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Lecture

Biomechanics: Tissue Characterisation through Constitutive Laws

In course

ME-482: Biomechanics of the musculoskeletal system

The basis for a mechanical description of the musculoskeletal system are presented. This description is based on the concepts of solid mechanics, physiology and anatomy of the musculoskeletal system. Concrete examples of the development of implants are als ...

Description

This lecture covers the importance of characterising tissues in biomechanics through constitutive laws, focusing on linear and non-linear laws, tissue characterisation, and matrix notation of Hooke's law. It also discusses the relationship between stress and strain, Voigt notation, and the isotropic stiffness tensor. The instructor explains the tensorial formulation for linear elastic isotropic material and the relation between different isotropic elastic linear parameters. Furthermore, the lecture delves into material symmetries of various tissues, including orthotropic, transverse isotropic, and isotropic materials, highlighting the significance of constitutive laws in biomechanics.

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Instructor

Dominique Pioletti

Dominique Pioletti received his Master in Physics from the Swiss Federal Institute of Technology Lausanne (EPFL) in 1992. He pursued his education in the same Institution and obtained his PhD in biomechanics in 1997. He developed original constitutive laws taking into account viscoelasticity in large deformations. Then he spent two years at UCSD as post-doc fellow acquiring know-how in cell and molecular biology. He was interested in particular to gene expression of bone cells in contact to orthopedic implant. In April 2006, Dominique Pioletti was appointed Assistant Professor tenure-track at the EPFL and is director of the Laboratory of Biomechanical Orthopedics. His research topics include biomechanics and tissue engineering of musculo-skeletal tissues; mechano-transduction in bone; development of orthopedic implant as drug delivery system. Since 2013, he has been promoted to the rank of Associate Professor.

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

Linear elasticity

Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.

Hooke's law

In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F_s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram.

Elasticity tensor

The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness tensor. Common symbols include and . The defining equation can be written as where and are the components of the Cauchy stress tensor and infinitesimal strain tensor, and are the components of the elasticity tensor. Summation over repeated indices is implied. This relationship can be interpreted as a generalization of Hooke's law to a 3D continuum.

Orthotropic material

In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational symmetry. These directional differences in strength can be quantified with Hankinson's equation. They are a subset of anisotropic materials, because their properties change when measured from different directions. A familiar example of an orthotropic material is wood.

Elasticity (physics)

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.

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Mechanics of Continuous Media

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Elasticity and Deformation

Covers stress, strain, modulus of elasticity, and material behavior under different loads.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

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