scholarly journals Relative Lagrangian Formulation of Finite Thermoelasticity

2021 ◽  
Vol 22 (4) ◽  
pp. 609-628
Author(s):  
I-S. Liu ◽  
M. G. Teixeira ◽  
G. T. A. Pereira
Keyword(s):  
Present State ◽  
Relative Motion ◽  
Finite Deformation ◽  
Small Deformation ◽  
The Body ◽  
Numerical Result ◽  
Entropy Principle ◽  
Repeated Applications ◽  
Eulerian Descriptions ◽  
Small On Large

The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

scholarly journals Relative Lagrangian Formulation of Finite Thermoelasticity

2017 ◽  
Author(s):  
I-Shih Liu ◽  
Marcello G. Teixeira
Keyword(s):  
Present State ◽  
Relative Motion ◽  
The Body ◽  
Lagrangian Formulation ◽  
Basic System ◽  
Field Equations ◽  
Entropy Principle ◽  
Eulerian Descriptions ◽  
Solid Bodies ◽  
Small On Large

Besides the Lagrangian and the Eulerian descriptions, the motion of a body can also be expressed relative to the present configuration of the body, known as the relative motion description. It is interesting to consider such a relative motion description in general to formulate the basic system of field equations for solid bodies. In doing so, when the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system becomes linear. This will be done for thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Relative Lagrangian formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. Some applications of such a formulation in numerical simulations are briefly reviewed.

scholarly journals CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

2010 ◽  
Vol 52 (2) ◽  
pp. 160-178 ◽  
Author(s):  
A. MATEI ◽  
R. CIURCEA
Keyword(s):  
Lagrange Multipliers ◽  
Variational Equation ◽  
Small Deformation ◽  
Contact Problems ◽  
Point Theory ◽  
The Body ◽  
Elastic Materials ◽  
Weak Formulation ◽  
Nonlinearly Elastic ◽  
Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

XIV.—The Absorption of Light by Inorganic Salts. No. XI.: Conclusion

1914 ◽  
Vol 33 ◽  
pp. 156-165
Author(s):  
R. A. Houstoun
Keyword(s):  
Special Reference ◽  
Present State ◽  
Light Wave ◽  
Wave Length ◽  
The Body ◽  
Inorganic Salts ◽  
Short Account ◽  
Absorption Of Light ◽  
Dispersion Of Light

In this paper a short account will be given of the present state of the theory of the absorption of light, with special reference to the results gained in this series of investigations.Theories of the dispersion of light may be divided into two classes: (1) those in which the body is regarded as consisting of particles which vibrate under the influence of the light wave; and (2) those in which the body is regarded as consisting of obstacles which diffract the light wave. According to (2), light is scattered, not absorbed; a wave going through the body diminishes in intensity, but the energy lost is radiated out laterally without change of wave-length.

Butterflies of Australia

2000 ◽  
Author(s):  
Michael F Braby
Keyword(s):  
Present State ◽  
The Body ◽  
Food Plants ◽  
Immature Stages ◽  
Larval Food ◽  
Educational Publishing ◽  
Butterfly Fauna ◽  
History Of ◽  
Outstanding Work ◽  
Reference Section

This outstanding work is the ultimate guide for the identification of Australia’s butterflies. Nearly 400 species – all those currently recognised from Australia, plus those from surrounding islands – are represented, with all adults and some immature stages displayed in stunning colour sections. Introductory chapters cover the history of publications, classification, morphology, distribution, conservation and collection, together with a checklist of the butterfly fauna. The body of the text is arranged systematically, providing a wealth of information including description, variation, similar behaviour, distribution and habitat, and major literature references, giving a comprehensive summary of the present state of knowledge of these insects. Appendices provide details of those species recorded from Australian islands outside the Australian faunal subregion, those protected by legislation, the larval food plants, and the attendant ants. Extensive references, a glossary and an index of scientific and common names complete the work. Joint Winner of the 2001 Whitley Medal. Finalist Scholarly Reference section - The Australian Awards for Excellence in Educational Publishing 2001.

