Basic Mechanical Theory

  • Hans Gregersen
Chapter

Abstract

Mechanics of a material deals with the behaviour of a solid body subjected to various types of loading. Mechanics is the study of motion of matter and the forces that cause such motion. It is applied to the analysis of any dynamical system ranging from atoms to solar systems. The analysis of stress, deformation and stability of thin-walled tubes is a classical subject of physics and engineering. Theories have been developed by Bernoulli, Cauchy, Euler, Flügge, Kirchhoff, Reissner, Timeshenko and many other famous scientists. All theories of thin-shell structures have the common objective to represent the three-dimensional structure by a two-dimensional surface. In the classical theory, this is accomplished through the Bernoulli-Kirchhoff hypothesis, which states that all points lying on a normal of the neutral surface before deformation do the same after deformation, that for all kinematical relations, the coordinate z of a point (distance from the neutral surface, positive outwards) is unaffected by the deformation of the shell, and for all considerations of the stress system, the stress σz may be ignored (Fung and Liu, 1995). The classical theories use four additional hypotheses: 1) that the material is homogenous, 2) that the stress-strain relationship is linear, 3) that the deformation is so small that the strain-displacement relationship is also linear, and 4) that the shell is stress-free when all the external loads are removed. In mechanics of structures like biological tissues, all four additional hypotheses needs relaxation but the Bernoulli-Kirchhoff hypothesis can be retained.

Keywords

Circumferential Stress Strain Energy Function Stretch Ratio Longitudinal Stress Tissue Strip 
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Copyright information

© Springer-Verlag London 2003

Authors and Affiliations

  • Hans Gregersen
    • 1
  1. 1.Centre for Sensory-Motor Interaction, Laboratory for Gastrointestinal Biomechanics and Sensory-Motor Funtion, Department of Surgical Gastroenterology, Aalborg HospitalAalborg UniversityDenmark

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