stress jump
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2021 ◽  
Vol 927 ◽  
Author(s):  
Pier Giuseppe Ledda ◽  
E. Boujo ◽  
S. Camarri ◽  
F. Gallaire ◽  
G.A. Zampogna

A formal framework to characterize and control/optimize the flow past permeable membranes by means of a homogenization approach is proposed and applied to the wake flow past a permeable cylindrical shell. From a macroscopic viewpoint, a Navier-like effective stress jump condition is employed to model the presence of the membrane, in which the normal and tangential velocities at the membrane are respectively proportional to the so-called filtrability and slip numbers multiplied by the stresses. Regarding the particular geometry considered here, a characterization of the steady flow for several combinations of constant filtrability and slip numbers shows that the flow morphology is dominantly influenced by the filtrability and exhibits a recirculation region that moves downstream of the body and eventually disappears as this number increases. A linear stability analysis further shows the suppression of vortex shedding as long as large values of the filtrability number are employed. In the control/optimization phase, specific objectives for the macroscopic flow are formulated by adjoint methods. A homogenization-based inverse procedure is proposed to obtain the optimal constrained microscopic geometry from macroscopic objectives, which accounts for fast variations of the filtrability and slip profiles along the membrane. As a test case for the proposed design methodology, a cylindrical membrane is designed to maximize the resulting drag coefficient.


2020 ◽  
Vol 892 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
François Gallaire


2020 ◽  
Vol 13 (3) ◽  
pp. 1155-1164
Author(s):  
Thomas Zwinger ◽  
Grace A. Nield ◽  
Juha Ruokolainen ◽  
Matt A. King

Abstract. We present a new, open-source viscoelastic solid earth deformation model, Elmer/Earth. Using the multi-physics finite-element package Elmer, a model to compute viscoelastic material deformation has been implemented into the existing linear elasticity solver routine. Unlike approaches often implemented in engineering codes, our solver accounts for the restoring force of buoyancy within a system of layers with depth-varying density. It does this by directly integrating the solution of the system rather than by applying stress-jump conditions in the form of Winkler foundations on inter-layer boundaries, as is usually needed when solving the minimization problem given by the stress divergence in commercial codes. We benchmarked the new model with results from a commercial finite-element engineering package (ABAQUS, v2018) and another open-source code that uses viscoelastic normal mode theory, TABOO, using a flat-earth setup loaded by a cylindrical disc of 100 km in diameter and 100 m in height at the density of ice. Evaluating the differences in predicted surface deformation at the centre of the load and two distinctive distances (100 and 200 km), average deviations of 7 and 2.7 cm of Elmer/Earth results to ABAQUS and TABOO, respectively, were observed. In view of more than 100 cm maximum vertical deformation and the different numerical methods and parameters, these are very encouraging results. Elmer is set up as a highly scalable parallel code and distributed under the (L)GPL license, meaning that large-scale computations can be made without any licensing restrictions. Scaling figures presented in this paper show good parallel performance of the new model. Additionally, the high-fidelity ice-sheet code Elmer/Ice utilizes the same source base as Elmer and thereby the new model opens the way to undertaking high-resolution coupled ice-flow–solid-earth deformation simulations, which are required for robust projections of future sea-level rise and glacial isostatic adjustment.


2019 ◽  
Vol 87 (2) ◽  
Author(s):  
Yin Yao ◽  
Zhilong Peng ◽  
Jianjun Li ◽  
Shaohua Chen

