Mechanical Modeling of Material Behavior - Continuum Mechanics of Anisotropic Materials - page 22

increased to F and held at that value until t ¼ T when it is decreased to

0 again and held at 0 thereafter.

1.8.9. In Example 1.8.1 a calculation was presented that mathematically equated the
permeability element and the dashpot element. However, the two elements do
not appear to be the same. How do they differ? How are they similar?

1.9 The Limits of Reductionism and Determinism

A basic method of approach in science and engineering is reductionism. The
philosophy of this approach is to decompose the object of study into its constituent
parts, analyze each part separately, then reconstruct the object and predict its
response to stimuli from a knowledge of response of the constituent parts to stimuli.
Mathematically, such a prediction of the response of the object from the superposi-
tion of the response of its constituent parts generally implies a linear model.
An example is the stress analysis of a large bridge that is accomplished by
decomposing the bridge into bars, beams, girders, and cables and analyzing the
structural capacity of each of these constituents individually. Since reductionism is
the philosophy followed in this topic, it is appropriate to mention some general and
some specific caveats. The prime caveat is that the mathematical model of the
system may be non-linear and that superposition of different responses from
different stimuli is not a valid assumption.
Determinism is the philosophical proposition that every event, including human
cognition and behavior, decision and action, is causally determined by prior
occurrences. In the more restricted domain of mechanics, determinism is the idea
that future mechanical events are predetermined by previous events. The philosophi-
cal concept of determinism is embedded in the representation of the motion of an
object employed in mechanics and described in the following chapter. As the concept
of determinism is employed in classical mechanics, it is the view of the determinism
of the eighteenth century. The quote of the Marquis Pierre-Simon de Laplace
(1759-1827) at the beginning of the next chapter captures the nineteenth century
idea of determinism. In the nineteenth century the eighteenth century idea was
modified by the Heisenberg uncertainty principle, the realization that certain pairs
of physical properties, like position and momentum, cannot both be known to
arbitrary precision. The greater the precision in measuring one variable limits
or compromises the ability to measure the other. The idea of the uncertainty principle
is also applied to the situation in which the measurement of a variable in an experi-
mental situation distorts the experimental situation. Laplace's concept of determin-
ism was also eroded in the twentieth century by the discovery of extreme sensitivity
to starting or initial conditions for differential equations known as “chaos.”
The quote of the Marquis Pierre-Simon de Laplace (1759-1827) at the beginning
of the next chapter captures the idea of determinism underlying the representation
(2.2). All the material in this topic is based on the idealistic deterministic extreme