FETI-DP for Elasticity with Almost Incompressible Material Components

2013 ◽  
pp. 353-360
Author(s):  
Sabrina Gippert ◽  
Axel Klawonn ◽  
Oliver Rheinbach
Keyword(s):  
Incompressible Material

scholarly journals Bias Truck Tire Deformation Analysis with Finite Element Modeling

2020 ◽  
Vol 10 (12) ◽  
pp. 4326
Author(s):  
Józef Pelc
Keyword(s):  
Incompressible Material ◽  
Axisymmetric Deformation ◽  
Thermal Shrinkage ◽  
Deformation Analysis ◽  
Truck Tire ◽  
Non Linear ◽  
Strain Relationship ◽  
Tire Modeling ◽  
Total Lagrangian Formulation

This paper presents a method for modeling of pneumatic bias tire axisymmetric deformation. A previously developed model of all-steel radial tire was expanded to include the non-linear stress–strain relationship for textile cord and its thermal shrinkage. Variable cord density and cord angle in the cord-rubber bias tire composite are the major challenges in pneumatic tire modeling. The variabilities result from the tire formation process, and they were taken into account in the model. Mechanical properties of the composite were described using a technique of orthotropic reinforcement overlaying onto isotropic rubber elements, treated as a hyperelastic incompressible material. Due to large displacements, the non-linear problem was solved using total Lagrangian formulation. The model uses MSC.Marc code with implemented user subroutines, allowing for the description of the tire specific properties. The efficiency of the model was verified in the simulation of mounting and inflation of an actual bias truck tire. The shrinkage negligence effect on cord forces and on displacements was examined. A method of investigating the influence of variation of cord angle in green body plies on tire apparent lateral stiffness was proposed. The created model is stabile, ensuring convergent solutions even with large deformations. Inflated tire sizes predicted by the model are consistent with the actual tire sizes. The distinguishing feature of the developed model from other ones is the exact determination of the cord angles in a vulcanized tire and the possibility of simulation with the tire mounting on the rim and with cord thermal shrinkage taken into account. The model may be an effective tool in bias tire design.

scholarly journals A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

2021 ◽  
Author(s):  
Chennakesava Kadapa
Keyword(s):  
Wave Propagation ◽  
Wave Speed ◽  
Critical Time ◽  
Incompressible Material ◽  
Implicit Scheme ◽  
Bulk Wave ◽  
Lumped Mass ◽  
Time Step ◽  
Material Models ◽  
Shear Wave Speed

AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

Wrinkling of a Fiber-Reinforced Membrane

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
E. Shmoylova ◽  
A. Dorfmann
Keyword(s):  
Boundary Conditions ◽  
Energy Function ◽  
Mechanical Response ◽  
Transverse Isotropy ◽  
Base Material ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Incompressible Material ◽  
Fiber Reinforced ◽  
Relaxed Energy

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

A Stabilized B-Splines FEM Formulation for the Solution of an Inverse Elasticity Problem Arising in Medical Imaging

2008 ◽  
Author(s):  
Carlos E. Rivas ◽  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Mechanical Properties ◽  
Diagnostic Value ◽  
Incompressible Material ◽  
High Order ◽  
Elasticity Problem ◽  
Parameter Distribution ◽  
Order Continuity ◽  
B Splines ◽  
Inverse Elasticity ◽  
Continuous Problem

Soft tissue pathologies are often associated with changes in mechanical properties. For example, breast and other tumors usually present as stiff lumps. Imaging the spatial distribution of the mechanical properties of tissues thus reveals information of diagnostic value. Doing so, however, typically requires the solution of an inverse elasticity problem. In this work we consider the inverse elasticity problem for an incompressible material in plane stress, formulated and solved as a constrained optimization problem. We formulate this inverse problem enforcing high order continuity for our variables. Driven by the requirements for the strong and weak solutions to this problem, we assume that our data field (i.e. the measured displacement) is in H2 and our parameter distribution (i.e. the sought shear modulus distribution) is in H1. This high order regularity requirement for the data is incompatible with standard FEM. We solve this problem using a FEM formulation that is novel in two respects. First, we employ quadratic b-splines that enforce C1 continuity in our displacement field, consistent with the variational requirements of the continuous problem. Second, we include Galerkin-least-squares (GLS) stabilization in the iterative optimization formulation. GLS adds consistent stability to the discrete formulation that otherwise violates an ellipticity condition that is satisfied by the continuous problem. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement.

scholarly journals Thermo elastic-plastic transition in a thin rotating disc with inclusion

2007 ◽  
Vol 11 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Kumar Gupta ◽  
P Pankaj
Keyword(s):  
Thermal Effect ◽  
Internal Surface ◽  
Angular Speed ◽  
Incompressible Material ◽  
Plastic State ◽  
Percentage Increase ◽  
Compressible Material ◽  
Rotating Disc ◽  
Elastic Plastic ◽  
Different Temperatures

