Disclaimer
The Catalogue of Computational Material Models is NEITHER a textbook NOR a
monograph, however, it is a Catalogue in its true encyclopaedic sense.
After starting out with elasticity as a reference that the reader is expected to be
familiar with, it outlines the theoretical formulation and algorithmic treatment of 15
different basic variants (5 Â each of visco-elasticity, plasticity, visco-plasticity,
respectively) of paradigmatic material models. The presentation for each of these
basic material models is a stand-alone account and intentionally follows exactly the
same structure.
Thereby, the central idea is that the reader can separately consult the Catalogue
for any of the computational material models and find a self-contained exposition
of the corresponding theoretical formulation and algorithmic treatment without the
need to cross-refer to other basic material models.
Nevertheless, this concept also allows easy comparison of the theoretical formulation and resulting algorithmic treatment for different basic material models
and, thereby, to uncover in detail similarities and differences.
It is, of course, obvious that one-dimensional material models are not immediately suited for real world analyses without extension to 3D. Yet, however, we are
firmly convinced that basic material models in a one-dimensional, geometrically
linear setting are indeed of utmost relevance and value, since they already highlight
the main characteristics and differences of paradigmatic material behaviour without
requiring mastering the intricacies of tensor calculus in multiple dimensions.
To facilitate comparison, the Catalogue analyses the response of each basic
material model for identical histories of prescribed strain and stress. This seemingly
repetitious approach allows clearly showcasing and contrasting the characteristics
of various modelling options.
Finally, it is clear that it is often necessary to adopt geometrically nonlinear
material models, e.g. when modelling metal forming or soft matter response.
However, the kinematical intricacies of a geometrically nonlinear approach, which
vii
The Catalogue of Computational Material Models is NEITHER a textbook NOR a
monograph, however, it is a Catalogue in its true encyclopaedic sense.
After starting out with elasticity as a reference that the reader is expected to be
familiar with, it outlines the theoretical formulation and algorithmic treatment of 15
different basic variants (5 Â each of visco-elasticity, plasticity, visco-plasticity,
respectively) of paradigmatic material models. The presentation for each of these
basic material models is a stand-alone account and intentionally follows exactly the
same structure.
Thereby, the central idea is that the reader can separately consult the Catalogue
for any of the computational material models and find a self-contained exposition
of the corresponding theoretical formulation and algorithmic treatment without the
need to cross-refer to other basic material models.
Nevertheless, this concept also allows easy comparison of the theoretical formulation and resulting algorithmic treatment for different basic material models
and, thereby, to uncover in detail similarities and differences.
It is, of course, obvious that one-dimensional material models are not immediately suited for real world analyses without extension to 3D. Yet, however, we are
firmly convinced that basic material models in a one-dimensional, geometrically
linear setting are indeed of utmost relevance and value, since they already highlight
the main characteristics and differences of paradigmatic material behaviour without
requiring mastering the intricacies of tensor calculus in multiple dimensions.
To facilitate comparison, the Catalogue analyses the response of each basic
material model for identical histories of prescribed strain and stress. This seemingly
repetitious approach allows clearly showcasing and contrasting the characteristics
of various modelling options.
Finally, it is clear that it is often necessary to adopt geometrically nonlinear
material models, e.g. when modelling metal forming or soft matter response.
However, the kinematical intricacies of a geometrically nonlinear approach, which
vii