Growth-induced compatible strains

2016 ◽  
Vol 22 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Manuela Minozzi ◽  
Paola Nardinocchi ◽  
Luciano Teresi ◽  
Valerio Varano
Keyword(s):  
Stress State ◽  
Time Evolution ◽  
Linear Elasticity ◽  
Free State ◽  
Evolution Problem ◽  
Euclidean Ball ◽  
Initial State ◽  
Non Linear ◽  
Stress Free State

We studied the time evolution problem driven by growth for a non-Euclidean ball which at its initial state is equipped with a non-compatible distortion field. The problem is set within the framework of non-linear elasticity with large growing distortions. No bulk accretive forces are considered, and growth is only driven by the stress state. We showed that, when stress-driven growth is considered, distortions can evolve along different trajectories which share a common attracting manifold; moreover, they eventually attain a steady and compatible form, to which there corresponds a stress-free state of the ball.

scholarly journals Stress-free state of the red blood cell membrane and the deformation of its skeleton

2012 ◽  
Vol 17 (2) ◽  
Author(s):  
Tjaša Švelc ◽  
Saša Svetina
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Variational Calculation ◽  
Lateral Distribution ◽  
Free State ◽  
Initial State ◽  
Proposed Model ◽  
Deformed State ◽  
Concentric Circles ◽  
Stress Free State

AbstractThe response of a red blood cell (RBC) to deformation depends on its membrane, a composite of a lipid bilayer and a skeleton, which is a closed, twodimensional network of spectrin tetramers as its bonds. The deformation of the skeleton and its lateral redistribution are studied in terms of the RBC resting state for a fixed geometry of the RBC, partially aspirated into a micropipette. The geometry of the RBC skeleton in its initial state is taken to be either two concentric circles, a references biconcave shape or a sphere. It is assumed that in its initial state the skeleton is distributed laterally in a homogeneous manner with its bonds either unstressed, presenting its stress-free state, or prestressed. The lateral distribution was calculated using a variational calculation. It was assumed that the spectrin tetramer bonds exhibit a linear elasticity. The results showed a significant effect of the initial skeleton geometry on its lateral distribution in the deformed state. The proposed model is used to analyze the measurements of skeleton extension ratios by the method of applying two modes of RBC micropipette aspiration.

Lung deformations at minimal volume

1980 ◽  
Vol 48 (3) ◽  
pp. 487-494 ◽  
Author(s):  
M. J. Kallok ◽  
S. J. Lai-Fook
Keyword(s):  
Volume Change ◽  
Linear Elasticity ◽  
Transpulmonary Pressure ◽  
Free State ◽  
Minimal Volume ◽  
Tissue Volume ◽  
Gravitational Deformation ◽  
The Difference ◽  
Stress Free State

Minimal volume (MV, gas plus tissue volume at zero transpulmonary pressure) was determined in excised dog lobes after inflation with air and with saline. MV was significantly greater in saline-filled lobes than air-filled lobes. Air inflation was performed with the lobe supported in two different ways, which were chosen to produce different deformations: 1) supported on the cephalic surface and 2) hung by strings attached to the cephalic surface. MV measured in hung lobes was significantly greater than MV measured in supported lobes. The problem of excised lobes deformed by gravity was analyzed in the two configurations using linear elasticity. The saline volume was assumed to be the stress-free state for the lobe, and the volume change was computed from the stress-free state due to the gravitational deformation. The analysis suggests that the difference between saline and air MV is due primarily to the gravitational deformation of air-filled lungs.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

STUDY OF THE SHELF LIFE OF SEALANTS BASED ON LIQUID THIOKOL IN A STRESS-FREE STATE

2021 ◽  
pp. 85-94
Author(s):  
Ja.A. Vakhrusheva ◽  
◽  
D.N. Smirnov ◽  
I.S. Makushchenko ◽  
◽  
...  
Keyword(s):  
Shelf Life ◽  
Physicomechanical Properties ◽  
Free State ◽  
Optimal Time ◽  
Thermal Light ◽  
Stress Free State ◽  
The Impact

The work carried out studies of the physicomechanical properties of polysulfide sealants of brands of U-30M and UT-31 after thermal, light aging, and the assessment of mushrooms. The data on the resistance of sealants of brands U-30M and UT-31 are investigated and summarized after the impact of accelerated climatic tests and aggressive environments. The optimal time and conditions for the storage of vulcanized sealants in the unattended state and components of sealants in warehouse conditions are determined, as well as the causes of different storage of sealing pastes based on liquid thiocola.

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