Stiffness of clays and silts: Normalizing shear modulus and shear strain

An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p9 (i.e., G=p9 versus log g) or undrained shear strength cu (i.e., G=cu versus log g) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus,Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions forGmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value Gmax, and shear strain g is normalized with respect to a reference strain gref at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gref is approximated as a function of the plasticity index.Aunique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/Gmax ±30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. © 2013 American Society of Civil Engineers.

Index properties, shear strenghts and consolidation characteristics of ODP Hole 164-995A sediments

Geotechnical properties of sediment from Ocean Drilling Program Leg 164 are presented as: (1) normalized shipboard strength ratios from the Cape Fear Diapir, the Blake Ridge Diapir, and the Blake Ridge; and (2) Atterberg limit, vane shear strength, pocket-penetrometer strength, and constant-rate-of-strain consolidation results from Hole 995A, located on the Blake Ridge. This study was conducted to understand the stress history in a region characterized by high sedimentation rates and the presence of gas hydrates. Collectively, the results indicate that sediment from the Blake Ridge exhibits significant underconsolidated behavior, except near the seafloor. At least 10 m of additional overburden was removed by erosion or mass wasting at Hole 993A on the Cape Fear Diapir, compared to nearby sites.

Consolidation properties and strength characteristics of ODP Site 204-1244 sediments

Eight whole-core samples from Ocean Drilling Program Site 1244, Hydrate Ridge, Cascadia continental margin, were provided to Massachusetts Institute of Technology (Cambridge, Massachusetts, USA) for geotechnical characterization. The samples were collected from depths ranging from 5 to 136 meters below seafloor (mbsf). Seven of the eight whole-core samples were located within the gas hydrate stability zone, whereas the eighth sample was located in the free gas zone. Atterberg limits testing showed that the average liquid limit of the soil is 81% and the average plastic limit is 38%, giving an average plasticity index of 43%. The liquid limit is sensitive to oven drying, shown by a drop in liquid limit to 64% when tests were performed on an oven-dried sample. Loss on ignition averages 5.45 wt%. Constant rate of strain consolidation (CRSC) tests were performed to obtain the compression characteristics of the soil, as well as to determine the stress history of the site. CRSC tests also provided hydraulic conductivity and coefficient of consolidation characteristics for these sediments. The compression ratio (Cc) ranges from 0.340 to 0.704 (average = 0.568). Cc is fairly constant to a depth of 79 mbsf, after which Cc decreases downhole. The recompression ratio (Cr) ranges from 0.035 to 0.064 (average = 0.052). Cr is constant throughout the depth range. In situ hydraulic conductivity varies between 1.5 x 10**-7 and 3 x 10**-8 cm/s and shows no trend with depth. Ko-consolidated undrained compression/extension (CKoUC/E) tests were also performed to determine the peak undrained shear strength, stress-strain curve, and friction angle. The normalized undrained strength ranges from 0.29 to 0.35. The friction angle ranges from 27 to 37. Because of the limited amount of soil, CRSC and CKoUC/E tests were also conducted on resedimented specimens.

Consolidation properties, permeabilities, grain sizes and age of samples from ODP Holes 194-1194A and 194-1198A

Uniaxial strain consolidation experiments were conducted to determine elastic and plastic properties and to estimate the permeability of sediments from 0 to 200 meters below seafloor at Ocean Drilling Program Sites 1194 and 1198. Plastic deformation is described by compression indices, which range from 0.19 to 0.37. Expansion indices, the elastic deformation measured during unload/reload cycles on samples, vary from 0.02 to 0.029. Consolidation experiments provide lower bounds on permeability between 5.4 x 10**-16 m**2 and 1.9 x 10**-18 m**2, depending on the consolidation state of the sample.

Constraint loss under dynamic loading in rate independent plastic solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J(2) flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J-Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K-dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K-dc for (K) over dot > 10(5) MPa rootm/s.

