Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations

Abstract

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. Also in colloidal gels an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.

Force Transmission in Disordered Fibre Networks

“…We therefore explore , 10 −3 , and 10 −2 . We furthermore emphasise that the network model that we use here has been shown previously to accurately describe the mechanical properties and fracture of real collagen networks ( Broedersz and MacKintosh, 2014 ; Burla et al, 2020 ; Tauber et al, 2022 ).…”

Structural Features and Nonlinear Rheology of Self-Assembled Networks of Cross-Linked Semiflexible Polymers

“…In future work, it would be prudent to explore how the behavior we observe near the critical strain might differ in networks with linkers capable of either breaking under sufficient tension 43,46,71 or transiently binding and unbinding. 72,73 In such systems, we anticipate a rich interplay between the slow relaxations associated with nonaffine rearrangements and the additional dynamics of network remodeling and fracture.…”

“…Extensive simulation-based studies have explored the nonlinear rheological properties of disordered networks of cross-linked stiff or semiflexible polymers, ,− in some cases with realistic three-dimensional geometries produced by either physical assembly processes ,− or artificial generation procedures. − However, efforts to specifically connect network structure with strain-controlled critical behavior have typically focused on simplified random spring networks. ,,− In spring networks, the critical strain coincident with the onset of stretching-dominated mechanics can be tuned by changing the average connectivity z , defined as the average number of bonds joined at each network junction . For a network of cross-linked filaments, z is controlled by the typical number of cross-links formed per filament, approaching an upper limit of z → 4 at high cross-linking density .…”

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

“…Connecting the chain-level deformation with the continuum-level deformation has been possible through homogenization assumptions, including the affine three-chain model (Wang and Guth, 1952), non-affine four-chain model (Flory and Rehner Jr, 1943), non-affine Arruda-Boyce eight-chain model (Arruda and Boyce, 1993), affine full-network microsphere model (Treloar and Riding, 1979;Wu and van der Giessen, 1992;Wu and Van Der Giessen, 1993), and non-affine full-network microsphere models (Arunachala et al, 2021;Diani and Le Tallec, 2019;Ghaderi et al, 2020;Guo and Zaïri, 2021;Miehe et al, 2004;Rastak and Linder, 2018;Tkachuk and Linder, 2012). The interplay between chain-level load sharing with the macro-to-micro deformation relationship has been shown to exert a significant role in local strain-stiffening and delocalized chain rupture (Basu et al, 2011;Black et al, 2011;Chen et al, 2021bChen et al, , 2020Tauber et al, 2022Tauber et al, , 2021.…”