kind of failure is very effectively captured by the forming limit curve, especially if nonlinear deformation effects are modelled. With the sharp increase in low-ductility (weight efficient) materials, direct fracture phenomena (surface cracks, edge cracks, shear cracks, etc.) increasingly enter the daily industrial stamping practice, especially in follow operations. Contrary to the classical FLC analysis, there exists nowadays no industry-wide standardization for characterizing these phenomena. This drives up modelling costs and reduces the expected improvement in the overall modelling uncertainty. It therefore becomes crucial to understand and detect the circumstances in which an advanced fracture characterization is necessary, such that limited resources can be effectively allocated. The present contribution aims to propose such a workflow. Firstly a reasonable lower bound for the fracture limits is estimated based on theoretical considerations and evidence from scientific literature. This estimation is used to conduct a first analysis step which is used to categorize the process based on whether a standard modelling approach is sufficient to deliver the required accuracy. A second step of accurate fracture identification is therefore only recommended for the subset of geometries with particularly high risk. The approach is tested on data for AA6016 and DP980 from literature and validated based on published experimental results.

Linear and Nonlinear Deformation Effects in the Permanent GNSS Network of Cyprus.

Permanent Global Navigation Satellite Systems (GNSS) reference stations are well established as a powerful tool for the estimation of deformation induced by man-made or physical processes. GNSS sensors are successfully used to determine positions and velocities over a specified time period, with unprecedented accuracy, promoting research in many safety-critical areas, such as geophysics and geo-tectonics, tackling problems that torment traditional equipment and providing deformation products with absolute accuracy. Cyprus, being located at the Mediterranean fault, exhibits a very interesting geodynamic regime, which has yet to be investigated thoroughly. Accordingly, this research revolves around the estimation of crustal deformation in Cyprus using GNSS receivers. CYPOS (CYprus POsitioning System), a network of seven permanent GNSS stations has been operating since 2008, under the responsibility of the Department of Lands and Surveys. The continuous flow of positioning data collected over this network, offers the required information to investigate the behavior of the crustal deformation field of Cyprus using GNSS sensors for the first time. This paper presents the results of a multi-year analysis (11/2011–01/2017) of daily GNSS data and provides inferences of linear and nonlinear deforming signals into the position time series of the network stations. Specifically, 3D station velocities and seasonal periodic displacements are jointly estimated and presented via a data stacking approach with respect to the IGb08 reference frame.

Analyzing onset of nonlinearity of a colloidal gel at the critical point

In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasi-linear integral model is developed with the time-strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation and validate the Bailey criterion using the developed viscoelastic framework.

Perturbation Method in the Problem of Compression-Shear Shock Load for a Nonlinear Elastic Half-Space

On the example of a one-dimensional nonstationary problem of oblique impact on the boundary of a nonlinear elastic isotropic half-space, the question of the manifestation of nonlinear deformation effects via basic evolution equations is studied. Much attention is given to the behavior of the solution behind the leading edge of a quasi-transverse shock wave. For particular cases of boundary conditions, it is shown that the onset region of the evolution equation of a quasi-transverse wave is preceded by a series of preliminary transitions to the intermediate internal problems of the small parameter method determined by the type of preliminary bulk deformation. This deformation consistently affects the distortion of the characteristic coordinates and the leading edge of the quasitransverse process. As a consequence, the transition to the evolution equation of quasi-transverse waves occurs with simultaneous change of all independent variables of the boundary value problem.

Nonlinear shear and uniaxial extensional rheology of polyether-ester-sulfonate copolymer ionomer melts

We present unique nonlinear shear and extensional rheology data of unentangled amorphous polyester ionomers based on polyethers and sulphonated phthalates with sodium/lithium counterions. Previous linear viscoelastic measurements showed significant elasticity in these ionomers due to the formation of strong ionic aggregates. These ionomer melts exhibit viscoelastic properties similar to well-entangled melts with an extended rubbery plateau. To evaluate the effects of nonlinear deformation, the rheology of these ionomers was investigated using uniaxial extension and shear. The measurements were performed on a filament stretching rheometer and on a strain controlled rotational rheometer equipped with a cone-partitioned-plate setup. In extension, ionomer samples exhibited a decreasing strain hardening trend with increasing extension rates. At the same Weissenberg number, the same strain hardening was observed for different counterions. The presence of high solvating poly(ethylene oxide), PEO, along the backb...