Stresses for the elastic-plastic transition and fully plastic state have been derived for a thin rotating disc with shaft at different temperatures and results have been discussed and depicted graphically. It has been observed that the rotating disc with inclusion and made of compressible material requires lesser angular speed to yield at the internal surface and higher percentage increase in angular speed to become fully plastic as compare to disc made of incompressible material. With the introduction of thermal effect the rotating disc with inclusion required lesser angular speed to yield at the internal surface. Rotating disc made of compressible material with inclusion requires higher percentage increase in angular speed to become fully-plastic as compare to disc made of incompressible material. Thermal effect also increases the values of radial and circumferential stresses at the internal surface for fully-plastic state. .

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

Hyperelastic Muscle Simulation

2007 ◽  
Vol 345-346 ◽  
pp. 1241-1244 ◽  
Author(s):  
Mohd. Zahid Ansari ◽  
Sang Kyo Lee ◽  
Chong Du Cho
Keyword(s):  
Skeletal Muscle ◽  
Silicone Rubber ◽  
Soft Tissues ◽  
Material Model ◽  
Incompressible Material ◽  
Material Behavior ◽  
Rubber Tube ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Behavior

Biological soft tissues like muscles and cartilages are anisotropic, inhomogeneous, and nearly incompressible. The incompressible material behavior may lead to some difficulties in numerical simulation, such as volumetric locking and solution divergence. Mixed u-P formulations can be used to overcome incompressible material problems. The hyperelastic materials can be used to describe the biological skeletal muscle behavior. In this study, experiments are conducted to obtain the stress-strain behavior of a solid silicone rubber tube. It is used to emulate the skeletal muscle tensile behavior. The stress-strain behavior of silicone is compared with that of muscles. A commercial finite element analysis package ABAQUS is used to simulate the stress-strain behavior of silicone rubber. Results show that mixed u-P formulations with hyperelastic material model can be used to successfully simulate the muscle material behavior. Such an analysis can be used to simulate and analyze other soft tissues that show similar behavior.

scholarly journals Application of P1-Nonconforming Element for Shell Structure of Incompressible Materiel

2011 ◽  
Vol 2-3 ◽  
pp. 1051-1056
Author(s):  
Lei Chen ◽  
Gang Won Jang ◽  
Tae Jin Chung ◽  
Tae Hyun Baek
Keyword(s):  
Topology Optimization ◽  
Shell Structure ◽  
Optimization Design ◽  
Incompressible Material ◽  
High Order ◽  
Solid Shell ◽  
Shell Elements ◽  
Volumetric Locking ◽  
Nonconforming Element ◽  
Nonconforming Elements

This research focused on solving volumetric locking problem of shell structure of incompressible material. Degenerated solid-shell elements are widely applied on curved structure. But, volumetric locking will take place when the structure is made of incompressible material, such as rubber. Due to Poisson’s locking free property of P1-nonconforming element, it is employed to solve volumetric locking problem of shell structure. Furthermore, the study on shell structure is extended to topology optimization design. To verify the volumetric locking free of P1-nonconforming element on shell structure of incompressible material, some structures are studied by different elements. Comparing with the utilization of high order elements to solve volumetric locking problems, P1-nonconforming elements can save calculation time and reduce the numerical cost.

scholarly journals Conditions of equivalence of effects for the solid body from incompressible material

2018 ◽  
Vol 196 ◽  
pp. 01031 ◽  
Author(s):  
Elephan Agakhanov ◽  
Murad Agakhanov ◽  
Lyudmila Sultanova ◽  
Zabiya Hizriyeva
Keyword(s):  
Solid Body ◽  
Design Research ◽  
Rotating Disk ◽  
Experimental Methods ◽  
Incompressible Material ◽  
Engineering Practice ◽  
General View ◽  
Deformable Solid ◽  
Special Cases ◽  
Deformable Solid Body

Polemicizing with the existing opinion that modern numerical methods allow to solve practically any problem of mechanics, it should be noted that analytical and experimental methods still are relevant, and a complex of methods leads to development of mechanics of a deformable solid body. At present one of the most important directions of development of mechanics of a deformable solid body is creation of the approaches that allow to combine organically great computing opportunities of modern supercomputers with experimental methods of the material and design research. In engineering practice at production of designs and products incompressible materials are widely used. Assessment of their durability requires detailed studying of deflected mode caused by action of various loadings and forces. For a solid body from incompressible material, using the resolving equations set of mechanics of a deformable solid body, at action of the compelled deformations of a general view, volume and superficial forces conditions of equivalence are established. It is shown that the known solutions are special cases of the established equivalence conditions. The efficiency of the analytical solution of a three-dimensional task on the rotating disk from incompressible material is shown by the method of equivalence of effects.

Sign in / Sign up

Export Citation Format

Share Document