Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids

2006 ◽  
Vol 84 (17-18) ◽  
pp. 1095-1114 ◽  
Author(s):  
Eduard Rohan ◽  
Robert Cimrman ◽  
Vladimír Lukeš
Keyword(s):  
Numerical Modelling ◽  
Constitutive Law ◽  
Heterogeneous Solids

scholarly journals Rotation of the Stress Tensor in a Westerly Granite Sample During the Triaxial Compression Test

2021 ◽  
Author(s):  
Szymon Cielesta ◽  
Beata Orlecka-Sikora ◽  
Musa Adebayo Idris
Keyword(s):  
Stress Field ◽  
Numerical Modelling ◽  
Triaxial Compression ◽  
Failure Process ◽  
Damage Zone ◽  
Focal Mechanisms ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Granite Sample ◽  
Significant Difference

AbstractWe simulated the spatiotemporal modelling of 3D stress and strain distributions during the triaxial compression laboratory test on a westerly granite sample using finite-difference numerical modelling implemented with FLAC3D software. The modelling was performed using a ubiquitous joint constitutive law with strain softening. The applied procedure is capable of reproducing the macroscopic stress and strain evolution in the sample during triaxial deformation until a failure process occurs. In addition, we calculated focal mechanisms of acoustic emission (AE) events and resolved local stress field orientations. This detailed stress information was compared with that from numerical modelling. The comparison was made based on the 3D rotation angle between the cardinal axes of the two stress tensors. To infer the differences in rotation, we applied ANOVA. We identified the two time levels as the plastic deformation phase and the after-failure phase. Additionally, we introduced the bin factor, which describes the location of the rotation scores in the rock sample. The p values of the test statistics F for the bin and phase effects are statistically significant. However, the interaction between them is insignificant. We can, therefore, conclude that there was a significant difference in the time between the rotation means in the particular bins, and we ran post hoc tests to obtain more information where the differences between the groups lie. The largest rotation of the stress field provided by the focal mechanisms of AE events from the numerically calculated stress field is observed in the edge bins, which do not frame the damage zone of the sample.

scholarly journals Nonlinear waves in solids with slow dynamics: an internal-variable model

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170024 ◽  
Author(s):  
H. Berjamin ◽  
N. Favrie ◽  
B. Lombard ◽  
G. Chiavassa
Keyword(s):  
Evolution Equations ◽  
Three Dimensional ◽  
Internal Variable ◽  
Constitutive Law ◽  
Slow Dynamics ◽  
Three Dimensional Model ◽  
Variable Model ◽  
Heterogeneous Solids ◽  
Specific Internal Energy ◽  
Finite Strain Theory

In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease, known as ‘slow dynamics’, occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. (2004 Phys. Rev. E 70, 015602. ( doi:10.1103/PhysRevE.70.015602 )) is based on a variable that describes the softening of the material. However, this model is one dimensional and it is not thermodynamically admissible. In the present article, a three-dimensional model is derived in the framework of the finite-strain theory. An internal variable that describes the softening of the material is introduced, as well as an expression of the specific internal energy. A mechanical constitutive law is deduced from the Clausius–Duhem inequality. Moreover, a family of evolution equations for the internal variable is proposed. Here, an evolution equation with one relaxation time is chosen. By construction, this new model of the continuum is thermodynamically admissible and dissipative (inelastic). In the case of small uniaxial deformations, it is shown analytically that the model reproduces qualitatively the main features of real experiments.

Hydrogen Cyanide Polymers from the Impact of Comet P/Shoemaker-Levy 9 on Jupiter

1997 ◽  
Vol 161 ◽  
pp. 179-187
Author(s):  
Clifford N. Matthews ◽  
Rose A. Pesce-Rodriguez ◽  
Shirley A. Liebman
Keyword(s):  
Amino Acids ◽  
Solar System ◽  
Hydrogen Cyanide ◽  
Nitrogen Heterocycles ◽  
Laboratory Studies ◽  
Heterogeneous Solids ◽  
The Many ◽  
Comet Halley ◽  
The Impact ◽  
By Products

AbstractHydrogen cyanide polymers – heterogeneous solids ranging in color from yellow to orange to brown to black – may be among the organic macromolecules most readily formed within the Solar System. The non-volatile black crust of comet Halley, for example, as well as the extensive orangebrown streaks in the atmosphere of Jupiter, might consist largely of such polymers synthesized from HCN formed by photolysis of methane and ammonia, the color observed depending on the concentration of HCN involved. Laboratory studies of these ubiquitous compounds point to the presence of polyamidine structures synthesized directly from hydrogen cyanide. These would be converted by water to polypeptides which can be further hydrolyzed to α-amino acids. Black polymers and multimers with conjugated ladder structures derived from HCN could also be formed and might well be the source of the many nitrogen heterocycles, adenine included, observed after pyrolysis. The dark brown color arising from the impacts of comet P/Shoemaker-Levy 9 on Jupiter might therefore be mainly caused by the presence of HCN polymers, whether originally present, deposited by the impactor or synthesized directly from HCN. Spectroscopic detection of these predicted macromolecules and their hydrolytic and pyrolytic by-products would strengthen significantly the hypothesis that cyanide polymerization is a preferred pathway for prebiotic and extraterrestrial chemistry.

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