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

Abstract

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 {\em 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.

arXiv comment9 pages, 10 figures

References in corpus (16)

• Dynamics of Viscoplastic Deformation in Amorphous Solids
• Programming Curvature using Origami Tessellations
• Deformation and Failure of Amorphous Solidlike Materials
• Algorithmic Lattice Kirigami: A Route to Pluripotent Materials
• Making the Cut: Lattice Kirigami Rules
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• Formation and growth of shear bands in glasses: existence of an underlying directed percolation transition
• 3-dimensional structure of a sheet crumpled into a ball
• Do solids flow?
• Direct observation of percolation in the yielding transition of colloidal glasses
• Microscopic origin of nonlinear non-affine deformation and stress overshoot in bulk metallic glasses
• Non-affine displacements in crystalline solids in the harmonic limit
• Emergent structure of multi-dislocation ground states in curved crystals
• Neutral versus charged defect patterns in curved crystals
• Do thermodynamically stable rigid solids exist?
• Equilibrium and dynamic pleating of a crystalline bonded network

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