Crackling Dynamics in the Mechanical Response of Knitted Fabrics

Geometric modeling of knitted fabrics

Knitting can turn a one-dimensional yarn into a highly ramified three-dimensional structure. As a method of additive manufacturing, it holds promise for a class of lightweight, ultrastrong materials. Here, we present a purely geometric model to predict the three-dimensional self-folding of knitted fabrics made only of the two traditional stitches, knit and purl.

Metastability of a Periodic Network of Threads: Shapes of a Knitted Fabric

Knitted fabrics are metamaterials with remarkable mechanical properties, such as extreme deformability and multiple history-dependent rest shapes. This Letter shows that those properties may stem from a continuous set of metastable states for a fabric free of external forces. This is evidenced through experiments, numerical simulations, and analytical developments. Those states arise from the frictional contact forces acting in the braid zone where the threads interlace and follow a line in the configuration space accurately described by a 2D-elastica model. The friction coefficient sets a terminal point along this line, and the continuous set of metastable states is obtained by varying the braid inclination while contact forces remain on the friction cone.

Mean-field theories for depinning and their experimental signatures

Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position u of its center of mass and the statistics of the forces F(u). There are two proposals how to model the latter: as a random walk (ABBM model), or as uncorrelated forces at integer u (discretized particle model, DPM). While for many experiments the ABBM model (in the literature misleadingly equated with mean-field theory) makes quantitatively correct predictions for the distributions of velocities, or avalanche size and duration, the microscopic disorder force-force correlations cannot grow linearly, and thus unboundedly as a random walk, with distance. Even the effective (renormalized) disorder forces which do so at small distances are bounded at large distances. To describe both regimes, we model forces as an Ornstein-Uhlenbeck process. The latter has the statistics of a random walk at small scales, and is uncorrelated at large scales. By connecting to results in both limits, we solve the model largely analytically, allowing us to describe in all regimes the distributions of velocity, avalanche size, and duration. To establish experimental signatures of this transition, we study the response function, and the correlation function of position u, velocity u[over ̇], and forces F under slow driving with velocity v>0. While at v=0 force or position correlations have a cusp at the origin and then decay at least exponentially fast to zero, this cusp is rounded at a finite driving velocity. We give a detailed analytic analysis for this rounding by velocity, which allows us, given experimental data, to extract the timescale of the response function, and to reconstruct the force-force correlator at v=0. The latter is the central object of the field theory, and as such contains detailed information about the universality class in question. We test our predictions by careful numerical simulations extending over up to ten orders in magnitude.

Experimental Study on Bi-Axial Mechanical Properties of Warp-knitted Meshes with and without Initial Notches

Warp-knitted meshes have been widely used for structural reinforcement of rigid, semi-rigid, and flexible composite materials. In order to meet the performance requirements of different engineering applications, four typical warp-knitted meshes (rectangular, square, circular, and diamond) were designed and developed. The mechanical behaviors of these meshes under mono-axial and multi-axial tensile loads were compared. The influence of the initial notch length and orientation on the mechanical performance was also analyzed. The results showed that the biaxial tensile behavior of warp-knitted meshes tended to be more isotropic. The anisotropy level of the diamond warp-knitted mesh was the lowest (λ = 0.099), while the rectangular one was the highest (λ = 0.502). The notch on a significantly anisotropic mesh was propagated along the direction of larger modulus, while for a not remarkably anisotropic mesh, notch propagation was probably consistent with the initial notch orientation. The breaking strength of warp-knitted meshes with the same initial notch orientation decreased with the increase in notch length in both the wale and course directions. For warp-knitted meshes with the same initial notch length, the breaking strength in the wale direction was kept stable at different notch orientations, while that in the course direction decreased remarkably with notch orientation from 0° to 90°.