Fig 1.
This figure shows different amount of bacteria loading and the corresponding stress—strain response.
(a) A representative biofilm microstructure subjected to shear load. (b) Bacteria loading of 26% (white portion signifies bacteria and black signifies the EPS matrix). (c) Bacteria loading of 42%. (d) Bacteria loading of 55%. (e) Shear stress—strain response of the biofilm for the three types of bacteria loading scenario. Since the bacteria are considered as rigid objects, larger volume fraction of bacteria leads to higher stiffness for the biofilm. Stiffness for each lattice spring element in the EPS matrix has been set in such a way that the biofilm with 26% bacteria loading follow the experimental shear stress—strain data obtained from Stoodley et al (2002). (f) Based on the stiffness of the EPS matrix and the bacteria, Hashin—Shtrikman (H-S) lower and upper bounds of shear stiffness for the biofilm has been evaluated. Shear stiffness of the biofilm at 5% and 35% shear strain falls within the Hashin—Shtrikman bounds. The parameters used in these simulations are given in Table 1.
Table 1.
List of parameters used for the comparison with experimental results reported in Stoodley et al.[5] are provided below.
The figure showing the strain-hardening behavior and comparison with experiments are provided in Fig 1(e).
Fig 2.
Force contours depict the corresponding regions which experience strain hardening.
No rupture has been considered in this simulation. (a) The cyan region signifies the portion which has undergone strain hardening behavior. Under shear loading, maximum shear strain has been observed along the diagonal directions. This is equivalent to the formation of shear bands observed in conventional solid materials. (b) Force contour observed at 5% shear strain. The magnitude of force is in the order of 0.3N. (c) Force contour observed at 35% shear strain. Magnitude of force is around 4.5N, which is an order of magnitude greater than the forces observed under 5% strain. Larger amount of forces accumulate along diagonal directions, which eventually leads to enhanced strain hardening along the diagonal direction. Similar behavior has been reported in part (b) of this image. The parameters used in these simulations are given in Table 1.
Fig 3.
Different clustering of bacteria inside the biofilm along with the rupture patterns are displayed here.
(a) Uniform distribution of bacteria within a biofilm. (b) Clustering of bacteria in the central portion of the domain. (c) Clustering of bacteria is observed around the corner of the domains. (d) Schematic representation of uniformly distributed bacteria inside biofilms. (e) Schematic representation of central clustering observed in biofilms. (f) Schematic representation of corner clustering within biofilms. (g) Distribution of rupture within the uniformly distributed bacteria. When all the bacteria are well dispersed, damage in the biofilm is not localized enough for an entire bacterium to be completely detached from the EPS matrix. (h) Rupture profile as observed for centrally clustered bacteria. When the bacteria are clustered within the biofilm, force concentration is very high around the bacterium, which leads to mechanical detachment of the EPS matrix from certain bacteria. (i) Evolution of damage for corner clustering scenario. Purpose of the corner clustering is to investigate how the tear would propagate through the EPS between two clusters of bacteria. It can be concluded that cracks through EPS matrix propagates to the nearest cluster. There is very little possibility for a tear through EPS to span between two clusters which are located far away from each other. The parameters are given in Table 2.
Table 2.
List of parameters used for comparison with rupture experiments reported in Korstgens et al.[19] are provided below.
Figure showing the rupture behavior and comparison with experimental results are provided Fig 4(a).
Fig 4.
Evolution of stress and stiffness for a biofilm under shear loading.
(a) Shear stress is plotted against shear strain. For biofilms with bacterial clustering, rupture initiates at a stress level of approximately 1100N/m2. Whereas, for biofilms with uniformly dispersed bacteria, rupture initiates at a higher stress magnitude, around 1300 N/m2. (b) Evolution of shear stiffness of the biofilm under increasing shear strain. Initially, because of strain hardening, stiffness of the biofilm increases. But after sometime, rupture starts to dominate and the overall stiffness of the biofilm drops. The two regions are clearly demonstrated in the figure, where, strain hardening dominates initially and rupture takes over towards the end. Reduction in stiffness starts earlier for biofilms with central clustering. This means, it is easier to tear the biofilms with clustering as compared to biofilms with uniformly distributed bacteria. The parameters used in these simulations are given in Table 2.
Fig 5.
These figures demonstrate a schematic diagram of the lattice spring network, digitization of the biofilm domain and a schematic representation of the unfolding of springs.
(a) The lattice spring network consists of a triangular mesh of spring elements. Each spring shows only axial stiffness. The mass remains concentrated at each node. The bottom of the network is fixed and shear force is applied at the top. (b) The digitized biofilm domain is displayed here. The red boundaries signify the boundaries for each of the bacteria. Blue portion is the mesh used to discretize the biofilm domain. (c) A schematic representation of the unfolding of springs. Under externally applied load, as the energy in a spring exceeds its unfolding threshold (the spring in the middle), it becomes straight and displays an infinite stiffness.