Propagation of elastic waves through structural connections. Work carried out...for the Applied Physics Laboratory, Johns Hopkins University under contract number APL/CU-33031-2.

[1] Progress report no. 1, Jan. 15, 1954.--[2] Final report, June 30, 1954.

The random vibration of elastic strings-- theoretical.

"Materials Laboratory, Contract no. AF 33(616)-5426, project no. 7360."

Damping of flexural vibrations by alternate visco-elastic and elastic layers

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Yield criterion of porous materials subjected to complex stress states

Finite-element simulations are used to obtain many thousands of yield points for porous materials with arbitrary void-volume fractions with spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic three-dimensional arrays. Multi-axial stress states are explored. We show that the data may be fitted by a yield function which is similar to the Gurson-Tvergaard-Needleman (GTN) form, but which also depends on the determinant of the stress tensor, and all additional parameters may be expressed in terms of standard GTN-like parameters. The dependence of these parameters on the void-volume fraction is found. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Yield functions for porous materials with cubic symmetry using different definitions of yield

Plastic yield criteria for porous ductile materials are explored numerically using the finite-element technique. The cases of spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple-cubic and body-centred cubic arrays - in contrast to the famous Gurson-Tvergaard-Needleman (GTN) formula - while there is no such dependence for face-centred cubic arrays within the accuracy of the finite-element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield-function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body-centred and face-centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics

Spin transition of 1D, 2D and 3D iron(II) complex polymers - the tug-of-war between elastic interaction and a shock-absorber effect

The structures of linear chain Fe(II) spin-crossover compounds of α,β- and α,ω-bis (tetrazol-1-yl)alkane type ligands are described in relation to their magnetic properties. The first threefold interlocked 3-D catenane Fe(II) spin-transition system, [μ-tris(1,4-bis(tetrazol-1-yl)butane-N1,N1′) iron(II)] bis(perchlorate), will be discussed. An analysis is made among the structures and the cooperativity of the spin-crossover behaviour of polynuclear Fe(II) spin-transition materials.

Effect of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone

Many biological materials are known to be anisotropic. In particular, microstructural components of biological materials may grow in a preferred direction, giving rise to anisotropy in the microstructure. Nanoindentation has been shown to be an effective technique for determining the mechanical properties of microstructures as small as a few microns. However, the effects of anisotropy on the properties measured by nanoindentation have not been fully addressed. This study presents a method to account for the effects of anisotropy on elastic properties measured by nanoindentation. This method is used to correlate elastic properties determined from earlier nanoindentation experiments and from earlier ultrasonic velocity measurements in human tibial cortical bone. Also presented is a procedure to determine anisotropic elastic moduli from indentation measurements in multiple directions. © 2001 John Wiley & Sons, Inc. J Biomed Mater Res.

Elastic and plastic properties of Mo3Si measured by nanoindentation

Single crystal Mo3Si specimens were grown and tested at room temperature using established nanoindentation techniques at various crystallographic orientations. The indentation modulus and hardness were obtained for loads that were large enough to determine bulk properties, yet small enough to avoid cracking in the specimens. From the indentation modulus results, anisotropic elastic constants were determined. As load was initially increased to approximately 1.5 mN, the hardness exhibited a sudden drop that corresponded to a jump in displacement. The resolved shear stress that was determined from initial yielding was 10-15% of the shear modulus, but 3 to 4 times the value obtained from the bulk hardness. Non-contact atomic force microscopy images in the vicinity of indents revealed features consistent with {100}(010) slip.

An energy based nanomechnical properties evaluation method for cementitious materials