Nonlinear Rheology of Lightly Sulfonated Polystyrene Ionomers

The effects of nonlinear deformation on the melt rheology of low molecular weight lightly sulfonated polystyrene ionomers (SPS) were investigated with dynamic, steady shear, and transient shear exp...

Electro-dynamic behavior of an electrically actuated micro-beam: Effects of initial curvature and nonlinear deformation

This paper presents a curved beam model for the nonlinear electro-dynamic analysis of micro-beams with initial curvature, taking into account the nonlinear electric force and nonlinear deformation. The governing equations of motion and boundary conditions are derived in an arc coordinate system. Unlike previous studies based on von Karman nonlinearity or considering mid-plane stretching only, the present study does not involve any assumptions on nonlinear deformation. Differential quadrature method and Petzold–Gear BDF method are employed to obtain the nonlinear electro-dynamic behavior of curved micro-beams. The effects of nonlinear deformation, initial gap and initial rise on the nonlinear electro-dynamic characteristics are studied.

Non-Linear Fatigue Fracture Analysis of Composite Laminates

In this paper, results of an experimental and numerical investigation of the effects of non-linear deformation on the fatigue crack growth in composite laminates are presented and discussed. Mode I fatigue fracture experiments are carried out on extended compact tension specimens under sinusoidal load control at a frequency of 4 Hz. The fatigue fracture test data are analysed using a power law relationship between the crack growth rates and the range of the path-independent J-integral. A two- dimensional finite element model of the extended compact tension specimen is set up in order to compute the J-integral values. The model is coupled with damage analysis in order to study the effect of non-linear deformation on the fatigue fracture performance. The damage analysis is based on the Tsai-Wu failure criterion. The non-linear model is verified by carrying out comparisons between the simulated mechanical behaviour of the extended compact tension specimen and the measured one. The damage distribution within the specimen is analyzed. The J-integral is computed over paths surrounding the crack tip and not crossing the damage zone. It is shown that taking into account the damage behaviour improves the fatigue fracture resistance, which is attributed to increased strain energy dissipation as a result of non-linear deformation.

Geometrical Nonlinear Deformation Effects in Composite Sandwich Plates Subjected to In-Plane Shear Loads

An experimental and analytical study is presented to investigate the nonlinear behavior of foam core sandwich plates subjected to in-plane shear loads. Due to the low flexural stiffness of sandwich structures, the geometrical nonlinear deformation effects tend to appear earlier in foam core sandwich plates than in other laminated and sandwich plates. However, the analysis performed is applicable to any laminated or sandwich composite plate. In studies presented herein the Theorem of Minimum Potential Energy has been used to determine the deflections, strains, and stresses in the plate. Polynomial functions are used that satisfy all of the boundary conditions. It is seen from the analytical results that the lateral deflection and the in-plane shear strains and stresses are nonlinear functions of the applied loads. In addition, the in-plane normal strains do occur under the laterally applied loads which cause the inequality of principle strains between the compressive face strains and the tensile face strains.

係留索の動的挙動を考慮した完全没水浮体の振動特性

In case of completely submerged floating structure, no change in buoyancy can beexpected with its dynamic motion and the restoring force fully depends on cables. Consequently, it is necessary to seize the relation between structural displacement and restoring force and to evaluate the effect ofnonlinear deformation of cables on the dynamic response. This study aims to evaluate the effect of deformation of mooring cable caused by self-weight, inertia and fluid force on the vibration of the structure. This paper introduces nonlinear equations of motion considering the dynamic behavior of the cables and investigates the effect of dynamic deformation of cables on whole behavior with numerical examples.