Large deformation extensional rheology of bread dough

The stress–strain curves of bread dough were derived under uniaxial compression, uniaxial tension and equi-biaxial tension loading conditions. In uniaxial compression, a lubricant was used to eliminate frictional effects between the loading platens and the sample. In uniaxial tension, cylindrical samples with thin flat discs at both ends (‘I’ samples) were tested. The discs at both ends were allowed to air-dry and were subsequently glued onto the loading platens. In equi-biaxial tension, a thin disc of dough was inflated into a bubble using pressurised air. The thickness at the top of the bubble was measured by shining a light through the walls of the bubble and recording the change in light intensity as the wall becomes thinner. All methods ensured that uniform deformation was obtained. Stress and strain were accurately evaluated using image analysis techniques. The tests were performed at various strain rates and speeds that defined the time dependence of the material. A non-linear viscoelastic model based on the Prony series and Van der Waals hyperelasticity was used to predict all test data. The model had a total of five material parameters and two time constants, which were set to represent the actual time scales of the experiments. A reasonable agreement between the experimental data and the chosen material model was observed.     

The effect of pre-test deformation on dough rheology

We show that the strain involved in forming a dough specimen before testing will often radically alter the measured rheological properties in shear and in elongation if these pre-strains are greater than about 0.5 (Hencky strain). It is shown that this may be accounted for by changing the G(1) value used in the damage function model to a relevant value.     

The rheology of bread dough made from four commercial flours

 A selection of four commercial flours has been subjected to extensive rheological measurements as part of a comprehensive program of wheat improvement. The results have been used to determine which of the many types of rheological measurements provide significant discrimination between various types of modern baker's flours (including biscuit flours) and to procure data suitable for use in mathematical models describing the dough rheology. The rheological measurements undertaken include oscillatory shear at low amplitude, steady shear at a low shear rate, stress relaxation and extensional viscosity testing. Although oscillatory shear data show minor differences between these flours, the other tests show significant variations and these provide very good discrimination between the different flour types in comparison with conventional dough testing (e.g. by the extensograph). The current dough rheological measurements provide further insight into molecular structure. In the future, mathematical (constitutive) models are expected to provide a means of predicting processing and baking behaviour of bread dough. Received: 27 June 2001 Accepted: 28 August 2001     

The time-dependent rheology of fermenting wheat flour dough: effects of salt and sugar

The in situ study of the linear viscoelastic behaviour of complex biological materials with changing volume, such as fermenting dough, poses great challenges to the rheologist. The aim of this study is to develop a new methodology involving a parallel-plate setup with an adjustable gap, to enable time-tracking of the dynamic moduli and density of fermenting dough. Frequency sweep snapshots at specific points in time were obtained in multiwave mode to reduce measurement times, and overfilling effects were taken into account by establishing a calibration curve with unfermented dough. The new test protocol allowed to distinguish the rheological impact of the CO₂ gas from that of the other metabolites produced during fermentation. A further validation of the test protocol was achieved by studying the impact of sugar and salt on the fermentation kinetics, for which the results of the oscillatory tests were combined with gas production data obtained with a rheofermentometer.     

The damping function in rheology

The damping function has been a concept introduced in rheology since more than 30 years ago, and although a similar concept was already earlier implemented in studying rubber materials, its implementation in the modeling of polymer melts was an essential step forward in the classification and understanding of nonlinear viscoelasticity phenomena. It is the objective of this contribution to give an overview on the theoretical background and physical interpretation of the concept of the damping function for different types of deformation, as well as a review on the experimental results including the experimental artefacts to be considered. Besides homopolymers, a summary is given on different investigations of other types of systems, where the concept of the damping function has also been applied, for example, rubbers, rubber-like materials, block copolymers, polymer composites, liquid crystals, polymer blends, suspensions, emulsions, micellar systems, and in food rheology.

Characterization of story-level seismic damage using an energy-based damage model

An energy-based damage model currently used for seismic analysis of structures is modified to ensure a positive value in the damage index at all levels of inelastic response. At the ultimate limit state, the modified model gives the same plastic strain energy capacity as the previous damage model. Testing of small-scale cantilever specimens showed different strength deterioration parameters for coldrolled and hot-rolled steel and composite systems of double cantilevers. The strength deterioration parameter for the composite system is smaller than that of the individual cantilevers. Various weighted-average rules for combining local member damage indices into story-level damage indices are compared with measured story-level damage indices. Based on testing of small-scale steel cantilevers, the current combination rules predict the story-level damage reasonably well near the ultimate limit state but tend to underestimate the story-level damage in the less severely damaged states. A combination rule based on best fitting of the experimental data obtained in this study is presented.     

