Cell and Tissue Mechanics

2004 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Mechanical Properties ◽  
Tissue Mechanics ◽  
Elastic Materials ◽  
Robert Hooke ◽  
Hooke’S Law ◽  
Original Shape ◽  
Hooke's Law ◽  
Natural Counterpart ◽  
Tensile Elastic Modulus ◽  
And Function

Mechanics is the branch of physics that is concerned with the action of forces on matter. Tissue engineers can encounter mechanics in various settings. Often, the mechanical properties of replacement biological materials must replicate the normal tissue: for example, there is limited use for a tissue-engineered bone that cannot support the load encountered by its natural counterpart. In addition, the mechanical properties of cells and cell–cell adhesions can determine the architecture of a tissue during development. This phenomenon can sometimes be exploited, since the final form of engineered tissues depends on the forces encountered during assembly and maturation. Finally, the mechanics of individual cells—and the molecular interactions that restrain cells—are important determinants of cell growth, movement, and function within an organism. This chapter introduces the basic elements of mechanics applied to biological systems. Some examples of biomechanical principles that appear to be important for tissue engineering are also provided. For further reading, comprehensive treatments of various aspects of biomechanics are also available. Consider an elongated object—for example, a segment of a biological tissue or a synthetic biomaterial—that is fixed at one end and suddenly exposed to a constant applied load. The material will change or deform in response to the load. For some materials, the deformation is instantaneous and, under conditions of low loading, deformation varies linearly with the magnitude of the applied force: . . . σ[≡F/A]= Eε (5-1) . . . where σ is the applied stress and ε is the resulting strain. This relationship is called Hooke’s law, after the British physicist Robert Hooke, and it describes the behavior of many elastic materials, such as springs, which deform linearly upon loading and recover their original shape upon removal of the load. The Young’s modulus or tensile elastic modulus, E, is a property of the material; some typical values are provided in Table 5.1. Not all elastic materials obey Hooke’s law (for example, rubber does not); some materials will recover their original shape, but strain is not linearly related to stress. Fortunately, many interesting materials do follow Equation 5-1, particularly if the deformations are small.

scholarly journals Robert Hooke, F. R. S. (1635-1703)

1960 ◽  
Vol 15 (1) ◽  
pp. 137-145 ◽  
Keyword(s):  
History Of Science ◽  
Royal Society ◽  
Robert Hooke ◽  
Hooke’S Law ◽  
Hooke's Law ◽  
History Of ◽  
New Instruments

The period which saw the foundation of the Royal Society is rich in names remarkable for original achievement in the field of science, but, if we except Newton—and his first paper appeared eleven years after the foundation of the Society which is now being celebrated—none is more noteworthy than Robert Hooke. Without any advantages of birth or influence, poor in health and poor, as a young man, in worldly goods, he carried out work of the first importance in most branches of science then known, and of one branch, meteorology, he may claim to be the founder. Not only was he outstanding as an experimenter and as the inventor of new instruments, but he had an informed imagination which led him to astonishingly correct anticipations of many advances subsequently to be made. Although to many his name is known only through Hooke’s Law, outstanding figures in the history of science have been loud in his praises. Thomas Young wrote of the ‘inexhaustible but neglected mines of nascent inventions, the works of the great Robert Hooke’, a most apt phrase, since Hooke’s work contains so much that is suggestive and original, which his restless spirit lacked time to develop.

Gel Structure. VI. Preparation of Gels and Globular Structures from Rubbers by Vulcanization of Solutions

1956 ◽  
Vol 29 (1) ◽  
pp. 296-301
Author(s):  
P. I. Zubov ◽  
Z. N. Zhurkina ◽  
V. A. Kargin
Keyword(s):  
Mechanical Properties ◽  
Natural Rubber ◽  
Gel Structure ◽  
Hooke’S Law ◽  
Sulfur Monochloride ◽  
Synthetic Rubber ◽  
Wide Range ◽  
Polybutadiene Rubber ◽  
Hooke's Law

Abstract 1. The mechanical properties of gels prepared from solutions of natural rubber and synthetic rubber were studied. 2. It was established that gels of synthetic rubber (polybutadiene rubber) have a wide range of relaxation periods. Gels of natural rubber (smoked sheet) behave like ideally elastic substances, following Hooke's law in the change of rate of deformation by 1000 times. 3. The viscosity of solutions of natural rubber and of polybutiadiene rubber in the presence of sulfur monochloride was studied. 4. We observed that sulfur monochloride sharply decreases the viscosity of natural rubber solutions and has almost no influence on the viscosity of synthetic rubber solutions.

Hooke’s Law

2020 ◽  
pp. 207-225
Author(s):  
Brian Cantor
Keyword(s):  
Civil Wars ◽  
Royal Society ◽  
Three Dimensional ◽  
Robert Hooke ◽  
Robert Boyle ◽  
Hooke’S Law ◽  
Charles I ◽  
King Charles I ◽  
Hooke's Law ◽  
Set Up

When a material is stretched, the extension is proportional to the stretching force, with the elastic modulus defined as the constant of proportionality. This is called Hooke’s law and was discovered by Robert Hooke, just after the end of the English civil wars in the mid-17th century. This chapter examines the underlying atomic forces responsible for Hooke’s law, the use of tensors to describe three-dimensional stresses and strains in a material, and the relationships between the different elastic moduli under different loading conditions. Hooke was the son of a clergyman, born and brought up on the Isle of Wight, a royalist stronghold, where King Charles I fled after his imprisonment by Parliament, only to be recaptured and executed. Hooke was smuggled to London and then Oxford under the protection of Royalist academics, where he became a member of the group of intellectuals who, after the restoration of the monarchy, led the Enlightenment and set up the Royal Society. He took on many jobs: Lab Assistant to Robert Boyle, Curator at the Royal Society, Professor of Geometry at Gresham’s College, City Surveyor for the rebuilding of London after the Great Fire, and First Officer in Christopher Wren’s architectural firm. He was paranoid about his need for money and about people stealing his scientific ideas. He feuded with many of the great scientists of his age, claiming that he invented their ideas first, notably with Newton about his theories of gravity.

