Elastic shear modulus constitutive law found from entropy considerations

On the Mg-Pb system. Calorimetric studies and thermodynamic calculations

The interstitialcy theory is used to calculate the kinetics of shear modulus relaxation induced by structural relaxation of metallic glasses. A continuous distribution of activation energies is shown to be a salient feature of the relaxation. High precision in situ contactless electromagnetic acoustic-transformation shear modulus (600- kHz) measurements performed on a Zr-based bulk metallic glass are found to strongly support the approach under consideration. It is revealed that the activation energy spectra derived from isothermal and isochronal shear modulus measurements are in good agreement with each other. It is concluded that the increase of the shear modulus during structural relaxation can be understood as a decrease of the concentration of structural defects similar to dumbbell interstitials in simple crystalline metals.

Acute and chronic effects of static stretching of different target muscles on shear elastic modulus: A narrative review

We investigate the lattice constant, formation enthalpy, elastic constants, bulk modulus, shear modulus, Young’s modulus, specific heat, thermal expansion coefficient and microhardness as a function of Al content for B2-FeAl and D03-Fe3Al using static and dynamics simulations with a long-range analytical embedded atom method (la-EAM). The lattice constants of both B2-FeAl and D03-Fe3Al crystals increase with Al content, opposite to the elastic constants, bulk modulus and shear modulus. Stoichiometric B2-FeAl has the lowest formation enthalpy and Young’s modulus. The calculation results of Gibbs free energies show that the phase transformation temperature from D03 to B2 decreases with Al content, which is in good agreement with experiments. The microhardness resulting from vacancies for B2-FeAl increases monotonically with Al content, indicating that the resultant microhardness is controlled by the vacancies, which agrees well with experiments.

Dynamic mechanical testing was used to qualitatively study the effects of various constituents of sheet molding compound (SMC) and bulk molding compound (BMC) materials, including unsaturated polyester resin, a chemical thickener (magnesium oxide), a filler (calcium carbonate), and glass fibers. Tests were designed to evaluate the influence of each constituent as it was added to the overall composition. The parameters tested were elastic shear modulus, viscous shear modulus, and complex viscosity as functions of frequency for non-cross-linked materials, and elastic shear modulus, viscous shear modulus, and damping as functions of temperature for cross-linked materials. The chemical thickener was observed to change the molecular weight of the polyester resin, as indicated by the appearance of a rubbery plateau in the viscoelastic spectrum, while cross-linking, filler, and glass fibers were observed to contribute heavily to the elastic shear modulus and temperature sensitivity.

Gels formed by semiflexible filaments such as most biopolymers exhibit non-linear behavior in their response to shear deformation, e.g., with a pronounced strain stiffening and negative normal stress. These negative normal stresses suggest that networks would collapse axially when subject to shear stress. This coupling of axial and shear deformations can have particularly important consequences for extracellular matrices and collagenous tissues. Although measurements of uniaxial moduli have been made on biopolymer gels, these have not directly been related to the shear response. Here, we report measurements and simulations of axial and shear stresses exerted by a range of hydrogels subjected to simultaneous uniaxial and shear strains. These studies show that, in contrast to volume-conserving linearly elastic hydrogels, the Young’s moduli of networks formed by the biopolymers are not proportional to their shear moduli and both shear and uniaxial moduli are strongly affected by even modest degrees of uniaxial strain.

Relationship Between Powder Surface Characteristics and Viscoelastic Properties of Powder-Filled Semisolids

Coefficients for analytic constitutive and equation of state models (EOS), which are used by many hydro codes at LLNL, are currently stored in a legacy material database (Steinberg, UCRL-MA-106349). Parameters for numerous materials are available through this database, and include Steinberg-Guinan and Steinberg-Lund constitutive models for metals, JWL equations of state for high explosives, and Mie-Gruniesen equations of state for metals. These constitutive models are used in most of the simulations done by ASC codes today at Livermore. Analytic EOSs are also still used, but have been superseded in many cases by tabular representations in LEOS (http://leos.llnl.gov). Numerous advanced constitutive models have been developed and implemented into ASC codes over the past 20 years. These newer models have more physics and better representations of material strength properties than their predecessors, and therefore more model coefficients. However, a material database of these coefficients is not readily available. Therefore incorporating these coefficients with those of the legacy models into a portable database that could be shared amongst codes would be most welcome. The goal of this paper is to describe the MatProp effort at LLNL to create such a database and associated access library that could be used by codes throughout the DOE complex and beyond. We have written an initial version of the MatProp database and access library and our DOE/ASC code ALE3D (Nichols et. al., UCRL-MA-152204) is able to import information from the database. The database, a link to which exists on the Sourceforge server at LLNL, contains coefficients for many materials and models (see Appendix), and includes material parameters in the following categories--flow stress, shear modulus, strength, damage, and equation of state. Future versions of the Matprop database and access library will include the ability to read and write material descriptions that can be exchanged between codes. It will also include an ability to do unit changes, i.e. have the library return parameters in user-specified unit systems. In addition to these, additional material categories can be added (e.g., phase change kinetics, etc.). The Matprop database and access library is part of a larger set of tools used at LLNL for assessing material model behavior. One of these is MSlib, a shared constitutive material model library. Another is the Material Strength Database (MSD), which allows users to compare parameter fits for specific constitutive models to available experimental data. Together with Matprop, these tools create a suite of capabilities that provide state-of-the-art models and parameters for those models to integrated simulation codes. This document is broken into several appendices. Appendix A contains a code example to retrieve several material coefficients. Appendix B contains the API for the Matprop data access library. Appendix C contains a list of the material names and model types currently available in the Matprop database. Appendix D contains a list of the parameter names for the currently recognized model types. Appendix E contains a full xml description of the material Tantalum.

