TY - JOUR

T1 - Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams

AU - Raufaste, Christophe

AU - Marmottant, Phillippe

AU - Cox, Simon

AU - Graner, François

N1 - C. Raufaste, S.J. Cox, P. Marmottant and F. Graner (2010) Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams. Phys. Rev. E 81:031404.
Sponsorship: SJC
thanks the British Council Alliance programme, CNRS
and EPSRC (EP/D048397/1, EP/D071127/1) for financial
support and UJF for hospitality during the period in
which this work was conceived. CR thanks the Alliance
programme for having supported one visit to Aberystwyth
University, project 15154XB Foam rheology in two
dimensions.

PY - 2010

Y1 - 2010

N2 - We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as
a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual
objects is taken into account through statistical quantities, such as the elastic strain of the structure,
the yield strain and the yield function. The past history of the sample plays no explicit role, except
through its effect on these statistical quantities. They suffice to relate the discrete scale with the
collective, global scale. At this global scale, the material behaves as a continuous medium; it is
described with tensors such as elastic strain, stress and velocity gradient. We write the differential
equations which predict their elastic and plastic behaviour in both the general case and the case
of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the
deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of
order 0.3. We suggest practical applications, including: when to choose a scalar formalism rather
than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a
high, yield strain.

AB - We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as
a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual
objects is taken into account through statistical quantities, such as the elastic strain of the structure,
the yield strain and the yield function. The past history of the sample plays no explicit role, except
through its effect on these statistical quantities. They suffice to relate the discrete scale with the
collective, global scale. At this global scale, the material behaves as a continuous medium; it is
described with tensors such as elastic strain, stress and velocity gradient. We write the differential
equations which predict their elastic and plastic behaviour in both the general case and the case
of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the
deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of
order 0.3. We suggest practical applications, including: when to choose a scalar formalism rather
than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a
high, yield strain.

U2 - 10.1103/PhysRevE.81.031404

DO - 10.1103/PhysRevE.81.031404

M3 - Article

C2 - 20365733

SN - 1550-2376

SN - 2470-0053

VL - 81

JO - Physical Review E

JF - Physical Review E

IS - 3

ER -