scholarly journals Diffusion of Chemically Reacting Fluids through Nonlinear Elastic Solids and 1D Stabilized Solutions

Author(s):  
Richard Hall ◽  
H. Gajendran ◽  
A. Masud
2008 ◽  
Vol 23 (8) ◽  
pp. 2157-2165 ◽  
Author(s):  
Shahram Amini ◽  
Aiguo Zhou ◽  
Surojit Gupta ◽  
Andrew DeVillier ◽  
Peter Finkel ◽  
...  

Herein we report on the synthesis and characterization of Cr2GeC, a member of the so-called Mn+1AXn (MAX) phase family of layered machinable carbides and nitrides. Polycrystalline samples were synthesized by hot pressing pure Cr, Ge, and C powders at 1350 °C at ∼45 MPa for 6 h. No peaks other than those associated with Cr2GeC and Cr2O3, in the form of eskolaite, were observed in the x-ray diffraction spectra. The samples were readily machinable and fully dense. The steady-state Vickers hardness was 2.5 ± 0.1 GPa. The Young’s moduli measured in compression and by ultrasound were 200 ± 10 and 245 ± 3 GPa, respectively; the shear modulus and Poisson’s ratio deduced from the ultrasound results were 80 GPa and 0.29, respectively. The ultimate compressive strength for a ∼20 μm grain size sample was 770 ± 30 MPa. Samples compressively loaded from 300 to ∼570 MPa exhibited nonlinear, fully reversible, reproducible, closed hysteretic loops that dissipated ∼20% of the mechanical energy, a characteristic of the MAX phases, in particular, and kinking nonlinear elastic solids, in general. The energy dissipated is presumably due to the formation and annihilation of incipient kink bands. The critical resolved shear stress of the basal plane dislocations—estimated from our microscale model—is ∼22 MPa. The incipient kink band and reversible dislocation densities, at the maximum stress of 568 MPa, are estimated to be 1.2 × 10−2 μm−3 and 1.0 × 1010 cm−2, respectively.


Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 65-78 ◽  
Author(s):  
Harold Berjamin ◽  
Bruno Lombard ◽  
Guillaume Chiavassa ◽  
Nicolas Favrie

2009 ◽  
Vol 94 (24) ◽  
pp. 241904 ◽  
Author(s):  
P. Finkel ◽  
A. G. Zhou ◽  
S. Basu ◽  
O. Yeheskel ◽  
M. W. Barsoum

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Katia Bertoldi ◽  
Oscar Lopez-Pamies

In filled elastomers, the mechanical behavior of the material surrounding the fillers -termed interphasial material-can be significantly different (softer or stiffer) from the bulk behavior of the elastomeric matrix. In this paper, motivated by recent experiments, we study the effect that such interphases can have on the mechanical response and stability of fiber-reinforced elastomers at large deformations. We work out in particular analytical solutions for the overall response and onset of microscopic and macroscopic instabilities in axially stretched 2D fiber-reinforced nonlinear elastic solids. These solutions generalize the classical results of Rosen (1965, “Mechanics of Composite Strengthening,” Fiber Composite Materials, American Society for Metals, Materials Park, OH, pp. 37–75), and Triantafyllidis and Maker (1985, “On the Comparison between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites,” J. Appl. Mech., 52, pp. 794–800), for materials without interphases. It is found that while the presence of interphases does not significantly affect the overall axial response of fiber-reinforced materials, it can have a drastic effect on their stability.


2021 ◽  
Vol 11 (19) ◽  
pp. 9208
Author(s):  
Ehsan Motevali Haghighi ◽  
Seonhong Na

A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme.


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