Phase transition, elastic and thermodynamical properties of technetium monocarbide (TcC) in the WC, NiAs, NaCl, CsCl, and ZnS structures have been studied by full-potential linearized augmented-plane-wave (FP-LAPW) theory. From the enthalpy difference between the five structures, we predict that the structural phase transition from WC-type structure to CsCl-type structure occurs at ca. 411.4 GPa. Meanwhile, it is found that the NiAs, NaCl, and ZnS types are not stable phases in whole pressure ranges considered. In particular, for the first time we calculate the elastic properties and phase transition of TcC under high pressures. For WC TcC and CsCl TcC structures, the elastic constants, bulk modulus, shear modulus, and Young's modulus are predicted to increase monotonically with increasing pressure. The Vickers hardness of TcC under high pressure is estimated. The brittle–ductile behavior of TcC has been obtained by Pugh's criteria. Finally, the Debye temperature, isochoric heat capacity and thermal expansion coefficient are predicted by the quasiharmonic Debye model method.

A test method for the determination of the shear modulus and the modulus of elasticity of laminated anisotropic composite materials is presented. Two tests are required. In one test, a ring is simply supported at two diametrically opposite supports and subjected to two diametrically opposite concentrated loads normal to the plane of the ring and located 90° from the supports. The second test employs a split ring. Each end of the ring is subjected to a concentrated load normal to the plane of the ring. By conducting these two tests and measuring the normal deflections corresponding to the applied loads, shear modulus and modulus of elasticity of the ring can be determined from the formulas derived in the paper. It should be noted that for laminated composite anisotropic materials these moduli cannot be determined from the tests as known in the literature, one of which involves out-of-plane loading and the other an in-plane loading as suggested in Paper 4709, Douglas Missile and Space Systems Division, McDonnell Douglas Corporation, November, 1967.

Characterization of nonlinear hysteretic responses plays a significant role in predicting soil behaviors. They are mostly described with either simple empirical functions or complex constitutive models. However, the input parameters lack both a physical basis and robustness, and the use of these models is limited to some typical soils. Therefore, there is a need for a simple but robust model that uses only a small number of physically meaningful parameters. This study proposes explicit formulas to capture different nonlinear hysteretic soil responses, including a constitutive model, backbone curve, tangent shear modulus, secant shear modulus, and damping ratio. In particular, the Davidenkov model, with two physically meaningful parameters, is adopted to assess the constitutive relationships of soils under steady-state cyclic loading. The proposed models are validated with resonant column test (RCT) data (shear modulus and damping ratio). This paper finds that the use of the linear characteristic equation to calculate the shear modulus from the resonance frequency in the RCT, which is clearly irrelevant and approximate, produces data interpretation errors.