How to Carry Loads Economically: Analysis Based on a Predictive Biped Model

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Tong Li ◽  
Qingguo Li ◽  
Tao Liu ◽  
Jingang Yi
Keyword(s):  
Relative Motion ◽  
Energy Cost ◽  
Interaction Force ◽  
The Body ◽  
Additional Energy ◽  
Load Carrying ◽  
Walking Motion ◽  
Carrier Interaction ◽  
Heavy Loads ◽  
And Control

Abstract Carrying heavy loads costs additional energy during walking and leads to fatigue of the user. Conventionally, the load is fixed on the body. Some recent studies showed energy cost reduction when the relative motion of the load with respect to the body was allowed. However, the influences of the load's relative motion on the user are still not fully understood. We employed an optimization-based biped model, which can generate human-like walking motion to study the load–carrier interaction. The relative motion can be achieved by a passive mechanism (such as springs) or a powered mechanism (such as actuators), and the relative motion can occur in the vertical or fore-aft directions. The connection between the load and body is added to the biped model in four scenarios (two types × two directions). The optimization results indicate that the stiffness values affect energy cost differently and the same stiffness value in different directions may have opposite effects. Powered relative motion in either direction can potentially reduce energy cost but the vertical relative motion can achieve a higher reduction than fore-aft relative motion. Surprisingly, powered relative motion only performs marginally better than the passive conditions at similar peak interaction force levels. This work provides insights into developing more economical load-carrying methods and the model presented may be applied to the design and control of wearable load-carrying devices.

Parallel Algorithm for Modeling Constrained Multi-Flexible Body System Dynamics

2013 ◽  
Author(s):  
Rudranarayan Mukherjee ◽  
Jeremy Laflin
Keyword(s):  
Parallel Implementation ◽  
Equations Of Motion ◽  
Small Deformation ◽  
The Body ◽  
Deformation Field ◽  
Flexible Body ◽  
Disassembly Process ◽  
Joint Constraints ◽  
Kinematic Loop ◽  
Kinematic Joint

This paper presents an algorithm for modeling the dynamics of multi-flexible body systems in closed kinematic loop configurations where the component bodies are modeled using the large displacement small deformation formulation. The algorithm uses a hierarchic assembly disassembly process in parallel implementation and a recursive assembly disassembly process in serial implementation to achieve highly efficient simulation turn-around times. The operational inertias arising from the rigid body modes of motion at the joint locations on a component body are modified to account for the nonlinear inertial effects and body forces arising from the body based deformations. Traditional issues, such as motion induced stiffness and temporal invariance of deformation field related inertia terms, are robustly addressed in this algorithm. The algorithm uses a mixed set of coordinates viz. (i) absolute coordinates for expressing the equations of motion of a body fixed reference frame, (ii) relative or internal coordinates to express the kinematic joint constraints and (iii) body fixed coordinates to account for the body’s deformation field. The kinematic joint constraints and the closed loop constraints are treated alike through the formalism of relative coordinates, joint motion spaces and their orthogonal complements. Verification of the algorithm is demonstrated using the planar fourbar mechanism problem that has been traditionally used in literature.

Flowfield around a Body with Elastic Walls

2008 ◽  
Vol 33-37 ◽  
pp. 1083-1088
Author(s):  
Norio Arai ◽  
Kota Fujimura ◽  
Yoko Takakura
Keyword(s):  
Stokes Equation ◽  
Bluff Body ◽  
Incompressible Flows ◽  
Small Deformation ◽  
Uniform Flow ◽  
The Body ◽  
Body Motion ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Elastic Walls

When a bluff body is located in a uniform flow, the flow is separated and vortices are formed. Consequently, the vortices cause “flow-induced vibrations”. Especially, if the Strouhal number and the frequency of the body oscillation coincide with the natural frequency, the lock-in regime will occur and we could find the large damages on it. Therefore, it is profitable, in engineering problems, to clarify this phenomenon and to suppress the vibration, in which the effect of elastic walls on the suppression is focused. Then, the aims of this article are to clarify the oscillatory characteristics of the elastic body and the flowfield around the body by numerical simulations, in which a square pillar with elastic walls is set in a uniform flow. Two dimensional incompressible flows are solved by the continuity equation, Navier-Stokes equation and the Poisson equation which are derived by taking divergence of Navier-Stokes equation. Results show that a small deformation of elastic walls has a large influence on the body motion. In particular, the effect is very distinct at the back.

scholarly journals The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations

