TY - JOUR
T1 - Effective medium theory of random regular networks
AU - Damavandi, O. K.
AU - Manning, M. L.
AU - Schwarz, J. M.
N1 - Funding Information:
OKD wishes to thank Amanda Parker for discussion. JMS and MLM acknowledge financial support from NSF-PoLS-2014192. We would also like to acknowledge support from the Simons Foundation No 454947 (MLM and OKD), and NSF-DMR-1951921 (MLM).
Publisher Copyright:
Copyright © 2022 EPLA.
PY - 2022/4
Y1 - 2022/4
N2 - Disordered spring networks can exhibit rigidity transitions, due to either the removal of material in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the former, there is none for the latter. We, therefore, formulate an EMT for random regular, under-constrained spring networks with purely geometrical disorder to predict their stiffness via the distribution of tensions. We find a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. While EMT does not yield highly accurate predictions of shear modulus due to spatial heterogeneities, it requires only the distribution of tensions for an intact system, therefore making it an ideal starting point for experimentalists quantifying the mechanics of such networks.
AB - Disordered spring networks can exhibit rigidity transitions, due to either the removal of material in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the former, there is none for the latter. We, therefore, formulate an EMT for random regular, under-constrained spring networks with purely geometrical disorder to predict their stiffness via the distribution of tensions. We find a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. While EMT does not yield highly accurate predictions of shear modulus due to spatial heterogeneities, it requires only the distribution of tensions for an intact system, therefore making it an ideal starting point for experimentalists quantifying the mechanics of such networks.
UR - http://www.scopus.com/inward/record.url?scp=85130819149&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85130819149&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/ac6064
DO - 10.1209/0295-5075/ac6064
M3 - Article
AN - SCOPUS:85130819149
SN - 0295-5075
VL - 138
JO - EPL
JF - EPL
IS - 2
M1 - 27001
ER -