Effect of electro-mechanical coupling on actuation behavior of a carbon nanotube cellular structure

We demonstrate the effect of mechanical strain on the electrostrictive behavior of catalytically grown cellular structure of carbon nanotube (CNT). In the small strain regime, where the stress-strain behavior of the material is linear, application of an electric-field along the mechanical loading direction induces an instantaneous increase in the stress and causes an increase in the apparent Young's modulus. The instantaneous increase in the stress shows a cubic-polynomial dependence on the electric-field, which is attributed to the non-linear coupling of the mechanical strain and the electric-field induced polarization of the CNT. The electrostriction induced actuation becomes >100 times larger if the CNT sample is pre-deformed to a small strain. However, in the non-linear stress-strain regime, although a sharp increase in the apparent Young's modulus is observed upon application of an electric-field, no instantaneous increase in the stress occurs. This characteristic suggests that the softening due to the buckling of individual CNT compensates for any instantaneous rise in the electrostriction induced stress at the higher strains. We also present an analytical model to elucidate the experimental observations. (C) 2013 Elsevier Ltd. All rights reserved.

CROSS-SECTIONAL ANALYSIS OF PRE-TWISTED THICK BEAMS USING VARIATIONAL ASYMPTOTIC METHOD

An asymptotically-exact methodology is presented for obtaining the cross-sectional stiffness matrix of a pre-twisted moderately-thick beam having rectangular cross sections and made of transversely isotropic materials. The anisotropic beam is modeled from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy of the beam is computed making use of the constitutive law and the kinematical relations derived with the inclusion of geometrical nonlinearities and initial twist. Large displacements and rotations are allowed, but small strain is assumed. The Variational Asymptotic Method is used to minimize the energy functional, thereby reducing the cross section to a point on the reference line with appropriate properties, yielding a 1-D constitutive law. In this method as applied herein, the 2-D cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged as orders of the small parameters. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that renders the 1-D strain measures well-defined. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Electromechanical Analysis of Tapered Piezoelectric Bimorph at High Electric Field

Piezoelectric bimorph laminar actuator of tapered width exhibits better performance for out-of-plane deflection compared to the rectangular surface area, while consuming equal surface area. This paper contains electromechanical analysis and modeling of a tapered width piezoelectric bimorph laminar actuator at high electric field in static state. The analysis is based on the second order constitutive equations of piezoelectric material, assuming small strain and large electric field to capture its behavior at high electric field. Analytical expressions are developed for block force, output strain energy, output energy density, input electrical energy, capacitance and energy efficiency at high electric field. The analytical expressions show that for fixed length, thickness, and surface area of the actuator, how the block force and output strain energy gets improved in a tapered surface actuator compared to a rectangular surface. Constant thickness, constant length and constant surface area of the actuator ensure constant mass, and constant electrical capacitance. We consider high electric field in both series and parallel electrical connection for the analysis. Part of the analytical results is validated with the experimental results, which are reported in earlier literature.

Analysis of Transverse Shear Strains in Pre-Twisted Thick Beams using Variational Asymptotic Method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam reference curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Verificação do desempenho do ensaio de adensamento CRS comparado ao SIC.

A presente dissertação objetiva a verificação do desempenho dos ensaios do tipo CRS, com velocidade controlada, quando comparados aos ensaios de adensamento oedométricos convencionais, SIC. O ensaio SIC é executado em vários estágios de carga, cada qual com vinte e quatro horas de duração e razão unitária entre o incremento de tensão e a tensão anterior, requerendo um prazo total de cerca de 10 dias para sua execução. Já o ensaio de adensamento com velocidade controlada, CRS, tem sua duração bastante reduzida, o que levou diversos pesquisadores da área de Geotecnia a concentrarem esforços no estudo de seu desempenho, visando sua utilização mais ampla. Para este estudo foi adquirido equipamento da empresa Hogentogler Inc., designado por GeoStar. Sua instalação, montagem e calibração foram realizadas no Laboratório de Mecânica dos Solos. Foram executados ensaios em corpos de prova obtidos de amostras de caulim, preparadas em laboratório, e também em amostras de solos originários de dois depósitos de diferentes regiões no Estado do Rio de Janeiro: baixada de Jacarepaguá e Itaboraí. A dissertação procurou detalhar a execução dos ensaios, as dificuldades da interpretação das planilhas originadas pelo sistema de aquisição de dados, acoplado ao equipamento GeoStar, as mudanças efetuadas, as ocorrências não previstas, a análise e interpretação dos resultados e a comparação dos parâmetros obtidos com os ensaios SIC e CRS. Procurou-se estudar o efeito da velocidade de deformação, histórico de tensões, qualidade dos corpos de prova, parâmetros do ensaio, facilidade de execução e desempenho. Verificou-se a simplicidade, rapidez e o desempenho satisfatório do ensaio CRS. Sugere-se estender estudos semelhantes a outros locais e, principalmente, a amostras de qualidade superior, na expectativa de confirmar as conclusões detalhadas nesta pesquisa.