2021 ◽  
Vol 54 ◽  
Author(s):  
Kanognudge Wuttanachamsri ◽  
Nattapol Oangwatcharaparkan
Keyword(s):  
Immune System ◽  
Numerical Solutions ◽  
Time Derivative ◽  
The Body ◽  
Navier Stokes ◽  
Human Respiratory Tract ◽  
Brinkman Equations ◽  
Numerical Result ◽  
Human Lungs ◽  
Bottom Boundary Condition

In the human respiratory tract, air breathed in is often contaminated with strange particles such as dust and chemical spray, which may cause people respiratory diseases. However, the human body has an innate immune system that helps to trap the debris by secreting mucus to catch the foreign particles, which are removed from the body by the movement of tiny hairs lining on the surface of the epithelial cells in the immune system. The layer containing the tiny hairs or cilia is called Periciliary Layer (PCL). In this research, we find the velocity of the fluid in the PCL moved by a ciliary beating by using the Navier-Stokes-Brinkman equations. We apply the Galerkin finite element method to determine numerical solutions. For the steady linear case of the equation, the numerical result is in good agreement with an exact solution. Including the time derivative and nonlinear terms, we show that the velocity of the liquid is affected by the velocity of the solid, which follows the physical meaning of the fluid flow. The result can be applied as a bottom boundary condition of the mucous layer to be able to find the velocity of mucus in the human lungs.

Soft-Elastohydrodynamic Lubrication Line Contact Analysis on a Strip of Bio-Materials

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Qie-Da Chen ◽  
Wang-Long Li
Keyword(s):  
Relative Motion ◽  
Finite Deformation ◽  
Soft Tissues ◽  
Finite Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Transversely Isotropic ◽  
Von Mises Stress ◽  
Equivalent Model ◽  
Line Contact ◽  
Curvature Effects

Abstract The characteristics of anisotropic material, finite deformation, and lubrication in biological system diminish the friction and wear between soft tissues with relative motion. In this research, the lubrication between pleura surfaces in relative motion is analyzed by soft elastohydrodynamic lubrication (soft-EHL) line contact with an equivalent model. The model is a soft, transversely isotropic (TI) elastic strip with finite thickness sliding under a rigid sinusoidal surface, which is used to simulate the surface irregularities, with lubricant in between. The material nonlinearity and the curvature effects due to finite deformation, which are significant in soft-EHL, are considered in the present study. The pressure distribution, film thickness, von Mises stress, and material deformation are analyzed and discussed under various combinations of elastic moduli and Poisson's ratios for the transversely isotropic models. The simulation results reveal that the soft-EHL modeling fit actual result better than the traditional EHL (t-EHL) modeling. The Poisson's ratio νp = 0.1 and νpz = 0.49 situation will have more gentle stress distribution. The present soft-EHL solver can be used to realize some desired stress distributions and to identify the mechanical properties bio-materials under the aids of experiments.

scholarly journals Numerical Simulation of a Three-Dimensional Fish-like Body Swimming with Finlets

2012 ◽  
Vol 11 (4) ◽  
pp. 1323-1333 ◽  
Author(s):  
Shizhao Wang ◽  
Xing Zhang ◽  
Guowei He
Keyword(s):  
Three Dimensional ◽  
The Body ◽  
Hydrodynamic Performance ◽  
Rectangular Plates ◽  
Caudal Peduncle ◽  
Local Flow ◽  
Vortical Structures ◽  
Numerical Result ◽  
Simulation Based ◽  
3D Fish

AbstractThe swimming of a 3D fish-like body with finlets is numerically investigated at Re = 1000 (the Reynolds number is based on the uniform upstream flow and the length of the fish-like body). The finlets are simply modeled as thin rigid rectangular plates that undulate with the body. The wake structures and the flow around the caudal peduncle are studied. The finlets redirect the local flow across the caudal peduncle but the vortical structures in the wake are almost not affected by the finlets. Improvement of hydrodynamic performance has not been found in the simulation based on this simple model. The present numerical result is in agreement with that of the work of Nauen and Lauder [J. Exp. Biol., 204 (2001), pp. 2251-2263] and partially supports the hypothesis of Webb [Bull. Fish. Res. Bd. Can., 190 (1975), pp. 1-159].

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