A theorem of the congruence principle in nonlinear mechanics

1978 ◽  
Vol 14 (10) ◽  
pp. 1116-1119 ◽  
Author(s):  
A. A. Martynyuk
Keyword(s):  
Nonlinear Mechanics ◽  
Congruence Principle

Nonlinear Mechanics and Applied Analysis.

1995 ◽  
Author(s):  
John Maddocks
Keyword(s):  
Nonlinear Mechanics

scholarly journals Performance of SCAN Meta-GGA Functionals on Nonlinear Mechanics of Graphene-Like g-SiC

Crystals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 120
Author(s):  
Qing Peng
Keyword(s):  
Mechanical Properties ◽  
Density Functional ◽  
Large Strains ◽  
Two Dimensional ◽  
Nonlinear Mechanics ◽  
Generalized Gradient ◽  
Mechanics Of Materials ◽  
Nonlinear Mechanical ◽  
Direct Band ◽  
Simulations And Modeling

Although meta-generalized-gradient approximations (meta-GGAs) are believed potentially the most accurate among the efficient first-principles calculations, the performance has not been accessed on the nonlinear mechanical properties of two-dimensional nanomaterials. Graphene, like two-dimensional silicon carbide g-SiC, has a wide direct band-gap with applications in high-power electronics and solar energy. Taken g-SiC as a paradigm, we have investigated the performance of meta-GGA functionals on the nonlinear mechanical properties under large strains, both compressive and tensile, along three deformation modes using Strongly Constrained and Appropriately Normed Semilocal Density Functional (SCAN) as an example. A close comparison suggests that the nonlinear mechanics predicted from SCAN are very similar to that of Perdew-Burke-Ernzerhof (PBE) formulated functional, a standard Density Functional Theory (DFT) functional. The improvement from SCAN calculation over PBE calculation is minor, despite the considerable increase of computing demand. This study could be helpful in selection of density functionals in simulations and modeling of mechanics of materials.

Nonlinear mechanics of a slender beam composited by three-directional functionally graded materials

2021 ◽  
pp. 114088
Author(s):  
Ye Tang ◽  
Guo Wang ◽  
Taolin Ren ◽  
Qian Ding ◽  
Tianzhi Yang
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Nonlinear Mechanics ◽  
Graded Materials

Nonlinear mechanics of accretion

2019 ◽  
Vol 29 (4) ◽  
pp. 1813-1863 ◽  
Author(s):  
Fabio Sozio ◽  
Arash Yavari
Keyword(s):  
Nonlinear Mechanics

scholarly journals Nonlocal nonlinear mechanics of imperfect carbon nanotubes

2019 ◽  
Vol 142 ◽  
pp. 201-215 ◽  
Author(s):  
Ali Farajpour ◽  
Mergen H. Ghayesh ◽  
Hamed Farokhi
Keyword(s):  
Carbon Nanotubes ◽  
Nonlinear Mechanics ◽  
Nonlocal Nonlinear

Nonlinear Mechanics of Solids Containing Isolated Voids

2006 ◽  
Vol 59 (4) ◽  
pp. 210-229 ◽  
Author(s):  
Z. P. Huang ◽  
J. Wang
Keyword(s):  
Critical Review ◽  
Cell Model ◽  
Extreme Case ◽  
Local Deformation ◽  
Mechanics Of Solids ◽  
Nonlinear Mechanics ◽  
Theoretical Frameworks ◽  
Nonlinear Materials ◽  
A Cell ◽  
Nonlinear Composite

The ductile fracture of many materials is related to the nucleation, growth, and coalescence of voids. Also, a material containing voids represents an extreme case of heterogeneous materials. In the last few decades, numerous studies have been devoted to the local deformation mechanisms and macroscopic overall properties of nonlinear materials containing voids. This article presents a critical review of the studies in three interconnected topics in nonlinear mechanics of materials containing isolated voids, namely, the growth of an isolated void in an infinite medium under a remote stress; the macroscopic mechanical behavior of these materials predicted by using a cell model; and bounds and estimates of the overall properties of these materials as a special case of nonlinear composite materials. Emphasis are placed upon analytical and semianalytical approaches for static loading conditions. Both the classical methods and more recent approaches are examined, and some inadequacies in the existing methods are pointed out. In addition to the critical review of the existing methods and results, some new results, including a power-law stress potential for compressible nonlinear materials, are presented and integrated into the pertinent theoretical frameworks. This review article contains 118 references.

Biological Senescence: Loss of Integration and Resilience

1995 ◽  
Vol 14 (1) ◽  
pp. 106-120 ◽  
Author(s):  
F. Eugene Yates ◽  
Laurel A. Benton
Keyword(s):  
Degrees Of Freedom ◽  
Nonequilibrium Thermodynamics ◽  
Physical Basis ◽  
Biological Age ◽  
Chronological Age ◽  
Nonlinear Mechanics ◽  
Internal Time ◽  
Flow Of Time

ABSTRACTThe flow of time can be conceptualized either as a cycle or an arrow. We offer a combined view: a helix. Chronological age (geophysical time reference) is not necessarily identical to biological age (internal time reference), and aging does not necessarily imply senescence. A new scheme of senescence, based on homeodynamics (nonlinear mechanics and nonequilibrium thermodynamics), is introduced as a plausible physical basis for understanding senescence. We propose that energy throughput, initially constructive of forms and functions, becomes destructive once most of the available degrees of freedom have been “frozen out” by the construction. Senescence becomes manifested at that point.

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