The human skin is composed of several layers, each with an unique structure and function. Knowledge about the mechanical behavior of these skin layers is important for clinical and cosmetic research, such as the development of personal care products and the understanding of skin diseases. Until today, most research was performed in vivo and focused on the mid-layer, the dermis. However, clinical and cosmetic applications require more detailed knowledge about the skin layers at the skin surface, the viable epidermis and stratum corneum, and the deeper lying hypodermis. Studying these layers in an in vivo set up is very challenging. The different length scales, ranging from µm for the stratum corneum to cm for the hypodermis, the interwoven layered structure and the inverse relation between penetration depth and resolution of non-invasive measurement techniques form major problems. As a consequence, hardly any data are available for the viable epidermis and hypodermis and reported data for stratum corneum are inconsistent. The aim of this thesis was therefore to characterize the mechanical behavior of individual skin layers in vitro and, for that, to develop the required experimental procedures. It was considered essential to perform experiments with samples of consistent quality in an accurate measurement set-up in a well-controlled environment. Various isolation and preservation methods were investigated on tissue performance, reproducibility and ease of handling. Because of the inhomogeneous layered structure of the upper skin layers, mechanical properties of the stratum corneum and viable epidermis were determined for various loading directions. First, the stratum corneum and epidermis were subjected to shear over a wide frequency range and with varying temperature and humidity. The typical geometry of the upper skin layers required preliminary testing series in order to define the right experimental conditions to ensure reliable results. Subsequently, micro-indentation experiments were applied using a spherical tip with a relatively large diameter. The Young¿s moduli were derived via an analytical and numerical method. Because of the complexity of measuring those skin layers, it was decided to focus on small deformations first. For both types of loading, result were highly reproducible. The shear tests demonstrated that the shear modulus is influenced by humidity but not by temperature in the measured range. If the skin is compressed with an indenter, the stiffness of the epidermis and stratum corneum, which is about 1-2 MPa, is about a factor 100 higher than for shear. No significant differences in stiffness between the stratum corneum and viable epidermis were observed per loading type. The results of these tests prove that it is essential to take into account the highly anisotropy of the tissue in numerical models. Rheological methods were developed to study the mechanical response of the subcutaneous adipose tissue. In the small linear viscoelastic strain regime, the shear modulus showed a frequency- and temperature-dependent behavior and is about 7.5 kPa at 10 rad/s and 37°C. Time-Temperature Superposition is applicable through shifting the shear modulus horizontally. A power-law function model was able to describe the frequency dependent behavior at constant temperature as well as the measured stress relaxation behavior. Prolonged loading at small strains results into a dramatic stiffening of the material. Loading-unloading cycles showed that this behavior is reversible. In addition, various large strain history sequences showed that stress-strain responses are reproducible up to 0.15 strain. When the strain further increases, the stress is decreasing for subsequent loading cycles and, above 0.3 strain, the stress response becomes stationary. These results showing time and strain effects indicate that adipose tissue likely behaves as an (anti-)thixotropic material, meaning that a constitutive model should contain parameters to describe the build-up and breakdown of the material structure. However, further experimental research is needed to fully understand the thixotropic behavior before such a model can be worked out in detail. In conclusion, this thesis evaluates the mechanical behavior of stratum corneum, epidermis and hypodermis using various in vitro set-ups. It was proven that for all skin layers reproducible results can be obtained. The research was aimed at developing reliable methods to determine the mechanical behavior of individual human skin layers. Future work should be focused on the relationship between mechanical properties and tissue deformation using imaging techniques and heading to the determination of the skin¿s failure behavior in relation to clinical and cosmetic treatments.

This study presents a comprehensive non-destructive evaluation of a broad range of construction materials using the impulse excitation of vibration (IEV) technique. Tested specimens included low- and normal-strength concrete, fiber-reinforced concrete (with basalt, polypropylene, and glass fibers), lime mortars (NHL-2 and -3.5), plaster, and clay bricks (light and dark). Compressive and flexural strength tests complemented dynamic resonance testing on the same samples to ensure full mechanical characterization. Flexural and torsional resonance frequencies were used to calculate dynamic elastic modulus, shear modulus, and Poisson’s ratio. Strong correlations were observed between dynamic elastic modulus and shear modulus, supporting the compatibility of dynamic results with the classical elasticity theory. Flexural frequencies were more sensitive to material differences than torsional ones. Fiber additives, particularly basalt and polypropylene, significantly improved dynamic stiffness, increasing the dynamic elastic modulus/compressive strength ratio by up to 23%. In contrast, normal-strength concrete exhibited limited stiffness improvement despite higher strength. These findings highlight the reliability of IEV in mechanical properties across diverse material types and provide comparative reference data for concrete and masonry applications.

By minimizing a thermodynamic-like potential, we unbiasedly sample the potential energy landscape of soft and frictionless spheres under a constant shear stress. We obtain zero-temperature jammed states under desired shear stresses and investigate their mechanical properties as a function of the shear stress. As a comparison, we also obtain the jammed states from the quasistatic-shear sampling in which the shear stress is not well-controlled. Although the yield stresses determined by both samplings show the same power-law scaling with the compression from the jamming transition point J at zero temperature and shear stress, for finite size systems the quasistatic-shear sampling leads to a lower yield stress and a higher critical volume fraction at point J. The shear modulus of the jammed solids decreases with increasing shear stress. However, the shear modulus does not decay to zero at yielding. This discontinuous change of the shear modulus implies the discontinuous nature of the unjamming transition under nonzero shear stress, which is further verified by the observation of a discontinuous jump in the pressure from the jammed solids to the shear flows. The pressure jump decreases upon decompression and approaches zero at the critical-like point J, in analogy with the well-known phase transitions under an external field. The analysis of the force networks in the jammed solids reveals that the force distribution is more sensitive to the increase of the shear stress near point J. The force network anisotropy increases with increasing shear stress. The weak particle contacts near the average force and under large shear stresses it exhibit an asymmetric angle distribution.

Muscle shear elastic modulus is linearly related to muscle torque over the entire range of isometric contraction intensity