Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa. © 2011 IEEE.

The study of Indian shrimp larvae feeding by enriched rotifer with vitamin C and unsaturated fatty acid (epa, dha) and its effects on growth factors, survival rate and environmental stresses

In this experiment, the feeding of Indian white shrimp larvae by unenriched rotifers (treatment 1) and enriched with highly unsaturated fatty acid (treatment 2) and highly unsaturated fatty acid along with vitamin C (treatment 3) on the growth factors, survival and resistance against salinity and formalin stress tests were studied and their differences with control treatment including newly hatched Artemia nauplii is compared. In this the study four treatments in a completely randomized design with 3 replicates per treatment were used. Farming of shrimp larvae of Zoea II to postlarvae 5 was done in 20 liter plastic bucket. Present results indicated that growth factors and survival rate of stage Zoea II to postlarvae 1 in treatments 1, 2 and 3 improve rather than control in which this case was due to optimal size rotifer rather than Artemia nauplii. Also, treatments 2 and 3 feeding with oil liver cod emulsion enriched rotifer have the highest concentration of DHA (mg/g DW) and the ratio DHA/EPA in which due to have shown the highest growth factors and a significant difference (P<0.05) with treatments 1 and control. The highest survival at stage PL1 were observed in treatment 3 that was enriched with ascorbyl palmitate in which have to the synergistic properties of vitamin C rather than treatments 2, 1 and control and showed a significant difference (P<0.05). But in stage PL5 the highest amount of growth and survival rates were related to control treatment which showed a significant difference (P<0.05) with other treatments that control has higher size rather than treatments 1, 2 and 3. Also, among experiment treatments that the two treatments 2 and 3 due to enrichment had higher growth and survival rates compared with treatment 1 in which their differences have also been significant (P<0.05). In the case of stress tests, results indicated that the highest survival rate has been reported when specimens were offered a diet containing high levels of highly unsaturated fatty acids with vitamin C. So that in stage PL1 in the salinity stress tests 10 and 20 ppt the highest survival rate was observed in treatment 3. As for the second, treatment 2 showed a significant difference (P<0.05) with treatment 3. It is worth mentioning that treatment 3 showed a higher survival rate compared to treatment 2 due to the synergistic properties of vitamin C. The difference between these two treatments with treatment 1 and control was also significant. No significant difference was observed in formalin stress test 100 ppm in this stage between treatments 3 and 2 which shows the highest survival rate. But their difference with treatments 1 and control was significant (P<0.05). Also, in stage PL5 in the salinity stress tests 10 and 20 ppt the highest survival rate was observed in treatment 3 which showed no significant difference (P<0.05) with control treatment. While their difference in the amount of survival rate with treatment 1 and 2 was significant (P<0.05). In this stage, the highest observed survival rate in formalin stress test 100 ppm included treatments control, 3 and 2 among which there were no significant differences (P<0.05). While the difference between these three treatments with treatment 1 was significant.

Optimal control with stochastic PDE constraints and uncertain controls

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

Optimal design of Functionally Graded Materials using a procedural model and Particle Swarm Optimization

A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples. © 2011 Elsevier Ltd. All rights reserved.

The use of centrifuge tests in the study of arching

The horizontal arching mechanism transfers horizontal earth pressures acting on flexible retaining wall panels to stiffer neighbouring elements via soil shear stresses. In this research, the horizontal arching mechanism and lateral displacements of fixed cantilever walls in a model basement are investigated using centrifuge tests. A series of six tests was carried out at 45 gravities where the panel widths and thicknesses around the model basement were varied, so that the effects of panel geometry and stiffness on horizontal arching could be studied. It is shown that panel crest displacements and base bending moments of the most flexible, narrow panels can be an order of magnitude smaller than conventional active earth pressure calculations would allow. It is suggested that the reduction of earth pressure acting on a panel is directly correlated to the mobilized soil shear strength and hence, soil shear strain. Earth pressure coefficients K are plotted against panel displacements normalized by the panel width, u/B, to simulate the reduction of K with increasing soil strain.An idealized K-u/B curve is introduced, characterised by a reference distortion (u/B) ref beyond which fully plastic soil arching can be inferred, and which is related to the corresponding reference shear strain γ ref at which soil strength is fully mobilized in element tests. © 2006 Taylor & Francis Group, London.

Case study on a deep excavation in soft ground by centrifuge model tests

This paper provides a case study on the deepest excavation carried out so far in the construction of the metro network in Shanghai, which typically features soft ground. The excavation is 38 m deep with retaining walls 65 m deep braced by 9 levels of concrete props. To obtain a quick and rough prediction, two centrifuge model tests were conducted, in which one is for the 'standard' section with green field surrounding and the other with an adjacent piled building. The tests were carried out in a run-stop-excavation-run style, in which excavation was conducted manually. By analyzing the lateral wall displacement, ground deformation, bending moment and earth pressure, the test results are shown to be reasonably convincing and the design and construction were validated. Such industry orientated centrifuge modeling was shown to be useful in understanding the performance of geotechnical processes, especially when engineers lack relevant field experience. © 2010 Taylor & Francis Group, London.