Chapter 6
Visco-Plasticity
In serial music, the series itself is seldom audible.
—Steve Reich, b. 1936
Visco-plasticity is the quintessential characteristics of both non-reversible and ratedependent material behavior. Thereby experimental evidence for various classes of
materials, including thermoplastic polymers and ductile metals, suggests that a part
of the total strain is irreversible with its evolution being rate-dependent. Irreversibility
thus motivates the decomposition of the total strain into an elastic, stress producing
part and a visco-plastic, irreversible part. The onset and evolution of irreversibility
are then captured by a yield condition and a rate-dependent flow rule, concepts that
are at the core of any overstress-based visco-plasticity formulation. From a convex
analysis point of view, non-reversibility and rate-dependence are intimately related
to the non-smoothness and non-linearity of the convex dissipation potential and its
dual.
The Bingham model is the basic combined rheological model for a perfect rigidvisco-plastic solid that displays both non-reversible and rate-dependent material
behavior. It consists of a parallel arrangement of a frictional slider and a viscous dashpot. Parallel and serial arrangements of a Bingham model with an elastic spring render
the Bingham hardening model for a hardening rigid-visco-plastic solid (not considered here) and the Perzyna model for a perfect elasto-visco-plastic solid, respectively.
Further, the serial arrangement of an elastic spring and the Bingham hardening model
is established as the Perzyna model for a hardening elasto-visco-plastic solid.
© 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_6
285
Visco-Plasticity
In serial music, the series itself is seldom audible.
—Steve Reich, b. 1936
Visco-plasticity is the quintessential characteristics of both non-reversible and ratedependent material behavior. Thereby experimental evidence for various classes of
materials, including thermoplastic polymers and ductile metals, suggests that a part
of the total strain is irreversible with its evolution being rate-dependent. Irreversibility
thus motivates the decomposition of the total strain into an elastic, stress producing
part and a visco-plastic, irreversible part. The onset and evolution of irreversibility
are then captured by a yield condition and a rate-dependent flow rule, concepts that
are at the core of any overstress-based visco-plasticity formulation. From a convex
analysis point of view, non-reversibility and rate-dependence are intimately related
to the non-smoothness and non-linearity of the convex dissipation potential and its
dual.
The Bingham model is the basic combined rheological model for a perfect rigidvisco-plastic solid that displays both non-reversible and rate-dependent material
behavior. It consists of a parallel arrangement of a frictional slider and a viscous dashpot. Parallel and serial arrangements of a Bingham model with an elastic spring render
the Bingham hardening model for a hardening rigid-visco-plastic solid (not considered here) and the Perzyna model for a perfect elasto-visco-plastic solid, respectively.
Further, the serial arrangement of an elastic spring and the Bingham hardening model
is established as the Perzyna model for a hardening elasto-visco-plastic solid.
© 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_6
285