Advances in multiscale material modeling of structural concrete have created an upsurge of interest in the accurate evaluation of mechanical properties and volume fractions of its nano constituents. The task is accomplished by analyzing the response of a material to indentation, obtained as an outcome of a nanoindentation experiment, using a procedure called the Oliver and Pharr (OP) method. Despite its widespread use, the accuracy of this method is often questioned when it is applied to the data from heterogeneous materials or from the materials that show pile-up and sink-in during indentation, which necessitates the development of an alternative method. ^ In this study, a model is developed within the framework defined by contact mechanics to compute the nanomechanical properties of a material from its indentation response. Unlike the OP method, indentation energies are employed in the form of dimensionless constants to evaluate model parameters. Analysis of the load-displacement data pertaining to a wide range of materials revealed that the energy constants may be used to determine the indenter tip bluntness, hardness and initial unloading stiffness of the material. The proposed model has two main advantages: (1) it does not require the computation of the contact area, a source of error in the existing method; and (2) it incorporates the effect of peak indentation load, dwelling period and indenter tip bluntness on the measured mechanical properties explicitly. ^ Indentation tests are also carried out on samples from cement paste to validate the energy based model developed herein by determining the elastic modulus and hardness of different phases of the paste. As a consequence, it has been found that the model computes the mechanical properties in close agreement with that obtained by the OP method; a discrepancy, though insignificant, is observed more in the case of C-S-H than in the anhydrous phase. Nevertheless, the proposed method is computationally efficient, and thus it is highly suitable when the grid indentation technique is required to be performed. In addition, several empirical relations are developed that are found to be crucial in understanding the nanomechanical behavior of cementitious materials.^

Mechanochemistry for Active Materials and Devices

The coupling of mechanical stress fields in polymers to covalent chemistry (polymer mechanochemistry) has provided access to previously unattainable chemical reactions and polymer transformations. In the bulk, mechanochemical activation has been used as the basis for new classes of stress-responsive polymers that demonstrate stress/strain sensing, shear-induced intermolecular reactivity for molecular level remodeling and self-strengthening, and the release of acids and other small molecules that are potentially capable of triggering further chemical response. The potential utility of polymer mechanochemistry in functional materials is limited, however, by the fact that to date, all reported covalent activation in the bulk occurs in concert with plastic yield and deformation, so that the structure of the activated object is vastly different from its nascent form. Mechanochemically activated materials have thus been limited to “single use” demonstrations, rather than as multi-functional materials for structural and/or device applications. Here, we report that filled polydimethylsiloxane (PDMS) elastomers provide a robust elastic substrate into which mechanophores can be embedded and activated under conditions from which the sample regains its original shape and properties. Fabrication is straightforward and easily accessible, providing access for the first time to objects and devices that either release or reversibly activate chemical functionality over hundreds of loading cycles.

While the mechanically accelerated ring-opening reaction of spiropyran to merocyanine and associated color change provides a useful method by which to image the molecular scale stress/strain distribution within a polymer, the magnitude of the forces necessary for activation had yet to be quantified. Here, we report single molecule force spectroscopy studies of two spiropyran isomers. Ring opening on the timescale of tens of milliseconds is found to require forces of ~240 pN, well below that of previously characterized covalent mechanophores. The lower threshold force is a combination of a low force-free activation energy and the fact that the change in rate with force (activation length) of each isomer is greater than that inferred in other systems. Importantly, quantifying the magnitude of forces required to activate individual spiropyran-based force-probes enables the probe behave as a “scout” of molecular forces in materials; the observed behavior of which can be extrapolated to predict the reactivity of potential mechanophores within a given material and deformation.

We subsequently translated the design platform to existing dynamic soft technologies to fabricate the first mechanochemically responsive devices; first, by remotely inducing dielectric patterning of an elastic substrate to produce assorted fluorescent patterns in concert with topological changes; and second, by adopting a soft robotic platform to produce a color change from the strains inherent to pneumatically actuated robotic motion. Shown herein, covalent polymer mechanochemistry provides a viable mechanism to convert the same mechanical potential energy used for actuation into value-added, constructive covalent chemical responses. The color change associated with actuation suggests opportunities for not only new color changing or camouflaging strategies, but also the possibility for simultaneous activation of latent chemistry (e.g., release of small molecules, change in mechanical properties, activation of catalysts, etc.) in soft robots. In addition, mechanochromic stress mapping in a functional actuating device might provide a useful design and optimization tool, revealing spatial and temporal force evolution within the actuator in a way that might also be coupled to feedback loops that allow autonomous, self-regulation of activity.