Mechanical properties of the living dog aorta

1962 ◽  
Vol 202 (4) ◽  
pp. 619-621 ◽  
Author(s):  
Robert L. Evans ◽  
Eugene F. Bernstein ◽  
Evelyn Johnson ◽  
Carl Reller
Keyword(s):  
Mechanical Properties ◽  
Cross Section ◽  
Cross Sections ◽  
Hooke’S Law ◽  
Before And After ◽  
Hooke's Law ◽  
Pressure Changes ◽  
Relationship Of ◽  
The Relationship ◽  
Propagation Velocities

The variation of living dog aortic cross sections with volemic pressure changes is given for states before and after thoracotomy. The relationship of vessel cross section to pressure is approximately linear, does not follow Hooke's law, and is roughly the same for both dynamic and relatively static changes. The implied and directly measured propagation velocities are comparable to each other.

Rock Failure Under Dynamic Loading Conditions

1963 ◽  
Vol 3 (01) ◽  
pp. 1-8 ◽  
Author(s):  
N.T. Burdine
Keyword(s):  
The State ◽  
Cumulative Damage ◽  
Material Behavior ◽  
Particle Orientation ◽  
Loading Conditions ◽  
Hooke’S Law ◽  
Rock Samples ◽  
Cyclic Stresses ◽  
Hooke's Law ◽  
Failure Theories

BURDINE, N.T., SOCONY MOBIL OIL CO., INC., DALLAS, TEX Abstract The present investigation is concerned with the cumulative damage to rock samples when exposed to cyclic stresses under various loading conditions. Information on the response of rocks to repetitive deformational forces is an essential prerequisite to an understanding of the fundamentals of drilling. Using a laboratory designed and constructed dynamic-stress apparatus, preliminary data were obtained on cylindrical rock samples. The experiments consist of measuring the number of cycles to failure for a given axial load ( static plus dynamic). Data were obtained for various confining and pore pressures, pore fluids (air and water), frequencies of stress application and loading procedures. The results are related to failure theories and dynamic fatigue properties of other materials. Introduction In most conventional and new drilling processes, repetitive forces are applied to the bottom of the borehole. Furthermore, in hard-rock drilling the number of applications of the forces to a particular section of rock may become excessively large. The present investigation is concerned with the cumulative damage to rocks when exposed to cyclic stresses under various loading conditions. It is believed that the experiments will lead to a better understanding of the mechanical response of rocks to particular deformational forces and to a more efficient drillingprocedure.Thepresent investigation is the initial part of a general study of the behavior of inelastic materials under static and dynamic conditions, including both theoretical and experimental studies. SURVEY OF FAILURE THEORIES OF MATERIALS Few, even phenomenological, theories on rock deformation have been established because the state of knowledge of flow, fracture and strength of rocks is largely empirical. Most of the theories that do exist were originally formulated for other materials. HOOKE'S LAW The state of stress in continuous media is completely determined by the stress tensor and the state of deformation by the strain tensor . In the linear theory of elasticity the generalized Hooke's law is ..........................(1) where the coefficients are the components of the elasticity tensor. For homogeneous and isotropic conditions the number of independent coefficients reduce to two, and Eq. 1 becomes ..................(2) in which and are Lame's constants; is the kronecker delta; and is the dilation. This simplified version of Hooke's law has been used quite extensively in geophysical research where most of the information about the mechanical properties of the earth have been obtained. However, it has only limited application in rock fatigue studies. MATERIAL BEHAVIOR Many solids obey Hooke's law at small stresses, but for higher stresses a hysteretic effect occurs due to temporary or permanent residual deformation of the solid (inelastic deformation). Such deviations in mechanical behavior exist in varying degrees in different classes of materials. Most elastic materials have a microscopic heterogeneity due either to random distribution of anisotropic particles, or due to some preferred particle orientation, or both. Other materials are quite grossly heterogeneous. And the method of formation, particularly in rocks, oftentimes creates residual stress concentrations which have complicated states of imperfect equilibrium. Also, the thermal effects resulting from structural behavior give rise to nonuniform temperature distributions and the degradation of mechanical energy. When such bodies are exposed to certain large loading conditions, the inelastic behavior is intensified so strongly that the deformation, normally brittle, becomes ductile. SPEJ P. 1^

The Theoretical Treatment of Hooke's Law

1939 ◽  
Vol 7 (2) ◽  
pp. 134-134
Author(s):  
Zigmond Wilchinsky
Keyword(s):  
Theoretical Treatment ◽  
Hooke’S Law ◽  
Hooke's Law

scholarly journals Quantum Hooke's Law to Classify Pulse Laser Induced Ultrafast Melting

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Hao Hu ◽  
Hepeng Ding ◽  
Feng Liu
Keyword(s):  
Pulse Laser ◽  
Hooke’S Law ◽  
Hooke's Law
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