Mechanically Responsive Crystals: Analysis of Macroscopic Strain Reveals “Hidden” Processes

2019 ◽  
Vol 124 (2) ◽  
pp. 300-310 ◽  
Author(s):  
Israel Tilahun Desta ◽  
Stanislav A. Chizhik ◽  
Anatoli A. Sidelnikov ◽  
Durga Prasad Karothu ◽  
Elena V. Boldyreva ◽  
...  
Keyword(s):  
Macroscopic Strain

A macroscopic strain-space model of anisotropic, cyclic plasticity with hardening

2018 ◽  
Vol 149 ◽  
pp. 365-372 ◽  
Author(s):  
Harshad M. Paranjape ◽  
Aaron P. Stebner ◽  
Kaushik Bhattacharya
Keyword(s):  
Cyclic Plasticity ◽  
Macroscopic Strain ◽  
Space Model ◽  
Strain Space

scholarly journals New Deformation Twinning Mechanism Generates Zero Macroscopic Strain in Nanocrystalline Metals

2008 ◽  
Vol 100 (9) ◽  
Author(s):  
X. L. Wu ◽  
X. Z. Liao ◽  
S. G. Srinivasan ◽  
F. Zhou ◽  
E. J. Lavernia ◽  
...  
Keyword(s):  
Deformation Twinning ◽  
Nanocrystalline Metals ◽  
Macroscopic Strain

Hashin–Shtrikman bounds of periodic linear elastic media with cubic symmetry

2020 ◽  
Vol 25 (5) ◽  
pp. 1182-1198 ◽  
Author(s):  
George Mejak
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Elastic Media ◽  
Macroscopic Strain ◽  
Two Phase ◽  
Cubic Symmetry ◽  
Shear Moduli ◽  
Linear Elastic ◽  
Periodic Linear ◽  
Periodic Composite

Based on the Hashin–Shtrikman variational principle, novel bounds on the effective shear moduli of a two-phase periodic composite are derived. The composite constituents are assumed to be isotropic, while the microstructure is assumed to exhibit cubic symmetry. A solution of the subsidiary boundary value problem is expressed as a double contraction of a fourth-order cubic tensor with the applied macroscopic strain. The bounds for cubic shear moduli are new, while the bounds for the bulk modulus are equal to the classical ones. The new bounds are verified for composites with the cubic, frame, octet and cubic + octet structures. It is shown that they are nearly attained for the cubic, octet and cubic + octet structures.

Modeling of macroscopic strain localization in alloys with the L12 structure

2011 ◽  
Vol 54 (8) ◽  
pp. 885-897 ◽  
Author(s):  
V. A. Starenchenko ◽  
Yu. V. Solov’eva ◽  
Ya. D. Fakhrutdinova ◽  
L. A. Valuiskaya
Keyword(s):  
Strain Localization ◽  
Macroscopic Strain ◽  
L12 Structure

Characterization and Performance Optimization of 2D Lattice Materials With Hexagonal Bravais Lattice Symmetry

2009 ◽  
Author(s):  
Mostafa S. A. Elsayed ◽  
Damiano Pasini
Keyword(s):  
Strain Energy ◽  
Structural Performance ◽  
Bravais Lattice ◽  
Macroscopic Strain ◽  
Mass Ratio ◽  
Strain Fields ◽  
Lattice Symmetry ◽  
Lattice Materials ◽  
Stiffness Properties ◽  
Lattice Material

The current paper examines the static performance of 2D infinite lattice materials with hexagonal Bravais lattice symmetry. Two novel microscopic cell topologies are proposed. The first topology is a semi-regular lattice that has the modified Schafli symbol 34.6, which describes the type of regular polygons surrounding the joints of the lattice. Here, 34.6 indicates four (4) regular triangles (3) successively surrounding a node followed by a regular hexagon (6). The second topology is an irregular lattice that is referred here as Double Hexagonal Triangulation (DHT). The lattice material is considered as a pin-jointed micro-truss where determinacy analysis of the material micro structure is used to distinguish between bending dominated and stretching dominated behaviours. The finite structural performance of unit cells of the proposed topologies is assessed by the matrix methods of linear algebra. The Dummy Node Hypothesis is developed to generalize the analysis to tackle any lattice topology. Collapse mechanisms and states of self-stress are deduced from the four fundamental subspaces of the kinematic and the equilibrium matrices of the finite unit cell structures, respectively. The generated finite structural matrices are employed to analyze the infinite structural performance of the lattice using the Bloch’s theorem. To find macroscopic strain fields generated by periodic mechanisms, the Cauchy-Born hypothesis is adopted. An explicit expression of the microscopic cell element deformations in terms of the macroscopic strain field is generated which is employed to derive the strain energy density of the lattice material. Finally, the strain energy density is used to derive the material macroscopic stiffness properties. The results showed that the proposed lattice topologies can support all macroscopic strain fields. Their stiffness properties are compared with those of lattice materials with hexagonal Bravais symmetry available in literature. The comparison showed that the lattice material with 34.6 cell topology has superior isotropic stiffness properties. When compared with the Kagome’ lattice, the 34.6 lattice generates isotropic stiffness properties, with additional stiffness to mass ratio of 18.5% and 93.2% in the direct and the coupled direct stiffness, respectively. However, it generates reduced shear stiffness to mass ratio by 18.8%.

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