Structural design often includes geometrically nonlinear analysis to reduce structural weight and increase energy efficiency. The full-order finite element model can perform the analysis, but its computational cost is expensive. Therefore, reduced-order models (NLROMs) have been developed costs. non-intrusive NLROM has a lower than other due approximation of internal force by polynomial reduced...

Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped atherma...

This paper considers the hp-finite element discretization of an elliptic boundary value problem using tetrahedral elements. The discretization uses a polynomial basis in which the number of nonzero entries per row is bounded independently of the polynomial degree. The authors present an algorithm which computes the nonzero entries of the stiffness matrix in optimal complexity. The algorithm is ...

Unit cell homogenization techniques are applied on multiple length scales to compute the macroscopic hyperelastic stiffness characteristics of textile-reinforced polymer matrix composites. On the smallest scale (~50μm) the effective transversely isotropic properties of tows (or yarns) are computed based on both fiber and matrix properties. These position-dependent transversely isotropic effecti...

Stem cells regulate their fate by binding to, and contracting against, the extracellular matrix. Recently, it has been proposed that in addition to matrix stiffness and ligand type, the degree of coupling of fibrous protein to the surface of the underlying substrate, that is, tethering and matrix porosity, also regulates stem cell differentiation. By modulating substrate porosity without alteri...

Neural progenitor cell (NPC) culture within three-dimensional (3D) hydrogels is an attractive strategy for expanding a therapeutically relevant number of stem cells. However, relatively little is known about how 3D material properties such as stiffness and degradability affect the maintenance of NPC stemness in the absence of differentiation factors. Over a physiologically relevant range of sti...