一种改进的残余力向量法在结构损伤识别中的应用

残余力向量法是结构损伤识别中常用的方法,复杂结构中单元数量较多而损伤位置较少,容易造成无关变量增多,进而导致计算量过大的问题。鉴于此,本文提出一种改进的残余力向量法用于结构的损伤识别。该方法利用刚度联系向量与残余力向量之间线性相关的特性,以向量投影值作为损伤定位的影响系数,初步筛选出结构可能出现损伤的单元范围。在此基础上,构建出残余力向量对应的线性方程组,根据顺序主子式不为零的条件,对线性方程组进行行初等变换,再根据单元的数量保留前n维线性方程,通过求解该方程组的代数解可得到该结构单元的刚度损伤参数。以简支梁为例的数值模拟表明,本文方法可减少无关单元变量的计算,降低残余力向量的维度并且具有较好的抗噪能力。     

An improved nonlinear model for an automotive shock absorber

A new physical model for a shock absorber is presented which provides a more realistic representation of the stiffness characteristics than previous simple models. The new model is validated on experimental data.     

Effects of non-linear rheology on electrospinning process: A model study

We develop an analytical bead-spring model to investigate the role of non-linear rheology on the dynamics of electrified jets in the early stage of the electrospinning process. Qualitative arguments, parameter studies as well as numerical simulations, show that the elongation of the charged jet filament is significantly reduced in the presence of a non-zero yield stress. This may have beneficial implications for the optimal design of future electrospinning experiments.     

Oscillatory and simple shear flows of a flour-water dough: a constitutive model

We reported some dynamic and viscometric data on an Australia strong flour-water dough. In oscillatory shear flow experiments, we found the linear viscoelastic strain limit is extremely low, of O(10^–3), consistent with other published data on doughs. The relaxation spectrum derived from the dynamic data is broad, indicating the blend nature of dough. In the start-up of a simple shear flow, we found the shear stress increases nonlinearly with time to a peak value and then decreases rapidly, with no steady-state response. The concept of steady-state viscosity is not very meaningful here, unless the strain at which the measurements are taken is also specified. The stress peaks are strain-rate dependent; but they occur at a strain of O(10), for the strong flour/water dough used, over four decades of strain rates. The experimental data were used to construct a phenomenological model for dough, consisting of an hyperelastic term (representing the elastic gluten network of permanent cross-linked long chain polymers), and a viscoelastic contribution (representing the suspension of starch globules and other long-chain components in dough that are not parts of the permanent cross-linked gluten network). The model predictions compared favourably with experimental data in oscillatory and shear flows.     

NDE of metal damage: ultrasonics with a damage mechanics model

This research describes a nondestructive method for the quantitative estimation of property variations due to damage in metal materials. The method employs a damage mechanics model, which accounts for stiffness degradation and damage evolution of a metal medium with a measurement of ultrasonic velocity. In order to describe the progressive deterioration of materials prior to the initiation of macrocracks, we have developed a new damage mechanics model. Thereafter, a finite element model valid for numerically describing such damage process has been developed by ABAQUS/Standard code, and correlations between damage state, elastic stiffness and plastic strain could be found by the results of the finite element simulation. The property variations due to damage evolution are calculated based on the Mori–Tanaka theory, and then the ultrasonic velocity can be predicted by Christoffel’s equation. When the measured velocity is coupled with the theoretically predicted velocity, the unknown damage variable is solved, from which other residual properties are determined by the predictions of damage model. The proposed technique is performed on type 304 stainless steel bars. The numerical results obtained by the simulation were compared with experimental ones in order to verify the validity of the proposed finite element model and good agreement was found. It is shown that the damaged properties of metals can be estimated accurately by the proposed method.     

Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

The cubic-polynomial nonlinearity with N-shaped curve plays a crucial role in generating abundant electrical activities for the original FitzHugh-Nagumo (FHN) neuron model. The pioneer FHN neuron model is efficient in theoretical analysis and numerical simulation for these abundant electrical activities, but analog multipliers are indispensable in hardware implementation since the involvement of cubic-polynomial nonlinearity. Analog multiplier goes against the circuit integration of FHN neuron model due to its huge implementation costs. To avoid the involvement of analog multiplier in hardware implementation, a nonlinear function possessing N-shaped curve and multiplier-free implementation is presented in this paper. To confirm the availability of this nonlinear function in generating electrical activities, numerical simulations and hardware experiments are successfully executed on an improved two-dimensional (2D) FHN neuron model with externally applied stimulus. The results demonstrate that the improved FHN neuron model can generate rich electrical activities of periodic spiking behavior, chaotic behavior, and quasi-periodic behavior. Analog circuit implementation without any multiplier and its hardware experiment show the availability of the proposed nonlinear function, which is appropriate for analog circuit implementation of FHN neuron-based neuromorphic intelligence.

     

Non-linearity in rheology —an essay of classification

Different non-linear phenomena (such as non-Newtonian flow, large elastic deformations, instabilities of different types and many others) are the heart of rheology. Therefore many attempts were carried out to find quantitative, or at least qualitative, models of non-linear behavior. The general or perhaps most attractive way of developing rheological constitutive equations consists in the search for the most general method to describe everything in the framework of a single approach. Naturally, this leads to very complicated and ambiguous equations. Meanwhile, it is reasonable to try another way based on separating observed phenomena into different types depending on observed phenomena into different types depending on their physical origin. An attempt to propose such their physical origin. An attempt to propose such classification of nonlinear rheological effects is made.According to the assumed scheme three levels of non-linearity are distinguished. There is a group of phenomena which originate as a consequence of finite elastic deformations. This is weak non-linearity related to equilibrium properties of a matter. The second level can be characterized as strong non-linearity. It is related to reversible structure changes, developing in time and connected with changes in relaxation properties of a matter. This group of effects can be treated as kinetic phenomena. Lastly, the third level of non-linearity is connected with breaking or phase transitions induced by deformations. This leads to the most severe consequences and can be treated as effects of thermodynamic nature. It is shown that some well known rheological effects can be explained if we consider them as a superposition of non-linearity of different types.Presented as keynote lecture at the European Rheology Meeting, September 4–9, 1994, Sevilla, Spain     

High-order curvilinear mesh generation technique based on an improved radius basic function approach

A high-order curvilinear hybrid mesh generation technique is developed for high-order numerical method (eg, discontinuous Galerkin method) applications to improve the accuracy for problems with curve boundary. The grid generation technique is based on an improved radius basic function (RBF) approach by which the straight-edge mesh is converted into high-order curve mesh. Firstly, an initial straight-edge mesh is prepared by traditional grid generation software. Then, high-order interpolation points are inserted into the mesh entities such as edges, faces, and cells according to the final demand of mesh order. To preserve the original geometry, the inserted points on solid wall are then projected onto the CAD model using an open source tool “Open Cascade.” Finally, other inserted points in the field near the solid wall are moved to appropriate positions by the improved RBF approach to avoid tangled cells. If we use the original RBF approach, then the inserted points on the edge and face entities normal to the solid boundary in the region of boundary layer will move to improper positions. To overcome this problem, a weighting based on the local grid aspect ratio between normal direction and tangential direction is introduced into the baseline RBF approach. Three typical configurations are tested to validate the mesh generator. Meanwhile, a third-order solution of subsonic flow over an analytical 3D body of revolution in the second International Workshop on High-Order CFD Methods is supplied by a discontinuous Galerkin solver. These numerical tests demonstrate the potential capability of present technique for high-order simulations of complex geometries.     

Molecular network model for the rheology of gelling polymer solutions

A molecular network model is proposed to describe the rheology of macromolecular solutions undergoing chemical or physical gelation. The model is based on the Bird—Carreau network model [1] with the addition of chemical reaction kinetics to predict the formation of chemical crosslinks among the polymer molecules in solution. The goal is to provide a framework for describing the rheology of gels, that are currently used as fracturing fluids in oil well simulation, formed from polymer solutions that are crosslinked by the addition of transition metal ions. The model has the ability to predict an increase in storage modulus with time, shear thinning viscosity, stress overshoot upon the inception of shear flow, and viscosity changes during the simulation of flow histories that are representative of those encountered in fracturing operations.