Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness

Abstract

By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. The largest damage is observed close to rigidity points when the rupture thresholds are small. Fewer bonds are broken when the thresholds are increased. Irrespectively of network and spring properties, a more brittle fracture is observed upon increasing system size, even in sub-isostatic networks where the underlying force chains govern the mechanical response. Most of the fracture descriptors show power-law size-scaling dependent on rigidity properties. Strikingly, the maximum stress drop, a proxy for brittleness, displays a universal doubly-non-monotonic dependence on system size and can be used as a novel parameter to identify different failure regimes. Our results indicate how to tune these regimes. Finally, we speculate how the size-induced brittleness is influenced by thermal fluctuations. arXiv:1907.11466v1 [cond-mat.soft]

The role of temperature in the rigidity-controlled fracture of elastic networks

“…On the one hand, for low T* the peak stress is evidently controlled by the network rigidity, as previously investigated in the athermal limit. 12,13 On the other hand, when the thermal energy is of the order of E break ¼ 1 2 mðl' 0 Þ 2 the network structure is irrelevant, as springs spontaneously break and the system shows melting behaviour. We will later describe the melting point using the reduced quantity…”

“…Therefore, coarse-grained network models have been developed, which treat the material as a disordered network of elastic springs, and which explicitly take connectivity and disorder into account. [10][11][12][13] Recent computational studies, complemented with experiments on architectured elastic networks, have shown that under athermal and quasistatic conditions the elastic response and failure behaviour of an elastic network is controlled by both the connectivity of the network and the strength of the individual elements. [12][13][14][15] The network architecture, in particular its connectivity, determines the network rigidity.…”

“…16 Below the isostatic point, central-force spring networks are mechanically floppy. However, simulations have shown that even floppy or sub-isostatic networks can be rigidified by an external deformation 13,17,18 or by the presence of additional interactions such as a bending rigidity. 6,10,11,[19][20][21][22][23] These recent studies suggest that if the static network structure and the element strength of a soft athermal material are known, the material response can be predicted based on the physical concept of rigidity.…”

“…1), similar to previous studies. [12][13][14]26,27 To introduce thermal fluctuations into these systems we perform Langevin dynamics simulations, which means that the networks are effectively embedded in an implicit solvent. We find that the strength of the networks is dependent on temperature and that the effect of the thermal fluctuations is coupled to the rigidity of the network.…”

“…The peak stress s p is defined as the highest measured stress, and the peak strain e p is its corresponding strain value. The maximum stress drop Ds max is calculated according to a procedure 13,32 where we (i) calculate the derivative of the stress-strain curve, (ii) make a list of consecutive data points which have a negative derivative and note the initial and final strain of each interval, (iii) calculate the stress drops by subtracting the stress at the final strain from the stress at the initial strain, (iv) identify the largest stress interval, which corresponds to maximum stress drop Ds max . For the stress distribution analysis, we make instantaneous histograms of the bond lengths c i during the simulation at every percent strain.…”