  We apply the immersed boundary (or IB) method to simulate deformation and
detachment of a periodic array of wall-bounded biofilm colonies in response to
a linear shear flow. The biofilm material is represented as a network of
Hookean springs that are placed along the edges of a triangulation of the
biofilm region. The interfacial shear stress, lift and drag forces acting on
the biofilm colony are computed by using fluid stress jump method developed by
Williams, Fauci and Gaver [Disc. Contin. Dyn. Sys. B 11(2):519-540, 2009], with
a modified version of their exclusion filter. Our detachment criterion is based
on the novel concept of an averaged equivalent continuum stress tensor defined
at each IB point in the biofilm which is then used to determine a corresponding
von Mises yield stress; wherever this yield stress exceeds a given critical
threshold the connections to that node are severed, thereby signalling the
onset of a detachment event. In order to capture the deformation and detachment
behaviour of a biofilm colony at different stages of growth, we consider a
family of four biofilm shapes with varying aspect ratio. Our numerical
simulations focus on the behaviour of weak biofilms (with relatively low yield
stress threshold) and investigate features of the fluid-structure interaction
such as locations of maximum shear and increased drag. The most important
conclusion of this work is that the commonly employed detachment strategy in
biofilm models based only on interfacial shear stress can lead to incorrect or
inaccurate results when applied to the study of shear induced detachment of
weak biofilms. Our detachment strategy based on equivalent continuum stresses
provides a unified and consistent IB framework that handles both sloughing and
erosion modes of biofilm detachment, and is consistent with strategies employed
in many other continuum based biofilm models.
