Continuum Mechanics for Engineers

Mase, G; Mase, George E.

doi:10.1201/9780367803230

Cited by 72 publications

(59 citation statements)

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“…Using the summation convention (e.g. Mase and Mase, 1999, p. 5), this stiffness tensor can be viewed in a rotated coordinate system according to the rule: where direction cosines a ij are defined so that where and are the coordinate axes in the original and rotated coordinate systems (Mase and Mase, 1999, p. 221).…”

Section: Elastic Waves In Icementioning

confidence: 99%

Sonic methods for measuring crystal orientation fabric in ice, and results from the West Antarctic ice sheet (WAIS) Divide

et al. 2017

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ABSTRACT. We describe methods for measuring crystal orientation fabric with sonic waves in an ice core borehole, with special attention paid to vertical-girdle fabrics that are prevalent at the WAIS Divide. The speed of vertically propagating compressional waves in ice is influenced by vertical clustering of the ice crystal c-axes. Shear-wave speeds -particularly the speed separation between fast and slow shear polarizations -are sensitive to azimuthal anisotropy. Sonic data from the WAIS Divide complement thin-section measurements of fabric. Thin sections show a steady transition to strong girdle fabrics in the upper 2000 m of ice, followed by a transition to vertical-pole fabrics below 2500 m depth. Compressional-wave sonic data are inconclusive in the upper ice, due to noise, as well as the method's inherent insensitivity to girdle fabrics. Compared with available thin sections, sonic data provide better resolution of the transition to pole fabrics below 2500 m, notably including an abrupt increase in vertical clustering near 3000 m. Our compressional-wave measurements resolve fabric changes occurring over depth ranges of a few meters that cannot be inferred from available thin sections, but are sensitive only to zenithal anisotropy. Future logging tools should be designed to measure shear waves in addition to compressional waves, especially for logging in regions where ice flow patterns favor the development of girdle fabrics.

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Section: Elastic Waves In Icementioning

confidence: 99%

Sonic methods for measuring crystal orientation fabric in ice, and results from the West Antarctic ice sheet (WAIS) Divide

et al. 2017

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“…Most of the contents of this section can be found in standard textbooks, such as Findley et al. ( 1976 ) [chapters 1 and 5] and Mase ( 1970 ), and are reported here for the sake of completeness. Specific considerations of and applications to living tissues can be found in Fung ( 1993 ).…”

Section: Essentials Of Viscoelastic Materials and Stress–strain Constitutive Equationsmentioning

confidence: 99%

“…The SLS model, also known as the Kelvin model, relies on the assumption that viscous and elastic characteristics of a linear viscoelastic material can be captured by considering a Kelvin arm of elastic modulus and viscosity in series with a purely elastic spring of elastic modulus , as illustrated in Fig. 1 e. The corresponding stress–strain constitutive equation is Mase ( 1970 ) Jeffrey model. The Jeffrey model, also known as the Oldroyd-B or 3-parameter viscous model, relies on the assumption that viscous and elastic characteristics of a linear viscoelastic material can be captured by considering a Kelvin arm of elastic modulus E and viscosity in series with a purely viscous damper of viscosity , as illustrated in Fig.…”

Section: Essentials Of Viscoelastic Materials and Stress–strain Constitutive Equationsmentioning

confidence: 99%

Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress–Strain Constitutive Equations

et al. 2021

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Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a balance equation for the density of the extracellular matrix (ECM), and a force-balance equation describing the mechanical equilibrium of the cell-ECM system. Under the assumption that the cell-ECM system can be regarded as an isotropic linear viscoelastic material, the force-balance equation is often defined using the Kelvin–Voigt model of linear viscoelasticity to represent the stress–strain relation of the ECM. However, due to the multifaceted bio-physical nature of the ECM constituents, there are rheological aspects that cannot be effectively captured by this model and, therefore, depending on the pattern formation process and the type of biological tissue considered, other constitutive models of linear viscoelasticity may be better suited. In this paper, we systematically assess the pattern formation potential of different stress–strain constitutive equations for the ECM within a mechanical model of pattern formation in biological tissues. The results obtained through linear stability analysis and the dispersion relations derived therefrom support the idea that fluid-like constitutive models, such as the Maxwell model and the Jeffrey model, have a pattern formation potential much higher than solid-like models, such as the Kelvin–Voigt model and the standard linear solid model. This is confirmed by the results of numerical simulations, which demonstrate that, all else being equal, spatial patterns emerge in the case where the Maxwell model is used to represent the stress–strain relation of the ECM, while no patterns are observed when the Kelvin–Voigt model is employed. Our findings suggest that further empirical work is required to acquire detailed quantitative information on the mechanical properties of components of the ECM in different biological tissues in order to furnish mechanical and mechanochemical models of pattern formation with stress–strain constitutive equations for the ECM that provide a more faithful representation of the underlying tissue rheology.

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“…The relationship between changes in temperature and mechanical strain, for an isotropic material under free thermal expansion/contraction, has the following form (Mase and Mase, 1999):…”

Section: Temperature Dependenciesmentioning

confidence: 99%

Analytically describing the temperature-dependent constitutive parameters of an electromagnetic metamaterial

Arritt

Smith

Khraishi

2012

Journal of Intelligent Material Systems and Structures

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Analogous to mechanical systems, modeling the electromagnetic (EM) performance of large and complex metamaterial structures requires the use of effective-medium/constitutive properties. Constitutive properties are critical for efficiently bridging the gap between subwavelength geometry and performance at the mesoscale. In this article, the temperature-dependent effective medium properties for a metamaterial electric-inductive-capacitive (ELC) resonator are described analytically. ELC structures are commonly used in metamaterial designs to provide a tailored electric response to EM waves. An equivalent circuit model, coupled with analytic expressions for the capacitances, inductance, and resistance of the ELC resonator, is utilized to describe how thermally induced mechanical strain and changes in material properties manifest as temperature-dependent permittivity and permeability curves for the metamaterial. The resulting analytic expressions account for the effects of spatial dispersion and losses. This article also details how the process may be expanded to similarly describe the temperature-dependent constitutive properties of metamaterial magnetic resonators.

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Continuum Mechanics for Engineers

Cited by 72 publications

References 0 publications

Sonic methods for measuring crystal orientation fabric in ice, and results from the West Antarctic ice sheet (WAIS) Divide

Sonic methods for measuring crystal orientation fabric in ice, and results from the West Antarctic ice sheet (WAIS) Divide

Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress–Strain Constitutive Equations

Analytically describing the temperature-dependent constitutive parameters of an electromagnetic metamaterial

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