Abstract
Barodesy is, like hypoplasticity, a frame for an evolution equation where the stress rate is expressed as tensorial function of stress, stretching and other parameters like void ratio. This equation being non-linear and non-integrable allows to express the path-dependent evolution of stress with deformation. The specific feature of barodesy is that it is based on two very simple theorems on asymptotic behavior of sand. The first theorem states that proportional strain paths starting from the stress-free state lead to proportional stress paths. Barodesy shows that this can be easily modeled with an exponential mapping. The second theorem refers to proportional strain paths starting form a non-vanishing stress state. They lead asymptotically to proportional stress paths that would have been obtained starting at the stress free state. Barodesy models this by adding a simple term in the constitutive relation, and this is now the complete new constitutive relation. The so obtained mathematical relation allows to embed in a simple and elegant way many known principles of soil mechanics, allowing additionally for some asymptotic effects due to cyclic loading. The striking simplicity of the new model not only facilitates its application in numerical applications but also offers a frame for understanding the behavior of soil and granular matter, in general. Moreover, it offers a good starting point for further investigations towards open problems such as rate sensitivity and behavior at small strains.
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Notes
- 1.
The first versions were not yet named “hypoplastic”.
- 2.
Herein, D i are the principal values of D, and R j (D i ) are the principal values of R(D).
- 3.
Integrity of grains (or permanence of the grain size distribution) has not been assumed for the derivation of the constitutive relation so far. In fact, a constitutive relation that does not contain any measure for the strength of grains presupposes that grain crushing does not occur. In reality, however, grain crushing is inevitable, especially at higher stresses. The corresponding changes of the grain size distribution curve are hard to measure.
- 4.
“Many properties of sand are equally puzzling to science as the big bang is”, Neue Zuercher Zeitung, 13.2.2008.
- 5.
A prominent representative of a school of thought called Rational Mechanics. The main reference is the classical book “The Non-Linear Field Theories of Mechanics” [19].
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Kolymbas, D. (2014). Barodesy: The Next Generation of Hypoplastic Constitutive Models for Soils. In: Hofstetter, G. (eds) Computational Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-05933-4_2
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