Self-stresses control stiffness and stability in overconstrained disordered networks

Abstract

We investigate the interplay between pre-stress and mechanical properties in random elastic networks. To do this in a controlled fashion, we introduce an algorithm for creating random freestanding frames that support exactly one state of self stress. By multiplying all the bond tensions in this state of self stress by the same number---which with the appropriate normalization corresponds to the physical pre-stress inside the frame---we systematically evaluate the linear mechanical response of the frame as a function of pre-stress. After proving that the mechanical moduli of affinely deforming frames are rigourously independent of pre-stress, we turn to non-affinely deforming frames. In such frames, pre-stress has a profound effect on linear response: not only can it change the values of the linear modulus---an effect we demonstrate to be related to a suppressive effect of pre-stress on non-affinity---but pre-stresses also generically trigger bistable mechanical response. Thus, pre-stress can be leveraged to both augment the mechanical response of network architectures on the fly, and to actuate finite deformations. These control modalities may be of use in the design of both novel responsive materials and soft actuators.

arXiv comment13 pages, 9 figures

References in corpus (17)

• Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
• Programmable Mechanical Metamaterials
• Combinatorial Design of Textured Mechanical Metamaterials
• The origin of stiffening in cross-linked semiflexible networks
• Effects of compression on the vibrational modes of marginally jammed solids
• Elasticity of Stiff Polymer Networks
• Topological modes bound to dislocations in mechanical metamaterials
• Criticality and isostaticity in fiber networks
• On the Rigidity of Amorphous Solids
• Multi-step self-guided pathways for shape-changing metamaterials
• A coordination-based approach to elasticity of floppy and stiff random networks
• Designing allostery-inspired response in mechanical networks
• Auxetic metamaterials from disordered networks
• Jammed frictionless discs: connecting local and global response
• Geometry and the onset of rigidity in a disordered network
• Length scales and self-organization in dense suspension flows
• Disorder, pre-stress and non-affinity in polymer 8-chain models

Cited by in corpus (3)

• Building rigid networks with prestress and selective pruning
• Spectral approaches to stress relaxation in epithelial monolayers
• Viscoelastic scaling regimes for marginally-rigid fractal spring networks