Deployable membranes designed from folding tree leaves.

A simple model of deploying tree leaves is assembled in different arrangements to produce polygonal foldable membranes for use as deployable structures. One family of folding patterns exhibits a small strain mechanism, which is investigated. Variations on the basic arrangements can be used to fold membranes with a discretized curvature.

Fracture and energy partitioning in uncooked and cooked noodles

Humans perform fascinating science experiments at home on a daily basis when they undertake the modification of natural and naturally-derived materials by a cooking process prior to consumption. The material properties of such foods are of interest to food scientists (texture is often fundamental to food acceptability), oral biologists (foods modulate feeding behavior), anthropologists (cooking is probably as old as the genus Homo and distinguishes us from all other creatures) and dentists (foods interact with tooth and tooth replacement materials). Materials scientists may be interested in the drastic changes in food properties observed over relatively short cooking times. In the current study, the mechanical properties of one of the most common (and oldest at 4,000+ years) foods on earth, the noodle, were examined as a function of cooking time. Two types of noodles were studied, each made from natural materials (wheat flour, salt, alkali and water) by kneading dough and passing them through a pasta-making machine. These were boiled for between 2-14 min and tested at regular intervals from raw to an overcooked state. Cyclic tensile tests at small strain levels were used to examine energy dissipation characteristics. Energy dissipation was >50% per cycle in uncooked noodles, but decreased by an order of magnitude with cooking. Fractional dissipation values remained approximately constant at cooking times greater than 7 min. Overall, a greater effect of cooking was on viscoplastic dissipation characteristics rather than on fracture resistance. The results of the current study plot the evolution of a viscoplastic mixture into an essentially elastic material in the space of 7 minutes and have broad implications for understanding what cooking does to food materials. In particular, they suggest that textural assessment by consumers of the optimally cooked state of food has a definite physical definition. © 2007 Materials Research Society.

Climb-enabled discrete dislocation plasticity

A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-singular solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-singular solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state solution. © 2013 Elsevier Ltd. All rights reserved.

Measuring the compressive viscoelastic mechanical properties of human cervical tissue using indentation.

The human cervix is an important mechanical barrier in pregnancy which must withstand the compressive and tensile forces generated from the growing fetus. Premature cervical shortening resulting from premature cervical remodeling and alterations of cervical material properties are known to increase a woman׳s risk of preterm birth (PTB). To understand the mechanical role of the cervix during pregnancy and to potentially develop indentation techniques for in vivo diagnostics to identify women who are at risk for premature cervical remodeling and thus preterm birth, we developed a spherical indentation technique to measure the time-dependent material properties of human cervical tissue taken from patients undergoing hysterectomy. In this study we present an inverse finite element analysis (IFEA) that optimizes material parameters of a viscoelastic material model to fit the stress-relaxation response of excised tissue slices to spherical indentation. Here we detail our IFEA methodology, report compressive viscoelastic material parameters for cervical tissue slices from nonpregnant (NP) and pregnant (PG) hysterectomy patients, and report slice-by-slice data for whole cervical tissue specimens. The material parameters reported here for human cervical tissue can be used to model the compressive time-dependent behavior of the tissue within a small strain regime of 25%.

Time-dependent fracture toughness of cornea.

The fracture and time-dependent properties of cornea are very important for the development of corneal scaffolds and prostheses. However, there has been no systematic study of cornea fracture; time-dependent behavior of cornea has never been investigated in a fracture context. In this work, fracture toughness of cornea was characterized by trouser tear tests, and time-dependent properties of cornea were examined by stress-relaxation and uniaxial tensile tests. Control experiments were performed on a photoelastic rubber sheet. Corneal fracture resistance was found to be strain-rate dependent, with values ranging from 3.39±0.57 to 5.40±0.48kJm(-2) over strain rates from 3 to 300mmmin(-1). Results from stress-relaxation tests confirmed that cornea is a nonlinear viscoelastic material. The cornea behaved closer to a viscous fluid at small strain but became relatively more elastic at larger strain. Although cornea properties are greatly dependent on time, the stress-strain responses of cornea were found to be insensitive to the strain rate when subjected to tensile loading.