Mechanics of network materials using discrete network models and gpu accelerated multiscale finite elements

Abstract

The focus of this thesis is on improving the state of modeling of tissue-scale biological network materials by addressing three component topics: First, discrete fiber models are used to probe the fundamentals of network physics. Second, numerical, and algorithmic enhancements are made to a multiscale finite element code, MuMFiM, to enable modeling tissue-scale network materials. Finally, MuMFiM is used to enhance the understanding of the underlying cause of anomalous realignment in the facet capsular ligament. Using a discrete fiber network model with a Voronoi structure, the small strain point force boundary value problem is solved. It is shown that with appropriate boundary conditions, the asymptotic scaling matches that of the linear elasticity solution outside a threshold distance. When the distance to the point force is less than approximately two times the mean distance between crosslinks, the solution diverges from the classical solution. It is postulated that this divergence is caused by the nonlocal behavior of the fiber network. Similar Voronoi networks are employed to investigate indentation of fibrous materials. With a small spherical indenter radius, the modulus recovered by fitting the classical Hertz solution is lower than the true modulus and the force displacement relationship is not consistent with the Hertzian model. It is proposed, through elimination of other potential mechanisms, that nonlocality is the cause of this indenter radius size effect. The limits of applicability of the Hertz solution are determined in terms of the network parameters. This assists the interpretation of data from indentation experiments with soft fibrous materials. Material size effects are of critical importance to multiscale modeling because for the microstructure to be homogenized into a representative volume element (RVE) the discrete fiber network must exhibit behavior which is representative of the macroscopic material behavior. Many authors use periodic boundary conditions to circumvent the large model sizes required to obtain a RVE, however fibrous materials are not typically periodic. To be able to properly reduce the RVE size, ``generalized boundary conditions'' are applied to RVEs composed from fibrous materials. To support the ability to employ fibrous RVEs in the study of large scale tissue applications, a multiscale finite element, MuMFiM, code was developed building on a previously initiated framework. Methods developments included introduction of incremental deformation gradients and a dynamic relaxation method on the microscale which improved robustness and allow modeling large global strains as required for the solution of biological tissues. Two level parallelism as required for use of accelerator driven exascale computers was introduced and a new approach for the performant parallel solutions of RVE’s on GPUs developed that produced up to a 1000x speed-up. MuMFiM is shown to scale well on up to 128 nodes of AiMOS using 6 NVIDIA V100 GPUs on each node. Lastly, MuMFiM is used to investigate the root cause of anomalous fiber realignment (AR) in the facet capsular ligament (FCL) and it is shown that the cause of AR is not the highly heterogeneous structure of the FCL including the presence of subdomains with preferentially aligned collagen, but rather microscopic damage or local instability.