Multiple Contact and Axisymmetric Inflation of Hyperelastic Cylindrical Membranes

1993 ◽  
Vol 207 (3) ◽  
pp. 175-183 ◽  
Author(s):  
R E Khayat ◽  
A Derdouri ◽  
A Garcia-Rejon
Keyword(s):  
Constitutive Model ◽  
Boundary Conditions ◽  
Contact Problems ◽  
Radius Ratio ◽  
Elastic Membrane ◽  
Solid Boundary ◽  
Dimensionless Parameters ◽  
Cylinder Length ◽  
Tangency Condition ◽  
Inflation Parameter

The confined axisymmetric inflation of a hyperelastic isotropic and homogeneous cylindrical membrane, with ends fixed, is examined in this study. The material is assumed to obey the Mooney-Rivlin constitutive model. The radius and thickness distributions of the undeformed cylinder are non-uniform. The problem is formulated to account for single- and multiple contact. At a point of contact, in contrast to most existing formulations on contact problems, the tangency condition between elastic membrane and solid boundary is respected. This translates into compatibility relations which are derived in the form of boundary conditions. Contact is also assumed to be slipless. There are three dimensionless parameters in the problem: (a) the initial cylinder length-radius ratio S, (b) the ratio m = C2 C1 of the Mooney constants and (c) an inflation parameter Rp. The influence of S and m is closely examined in the context of free inflation. Numerical illustrations are given for single- and double-contact problems.

Mimetic finite-difference coupled-domain solver for anisotropic media

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. T45-T59
Author(s):  
Harpreet Sethi ◽  
Jeffrey Shragge ◽  
Ilya Tsvankin
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Model Building ◽  
Fluid Layer ◽  
Anisotropic Media ◽  
Horizontal Displacement ◽  
Solid Boundary ◽  
Ocean Bottom ◽  
Solid Interface ◽  
And Inversion

Accurately modeling full-wavefield solutions at and near the seafloor is challenging for conventional single-domain elastic finite-difference (FD) methods. Because they treat the fluid layer as a solid with zero shear-wave velocity, the energy partitioning for body and surface waves at the seafloor is distorted. This results in incorrect fluid/solid boundary conditions, which has significant implications for imaging and inversion applications that use amplitude information for model building. To address these issues, here we use mimetic FD (MFD) operators to develop and test a numerical approach for accurately implementing the boundary conditions at a fluid/solid interface. Instead of employing a single “global” model domain, we partition the full grid into two subdomains that represent the acoustic and elastic (possibly anisotropic) media. A novel split-node approach based on one-sided MFD operators is introduced to distribute grid points at the fluid/solid interface and satisfy the wave equation and the boundary conditions. Numerical examples demonstrate that such MFD operators achieve stable implementation of the boundary conditions with the same (fourth) order of spatial accuracy as that inside the split-domain interiors. We compare the wavefields produced by the MFD scheme with those from a more computationally expensive spectral-element method to validate our algorithm. The modeling results help analyze the events associated with the fluid/solid (seafloor) interface and provide valuable insights into the horizontal displacement or velocity components (e.g., recorded in ocean-bottom-node data sets). The developed MFD approach can be efficiently used in elastic anisotropic imaging and inversion applications involving ocean-bottom seismic data.

scholarly journals Domain decomposition algorithms for problems of thermomechanical contact between several elastic bodies

2017 ◽  
pp. 63-82 ◽  
Author(s):  
Ihor Prokopyshyn
Keyword(s):  
Boundary Conditions ◽  
Domain Decomposition ◽  
Program Implementation ◽  
Heat Conduction Problem ◽  
Thermal Contact ◽  
Contact Problems ◽  
Decomposition Algorithms ◽  
Weak Formulation ◽  
Variational Equations ◽  
Thermoelastic Contact

We consider a thermoelastic multibody contact problem for finite bodies with unilateral mechanical and imperfect thermal contact conditions. Using a penalty method, we obtain a weak formulation of this problem in the form of a system of linear and nonlinear variational equations in Hilbert space. To solve this variational system, we propose a class of iterative Robin type domain decomposition algorithms. In each iterative step of these algorithms one have to solve two linear variational equations for each of the bodies, which correspond to heat conduction problem with Newton boundary conditions on the possible contact areas and linear elasticity problem with additional volume forces and Robin boundary conditions respectively. The program implementation of proposed algorithms is made for plane thermoelastic contact problems with the use of linear and quadratic finite element approximations on triangles. The numerical analysis is performed for one-body and two-body thermoelastic contact problems.

scholarly journals NUMERICAL MODELING OF NON-COHESIVE CONTACT IN MULTI-BODY HYDRODYNAMIC SYSTEMS WITH SPH

2017 ◽  
pp. 49
Author(s):  
Mohammad Javad Mohajeri ◽  
Mehdi Shafieefar ◽  
Soheil Radfar
Keyword(s):  
Boundary Conditions ◽  
Contact Model ◽  
Solid Boundary ◽  
Sph Method ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Irregular Case ◽  
Multi Body ◽  
Solid Bodies ◽  
Hydrodynamic Systems

Enforcing solid boundary conditions is one of the most challenging parts of the Smoothed Particle Hydrodynamics (SPH) method and many different approaches have been recently developed. Better understanding of interaction forces between solid bodies is of great importance in the investigation of structural stability and armor layer displacement in breakwaters. In this study, performance of repulsive force and dynamic boundary conditions have been investigated and showed that non-physical results are presented in non-cohesive contact. In this paper, a non-cohesive contact model in multi-body hydrodynamic systems has been developed and validated against other common boundary conditions. Using the developed contact model, the effect of regular and irregular placement of cubic concrete armors has been investigated. Also, comparison has been made with Van Buchem (2009) experimental results and concluded that in the irregular case it is more possible that a unit moves toward instability.

scholarly journals Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

2021 ◽  
Vol 928 ◽  
Author(s):  
Martin Lellep ◽  
Moritz Linkmann ◽  
Bruno Eckhardt ◽  
Alexander Morozov
Keyword(s):  
Boundary Condition ◽  
Stability Analysis ◽  
Constitutive Model ◽  
Spatial Structure ◽  
Boundary Conditions ◽  
Shear Flows ◽  
Body Force ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Parallel Shear Flows

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

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