Plastic deformation of a permanently bonded network: stress relaxation by pleats

TY - JOUR

T1 - Plastic deformation of a permanently bonded network: stress relaxation by pleats

AU - Ganguly, Saswati

AU - Das, Debankur

AU - Horbach, Juergen

AU - Sollich, Peter

AU - Karmakar, Smarajit

AU - Sengupta, Surajit

PY - 2018/11/12

Y1 - 2018/11/12

N2 - We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing “pleats”; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local non-affine displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain – field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

AB - We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing “pleats”; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local non-affine displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain – field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

U2 - 10.1063/1.5051312

DO - 10.1063/1.5051312

M3 - Article

SN - 0021-9606

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

M1 - 184503

ER -