Abstract A continuum theory of elasticity based on the concept of interface free energy density is proposed to account for the effect of incoherent interfaces in nano-phase reinforced composites. With the help of the lattice model, the corresponding interface energy density is formulated in terms of the surface free energy densities of two bulk materials forming interfaces, the lattice relaxation parameters due to the spontaneous surface relaxation and lattice misfit parameters yielded by interface incoherency, while the stress jump at interfaces is formulated with an interface-induced traction as a function of interface free energy density. Compared with existing theories, the interface elastic constants difficult to determine are no longer introduced, and all the parameters involved in the present theory have definite physical meanings and can be easily determined. The coupling effects of characteristic size and interface structure in nanoparticle-reinforced composites are further analyzed with the present theory. It is found that both the decrease of nanoparticle size and the increase of interface incoherence will lead to the decrease of interface fracture toughness and increase of effective bulk and shear moduli of nanocomposites. All these results predicted by the present theory are consistent well with those obtained by previous experiments and computations, which further indicate that the present theory can effectively predict the mechanical properties of nanomaterials with complex interfaces, such as nano-phase reinforced composites and nano-scale metal multilayer composites.


2019 ◽  
Author(s):  
Thomas Zwinger ◽  
Grace A. Nield ◽  
Juha Ruokolainen ◽  
Matt A. King

Abstract. We present a new, open source visco-elastic Earth-deformation model, Elmer/Earth. Using the multi-physics Finite Element package Elmer, a model to compute visco-elastic material deformation has been implemented into the existing linear elasticity solver routine. Unlike approaches often implemented in engineering codes, our solver accounts for the restoring force of buoyancy within a system of layers with depth-varying density. It does this by directly integrating the solution of the system rather than by applying stress-jump conditions in the form of Winkler foundations on inter-layer boundaries, as is usually needed when solving the minimisation problem given by the stress-divergence in commercial codes. We benchmarked the new model with results from a commercial Finite Element engineering package (ABAQUS, v2018) and another open-source code that uses visco-elastic Normal Mode theory, TABOO, using a flat-earth setup loaded by a cylindrical disc of 100 km diameter and 100 m height of ice density. Evaluating the differences of predicted surface deformation at the centre of the load and two distinctive distances (100 km and 200 km), average deviations of 7 cm and 2.7 cm of Elmer/Earth results to ABAQUS and TABOO, respectively, were observed. In view of more than 100 cm maximum vertical deformation and the different numerical methods and parameters, these are very encouraging results. Elmer is set up as a highly scalable parallel code and distributed under the (L)GPL license, meaning that large scale computations can be made without any licensing restrictions. Scaling figures presented in this paper show good parallel performance of the new model. Additionally, the high fidelity ice sheet code Elmer/Ice utilises the same source-base of Elmer and thereby the new model opens the way to undertaking high-resolution coupled ice-flow - Earth deformation simulations, which are required for robust projections of future sea-level rise and glacial isostatic adjustment.


2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Gui-Lin Wang ◽  
Liang Zhang ◽  
Zhen Wang ◽  
Jian-Zhi Zhang ◽  
Fan Sun ◽  
...  

The study of the mechanical properties and cracking behaviors of jointed rock masses is important in rock engineering projects. In the present study, a series of uniaxial compression experiments were conducted on intact rock, and rock masses with single or double preexisting flaws, and then the strength, deformability, and fracture behavior of samples are investigated. Moreover, photographic monitoring technique and emission monitoring technique are introduced to explore the fracturing mode and the acoustic emission (AE) evolution characteristic of fractured rock during the whole loading process. The obtained results show that the preexisting flaw has a strong influence on the mechanical properties, fracture behavior, and AE characteristic of sandstone specimens. In detail, the stress-strain curves show that no significant stress jump occurs at prepeak and postpeak points for intact sandstone specimens; however, the flaw-contained sandstone specimens exhibit distinct stress jump during the entire loading process. Meanwhile, the strength parameters of the the rock specimen is obviously weakened by the preexisting fissures, and the uniaxial compression strength of rock specimens generally decreases with the increase in the number of preexisting fissure as well as the peak strain and the elastic modulus. The failure modes of intact and flaw-contained sandstone specimens exhibit the splitting failure and the mixed failure modes of shear and tension, respectively. Similarly, the maximum AE counts and AE energy both decrease with the increasing number of preexisting flaw. The present research can enhance the understanding of mechanical properties, cracking behaviors, and failure mechanism of jointed rock mass.


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