In the future, both the specific material and the general approach should be useful in enriching the responsive functionality of soft elastomeric materials and devices. We anticipate the development of new mechanophores that, like the materials, are reversibly and repeatedly activated, expanding the capabilities of soft, active devices and further permitting dynamic control over chemical reactivity that is otherwise inaccessible, each in response to a single remote signal.

A Finite Element to Perform 3D Shakedown Analysis for Limited Kinematic Hardening Materials

The use of the Design by Analysis (DBA) route is a modern trend in pressure vessel and piping international codes in mechanical engineering. However, to apply the DBA to structures under variable mechanical and thermal loads, it is necessary to assure that the plastic collapse modes, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. The tool available to achieve this target is the shakedown theory. Unfortunately, the practical numerical applications of the shakedown theory result in very large nonlinear optimization problems with nonlinear constraints. Precise, robust and efficient algorithms and finite elements to solve this problem in finite dimension has been a more recent achievements. However, to solve real problems in an industrial level, it is necessary also to consider more realistic material properties as well as to accomplish 3D analysis. Limited kinematic hardening, is a typical property of the usual steels and it should be considered in realistic applications. In this paper, a new finite element with internal thermodynamical variables to model kinematic hardening materials is developed and tested. This element is a mixed ten nodes tetrahedron and through an appropriate change of variables is possible to embed it in a shakedown analysis software developed by Zouain and co-workers for elastic ideally-plastic materials, and then use it to perform 3D shakedown analysis in cases with limited kinematic hardening materials

Shakedown Analysis Considering Limited Kinematic Hardening Materials

In design or safety assessment of mechanical structures, the use of the Design by Analysis (DBA) route is a modern trend. However, for making possible to apply DBA to structures under variable loads, two basic failure modes considered by ASME or European Standards must be precluded. Those modes are the alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case). Shakedown theory is a tool that permit us to assure that those kinds of failures will be avoided. However, in practical applications, very large nonlinear optimization problems are generated. Due to this facts, only in recent years have been possible to obtain algorithms sufficiently accurate, robust and efficient, for dealing with this class of problems. In this paper, one of these shakedown algorithms, developed for dealing with elastic ideally-plastic structures, is enhanced to include limited kinematic hardening, a more realistic material behavior. This is done in the continuous model by using internal thermodynamic variables. A corresponding discrete model is obtained using an axisymmetric mixed finite element with an internal variable. A thick wall sphere, under variable thermal and pressure loads, is used in an example to show the importance of considering the limited kinematic hardening in the shakedown calculations

Nanoindentation Relaxation Study and Micromechanics of Cement-Based Materials

Ce travail évalue le comportement mécanique des matériaux cimentaires à différentes échelles de distance. Premièrement, les propriétés mécaniques du béton produit avec un bioplastifiant à base de microorganismes efficaces (EM) sont etudiées par nanoindentation statistique, et comparées aux propriétés mécaniques du béton produit avec un superplastifiant ordinaire (SP). Il est trouvé que l’ajout de bioplastifiant à base de produit EM améliore la résistance des C–S–H en augmentant la cohésion et la friction des nanograins solides. L’analyse statistique des résultats d’indentation suggère que le bioplastifiant à base de produit EM inhibe la précipitation des C–S–H avec une plus grande fraction volumique solide. Deuxièmement, un modèle multi-échelles à base micromécanique est dérivé pour le comportement poroélastique de la pâte de ciment au jeune age. L’approche proposée permet d’obtenir les propriétés poroélastiques requises pour la modélisation du comportoment mécanique partiellement saturé des pâtes de ciment viellissantes. Il est montré que ce modèle prédit le seuil de percolation et le module de Young non drainé de façon conforme aux données expérimentales. Un metamodèle stochastique est construit sur la base du chaos polynomial pour propager l’incertitude des paramètres du modèle à travers plusieurs échelles de distance. Une analyse de sensibilité est conduite par post-traitement du metamodèle pour des pâtes de ciment avec ratios d’eau sur ciment entre 0.35 et 0.70. Il est trouvé que l’incertitude sous-jacente des propriétés poroélastiques équivalentes est principalement due à l’énergie d’activation des aluminates de calcium au jeune age et, plus tard, au module élastique des silicates de calcium hydratés de basse densité.