Biomedical Engineering Reference
In-Depth Information
3.2 Continuum Mechanics
3.2.1 Introduction
When any region of the human body comes into contact with a technical support
device (tSD) such as seating, bedding or shoe systems, the affected soft tissue
regions (adipose and muscle tissue of the gluteus, foot or leg etc.) are considerably
deformed due to contact loading. The term large or finite deformation is used in
mechanics and the quantification of such deformation and corresponding
mechanical stress becomes necessary. These processes may be considered and
described on the atomic level, the molecular or cell level or on the macroscopic
level. In the engineering-scientific approach, macroscopic modelling is preferred,
whereby a tissue region is considered as a large accumulation of single cells, and
thus is considered as a continua.
The existence of finite deformations is associated with non-linear material
behaviour of the biological structures. This makes non-linear continuum
mechanics an appropriate tool to describe such phenomena. The same approach
applies for the description of tSD materials (polymeric soft foams, rubberlike
materials etc.) which also exhibit finite deformation under loading.
Basic continuum mechanics connected with material parameter identification
needed for generation of human tissue modeling and tSD material characterization
is exemplified. The guidelines provide an overview of the theoretical aspects
classical textbooks and for thorough understanding of continuum mechanics for
instance Silber and Steinwender (2005), Holzapfel (2000), Mase (1970), Gurtin
(1981), Wriggers (2008), Ogden (1984), or Bowen (1989) may be used as
references.
The compact and coordinate-invariant notation is preferably used where scalars
are written in regular roman form (t, m, E etc.), vectors are written as italic bold
roman lower-case characters (u, b etc.) and tensors are written as italic bold roman
upper-case characters (F, C etc.). In addition to the compact representation of
mathematical formulae, matrix as well as Cartesian representation is used together
with the Einstein notation. The Einstein convention is as follows: a term of a tensor
expression that contains the repetition of an index denotes a summation with
respect to this index over its range.
3.2.2 Material Phenomenology
Characteristic material properties are illustrated in the form of stress-strain, stress-
time and strain-time diagrams. Some of these characteristics will be shown to be
relevant with respect to modeling and simulation aspects in subsequent chapters.
