Chapter 30
Complex Strain of Soils
30.1 Real State of the Mechanics of Non-elastic Strains
An overview of plasticity theory and the state of the primary variants of its
development described in the previous two parts of the book makes us agree that
the theory of non-elastic solid body strain remains one of the primary problems
in modern mechanics. Today, we have many models, concepts, postulates, and
principles, the most significant of which were included in these two sections.
However, we should admit that there is still no theory that would be, in terms of
correspondence to experience, comparable with the Cauchy–Navier elasticity theory
or the theory of motion of viscous liquids of Navier–Stokes [4, 6].
As M. Ya. Leonov believes [6], such prolonged stagnation in the development
of mathematical plasticity theory is caused not only by an extreme complexity
of the problem but also by a tradition not to consider the physical mechanism of
the respective processes. Non-elastic strains result from structural changes in some
volumes, and in essence, they are defined by the discrete structure of solid bodies.
For this reason, when building determinant ratios recently, more attention has been
paid to various ways of accounting for the physical mechanism of the plasticity
phenomenon. These approaches often undergo stages of hopes and disappointments.
The most shining example here is the Batdorf–Budiansky plasticity theory [2]
that we discussed in the previous section of the book. Experiments to check the
ratios of the Batdorf–Budiansky theory showed that its dependencies agreed with
experimental data for some loading paths (close to proportional) and were not
confirmed by other experiments [11, 13–15].
We have shown that the update of slip concepts undertaken in the previous
section removes the disadvantages of the Batdorf–Budiansky theory; however, it
significantly complicates the theory. A significant advantage of the proposed slip
model is its two-dimensional variant and a revealed opportunity to expand the
obtained results to the spatial case using the Ilyushin isotropy postulate.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_30
393
Complex Strain of Soils
30.1 Real State of the Mechanics of Non-elastic Strains
An overview of plasticity theory and the state of the primary variants of its
development described in the previous two parts of the book makes us agree that
the theory of non-elastic solid body strain remains one of the primary problems
in modern mechanics. Today, we have many models, concepts, postulates, and
principles, the most significant of which were included in these two sections.
However, we should admit that there is still no theory that would be, in terms of
correspondence to experience, comparable with the Cauchy–Navier elasticity theory
or the theory of motion of viscous liquids of Navier–Stokes [4, 6].
As M. Ya. Leonov believes [6], such prolonged stagnation in the development
of mathematical plasticity theory is caused not only by an extreme complexity
of the problem but also by a tradition not to consider the physical mechanism of
the respective processes. Non-elastic strains result from structural changes in some
volumes, and in essence, they are defined by the discrete structure of solid bodies.
For this reason, when building determinant ratios recently, more attention has been
paid to various ways of accounting for the physical mechanism of the plasticity
phenomenon. These approaches often undergo stages of hopes and disappointments.
The most shining example here is the Batdorf–Budiansky plasticity theory [2]
that we discussed in the previous section of the book. Experiments to check the
ratios of the Batdorf–Budiansky theory showed that its dependencies agreed with
experimental data for some loading paths (close to proportional) and were not
confirmed by other experiments [11, 13–15].
We have shown that the update of slip concepts undertaken in the previous
section removes the disadvantages of the Batdorf–Budiansky theory; however, it
significantly complicates the theory. A significant advantage of the proposed slip
model is its two-dimensional variant and a revealed opportunity to expand the
obtained results to the spatial case using the Ilyushin isotropy postulate.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_30
393