ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

stiffness of PCL to be compensated [13] (3) it can be processed into fibers using
common plastic extruders [8].
2.2 Dedicated FE code
Details of the code used in this study have been previously reported [10]. Briefly, the
approach aims at reproducing the nonlinear behavior of textile materials by simulating
the relative motions between fibers, individually modeled by an enriched kinematical
beam model accounting for cross-sectional strains within a large deformation
framework. The non-linear stress-strain response of isolated PLCL fibers is
approximated by a elastoplastic constitutive law consisting in a linear elastic part
followed by a Chaboche-type hardening, whose parameters have been determined by
using the least squares method from tensile tests on P(LL85/CL15) fibers for a given
tensile speed. The process of contact detection consists in (1) the determination of
proximity zones where contacts are likely to occur within the global assembly of beams
(2) the creation of intermediate geometries defined as the average of fibers axes (3) the
generation of contact elements at discrete locations on these intermediate geometries by
using planes orthogonal to these geometries. The contact-friction interactions are then
modeled in the form of a regularized penalty law in the normal direction and a
Coulomb's law for tangential friction. As far as the definition of boundary conditions
are concerned, rigid bodies attached to both ends of each layer of the multilayer braid
are used to prescribe loads or displacements to each layer, while isolated fibers bound to
these rigid bodies by means on average conditions are allowed to rearrange. As the
initial configuration of the scaffold can not be known a priori, we start from an arbitrary
configuration where trajectories of fibers are described by helices and where fibers are
therefore interpenetrated within the same layer (Fig. 1). This interpenetration is
gradually reduced by means of contact conditions starting from the braiding pattern of
the construct. As a result of this non linear iterative process, a non-interpenetrated
configuration of the braid is obtained as the equilibrium configuration of the assembly
of fibers which satisfies the braiding pattern of the scaffold. Once this first initial
configuration has been computed, a series of boundary conditions which aims at
reproducing the braiding tension needed to tighten fibers during the braiding process
and the pre-tension applied before the scaffold testing is prescribed. The tensile –and/or
torsion- test is then simulated by prescribing an increasing displacement –and/or
rotation- to one edge of each layer of the scaffold.
2.3 Determination of a suited scaffold configuration
The effects of three process parameters, namely the fiber diameter, the braiding angle
and the number of layers of the braid, on the tensile response were assessed. The
number of fibers per layer has been fixed to 16. In a previous work [8], the effect of
these parameters on the pore size distribution has been reported. The determination of a
suited scaffold configuration has been based on both morphological and mechanical
criteria, considering that the scaffold should: (1) offer a minimum pore size of 200-
250µm [9] (2) bear strains more than 4% often encountered during rehabilitation
exercises [11] (3) offer a stiffness around 120N/mm reported for native ACL [14].
Indeed, as the external loading of ACL is displacement-controlled rather than forcecontrolled
and its physiological function is to restrain the relative displacement between
femur and tibia, it has been considered that the mechanical requirements should be
considered in terms of minimal strain to rupture and stiffness rather than in terms of