  Fibrin is a structural protein key for processes such as wound healing and
thrombus formation. At the macroscale, fibrin forms a gel and has a mechanical
response that is dictated by the mechanics of a microscale fiber network.
Hence, accurate description of fibrin gels can be achieved using representative
volume elements (RVE) that explicitly model the discrete fiber networks of the
microscale. These RVE models, however, cannot be efficiently used to model the
macroscale due to the challenges and computational demands of multiscale
coupling. Here, we propose the use of an artificial, fully connected neural
network (FCNN) to efficiently capture the behavior of the RVE models. The FCNN
was trained on 1100 fiber networks subjected to 121 biaxial deformations. The
stress data from the RVE, together with the total energy on the fibers and the
condition of incompressibility of the surrounding matrix, were used to
determine the derivatives of an unknown strain energy function with respect to
the deformation invariants. During training, the loss function was modified to
ensure convexity of the strain energy function and symmetry of its Hessian. A
general FCNN model was coded into a user material subroutine (UMAT) in the
software Abaqus. The UMAT implementation takes in the structure and parameters
of an arbitrary FCNN as material parameters from the input file. The inputs to
the FCNN include the first two isochoric invariants of the deformation. The
FCNN outputs the derivatives of the strain energy with respect to the isochoric
invariants. In this work, the FCNN trained on the discrete fiber network data
was used in finite element simulations of fibrin gels using our UMAT. We
anticipate that this work will enable further integration of machine learning
tools with computational mechanics. It will also improve computational modeling
of biological materials characterized by a multiscale structure.
