Topic

# Shear modulus

About: Shear modulus is a research topic. Over the lifetime, 16092 publications have been published within this topic receiving 425813 citations. The topic is also known as: modulus of rigidity & Coulomb modulus.

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TL;DR: In this paper, the elastic and plastic properties of pure polycrystalline metals are discussed and a systematic relation between shear modulus, Burgers vector and plastic shear strength of metals possessing the same lattice structure is proposed.

Abstract: Relations between the elastic and plastic properties of pure polycrystalline metals are discussed and a systematic relation between shear modulus, Burgers vector and plastic shear strength of metals possessing the same lattice structure is proposed. In addition reasons are given for believing that in a limited temperature range malleability is related to Poisson's ratio.

5,719 citations

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TL;DR: In this article, the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations, which leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H 0 is a characteristic length that depends on the shape of the indenter, the shear modulus and H 0.

Abstract: We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].

3,655 citations

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TL;DR: In this paper, it was deduced that the general strain energy function, W, has the form W=G4 ∑ i=13(λi−1λi)2+H 4 ∑ t=13 (λi2−1 ε)2 + H 4, where the λi's are the principal stretches, G is the modulus of rigidity, and H is a new elastic constant not found in previous theories.

Abstract: It is postulated that (A) the material is isotropic, (B) the volume change and hysteresis are negligible, and (C) the shear is proportional to the traction in simple shear in a plane previously deformed, if at all, only by uniform dilatation or contraction. It is deduced that the general strain‐energy function, W, has the form W=G4 ∑ i=13(λi−1λi)2+H4 ∑ t=13(λi2−1λi2), where the λi's are the principal stretches (1+principal extension), G is the modulus of rigidity, and H is a new elastic constant not found in previous theories. The differences between the principal stresses are σi[minus]σi=λi∂ W/∂λi[minus]λi∂ W/∂λi.Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.

2,775 citations

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Mayo Clinic

^{1}TL;DR: The results indicate that displacement patterns corresponding to cyclic displacements smaller than 200 nanometers can be measured and suggest the feasibility of a medical imaging technique for delineating elasticity and other mechanical properties of tissue.

Abstract: A nuclear magnetic resonance imaging (MRI) method is presented for quantitatively mapping the physical response of a material to harmonic mechanical excitation. The resulting images allow calculation of regional mechanical properties. Measurements of shear modulus obtained with the MRI technique in gel materials correlate with independent measurements of static shear modulus. The results indicate that displacement patterns corresponding to cyclic displacements smaller than 200 nanometers can be measured. The findings suggest the feasibility of a medical imaging technique for delineating elasticity and other mechanical properties of tissue.

2,015 citations

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TL;DR: In this paper, the effective shear modulus of two types of composite material models are compared. And the results are found to differ from those of the well-known Kerner and Hermans formulae for the same models.

Abstract: S olutions are presented for the effective shear modulus of two types of composite material models. The first type is that of a macroscopically isotropic composite medium containing spherical inclusions. The corresponding model employed is that involving three phases: the spherical inclusion, a spherical annulus of matrix material and an outer region of equivalent homogeneous material of unlimited extent. The corresponding two-dimensional, polar model is used to represent a transversely isotropic, fiber reinforced medium. In the latter case only the transverse effective shear modulus is obtained. The relative volumes of the inclusion phase to the matrix annulus phase in the three phase models are taken to be the given volume fractions of the inclusion phases in the composite materials at large. The results are found to differ from those of the well-known Kerner and Hermans formulae for the same models. The latter works are now understood to violate a continuity condition at the matrix to equivalent homogeneous medium interface. The present results are compared extensively with results from other related models. Conditions of linear elasticity are assumed.

1,994 citations