Chapter 1
Introduction
What you have in your head, put down on paper. The head is a
fragile vessel.
— Dmitri Shostakovich, 1906–1975 —
1.1 Motivation
All materials respond in one way or other to external stimuli, e.g. mechanical, thermal, chemical, electro-magnetic (or other) loading. The material’s response may
typically be observed in terms of state variables—deformation, temperature, concentration and electro-magnetic potentials—and/or in terms of their spatial gradients—
strain, temperature gradient, concentration gradient, electric field and magnetic flux
-, together with the corresponding state functions—stress, heat and mass flux, electric
flux and magnetic field.
However, one should recall that from a philosophical point of view these observations already rely in some way on the underlying phenomenological concepts of the
above listed state variables and state functions (collectively forming the state quantities). Thus, even the most careful and sophisticated observations at smallest and
largest time and length scales are necessarily only phenomenological in nature. Any
model (including quantum and cosmological mechanics) based on necessarily phenomenological observations is consequently also only describing phenomena, since
true knowledge or understanding of the underlying nature is intrinsically unavailable
(recall also Plato’s cave allegory).
Of course, this is not at all a desperate state of affairs, mastering nature based on
a mere phenomenological understanding—to date ranging from the quantum to the
cosmological level—proves to be extremely powerful!
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
P. Steinmann and K. Runesson, The Catalogue of Computational Material Models,
https://doi.org/10.1007/978-3-030-63684-5_1
1
Introduction
What you have in your head, put down on paper. The head is a
fragile vessel.
— Dmitri Shostakovich, 1906–1975 —
1.1 Motivation
All materials respond in one way or other to external stimuli, e.g. mechanical, thermal, chemical, electro-magnetic (or other) loading. The material’s response may
typically be observed in terms of state variables—deformation, temperature, concentration and electro-magnetic potentials—and/or in terms of their spatial gradients—
strain, temperature gradient, concentration gradient, electric field and magnetic flux
-, together with the corresponding state functions—stress, heat and mass flux, electric
flux and magnetic field.
However, one should recall that from a philosophical point of view these observations already rely in some way on the underlying phenomenological concepts of the
above listed state variables and state functions (collectively forming the state quantities). Thus, even the most careful and sophisticated observations at smallest and
largest time and length scales are necessarily only phenomenological in nature. Any
model (including quantum and cosmological mechanics) based on necessarily phenomenological observations is consequently also only describing phenomena, since
true knowledge or understanding of the underlying nature is intrinsically unavailable
(recall also Plato’s cave allegory).
Of course, this is not at all a desperate state of affairs, mastering nature based on
a mere phenomenological understanding—to date ranging from the quantum to the
cosmological level—proves to be extremely powerful!
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
P. Steinmann and K. Runesson, The Catalogue of Computational Material Models,
https://doi.org/10.1007/978-3-030-63684-5_1
1