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The relation between single crystal elasticity and the ...

Single crystal elasticity and effective elastic behaviour 913 Table 1. Elastic constants (GPa). BaTiO3 BaTiO3 In ZrSiO4 cubic tetragonal tetragonal tetragonal c11 173 275.1 45.2 424 c12 82 179.0 40.0 70 c44 108 54.3 6.52 113 c33 — 164.9 44.9 490 c13 — 151.6 41.2 150 c66 — 113.1 12.0 48.5 The components of the fourth-order elasticity tensor with respect to the rotated frame are

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Section 4: Elastic Properties

All 36 elastic constants are independent. However in crystals many of them are the same due to symmetry. In particular, in cubic crystals C11 =C22 =C33 , C12 =C21 =C23 =C32 =C13 =C31 , C44 =C55 =C66 due the fact that x, y, and z axes are identical by symmetry. Also the off diagonal shear

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Calculations of single-crystal elastic constants made ...

Calculated single-crystal elastic constants of cubic diamond, hexagonal osmium, orthorhombic TiSi 2 and monoclinic Mg 5 Si 6 are given as examples. Previous article in issue; Next article in issue; Keywords. Elasticity. 1. Introduction The elasticity is a fundamental property of crystalline materials and is of great importance in physical sciences, including materials science, solid state ...

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An effective semi-implicit integration scheme for rate ...

The hypoelastic crystal plasticity adopted the Jaumann rate to treat the objective of lattice spin and material spin, the variables rely on the grains’ orientation are updated incrementally by the elastic lattice spin, which is obtain directly for the difference value between the material spin and plastic lattice spin, this feature makes the hypoelastic crystal plasticity computationally ...

Revision 1 Single-Crystal Elastic Properties of Minerals ...

Single-Crystal Elastic Properties of Minerals and Related Materialswith Cubic Symmetry Thomas S. Duffy Department of Geosciences Princeton University Abstract The single-crystal elastic moduli of minerals and related materials with cubic symmetry havebeen collectedand evaluated. The compileddatasetcovers measurements made overan approximately seventy year period and consists of 206 ...

Crystal Elasticity - ScienceDirect

Crystal Elasticity at Infinitesimal Strain as Revealed by Finite Strain Considerations We begin by mentioning that, as an "additional bonus," studies of lattice behavior at finite strain have provided deeper insight into the bases for certain aspects of crystal elasticity at infinitesimal strain. Three examples are presented in Sections 2.1-2.3. 2.1. Existence of unstressed tetragonal crystals ...

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The elastic crystals [email protected] with high quality and large size are crystalized by a simple and unique “self‐doping” process, which is a regular solution evaporation of crude product 1d (2,5‐dihydro‐3,6‐bis(octylamino)terephthalate) containing a minute amount of 2d (3,6‐bis(octylamino)terephthalate) as the oxidized byproduct. The host 1d is easily crystallized to form elastic ...

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A Simple Explicit Formula for the ... - Journal of Elasticity

The Voigt-Reuss-Hill (VRH) average provides a simple way to estimate the elastic constants of a textured polycrystal in terms of its crystallographic texture and the elastic constants of the constituting crystallites. Empirically the VRH estimates were found in most cases to have an accuracy comparable to those obtained by more sophisticated techniques such as self-consistent schemes.

Single-crystal elasto-viscoplasticity: application to ...

G. Simmons, H. WangSingle Crystal Elastic Properties and Calculated Aggregate Properties: A HANDBOOK. The MIT Press, Cambridge (1971) Google Scholar. S. Nemat-Nasser, L.Q. Ni, T. OkinakaA constitutive model for fcc crystals with application to polycrystalline ofhc copper. Mech. Mater., 30 (1998), pp. 325-341 . Article Download PDF View Record in Scopus Google Scholar. S. Balasubramanian, L ...

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(PDF) Facile measurement of single-crystal elastic ...

Single-crystal elastic constants are essential data not only for. constitutive and micro-mechanistic modeling of various properties (especially mechanical properties including plastic deformation ...

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Elastic properties of single crystals and polycrystalline ...

Elastic Properties of Single Crystals and Polycrystalline Aggregates 73 and due to lack of proper experimental techniques. The elastic properties of the aggregates depend on the closeness of packing, size of particles and arrangement of the crystallites composing the aggregate. If they are dis- tributed in a random manner in all possible orientations in space (having no preferred orientation ...

Evaluation of single crystal elastic constants and ...

Single crystal elastic constants of austenite and ferrite phases in high-nitrogen duplex stainless steel were evaluated by an elastic self-consistent model combined with an optimization process using in-situ neutron diffraction data. The optimized elastic constants were validated by the indentation moduli of each phase obtained by nanoindentation.

Single crystal elastic constants and calculated aggregate ...

Single crystal elastic constants and calculated aggregate properties Data provider: Information Systems Division, National Agricultural Library. The National Agricultural Library is one of four national libraries of the United States, with locations in Beltsville, Maryland and Washington, D.C. It houses one of the world's largest and most accessible agricultural information collections and ...

GEOL C365 Lecture 2: Elastic Properties of Crystal Structures

Cubic crystals: For cubic crystals the elastic constants, c ij, may be reduced to just three independent elastic constants: c 11 = c 22 = c 33 Þ modulus for axial compression, i.e., a stress s 11 results in a strain e 11 along an axis; c 44 = c 55 = c 66 Þ shear modulus, i.e., a shear stress s 23 results in a shear strain e 23 across a face; c 12 = c 13 = c 23 Þ modulus for dilation on ...

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Rectangular parallellepiped resonance method for ...

A theory is presented on the free osculations of a rectangular parallelepiped of piezoelectric crystal, by extending the theory of the rectangular parallelepiped resonance (RPR) method to determine elastic constants of crystals, as exemplified by an alpha-quartz specimen. The piezoelectric contribution to resonance frequencies was examined numerically on the specimen, and it was revealed that ...

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Crystalline “Hard” Elastic Materials | SpringerLink

“Hard” elastic materials are oriented, highly crystalline polymeric products (fibers or films) which show remarkable, long range elastic behavior on single and multiple extension over a very wide range of temperatures. They show a high elastic recovery from 50–100% extension (for example: polypropylene 68 to 97% length recovery from −190°C to 140°C) with a low embrittling effect ...

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Liquid crystalline elastomer - Wikipedia

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Density functional theory for calculation of elastic ...

A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi 2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA).

Photonic Rubber Sheets with Tunable Color by Elastic ...

Symmetric Continuously Tunable Photonic Band Gaps in Blue-Phase Liquid Crystals Switched by an Alternating Current Field. ACS Applied Materials & Interfaces 2019, 11 (24) , 22015-22020.

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Phys. Rev. E 88, 062507 (2013) - Rotational and ...

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Phys. Rev. E 103, 022709 (2021) - Molecular origin of the ...

The five elastic constants are obtained within the same approach, from which we were able to predict that a significant space variations of the order parameters can be observed within the $0.5--0.8\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\text{m}$ area around any small object, almost independently of its own dimension. Therefore, the liquid crystals can be a simple tool for the optical ...

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