We describe a multiscale model that incorporates force-dependent mechanical plasticity induced by interfiber cross-link breakage and stiffness-dependent cellular contractility to predict focal adhesion (FA) growth and mechanosensing in fibrous extracellular matrices (ECMs). The model predicts that FA size depends on both the stiffness of ECM and the density of ligands available to form adhesion...

We derive a new formula for the asymptotic eigenvalue distribution of stiffness matrices obtained by applying P1 Finite Elements with standard mesh refinement to the semi elliptic PDE of second order in divergence form −∇(K∇Tu) = f on Ω, u = g on ∂Ω. Here Ω ⊂ R and K is supposed to be piecewise continuous and pointwise symmetric semi positive definite. The symbol describing this asymptotic eige...

This paper investigates the synthesis of a spatial stiffness matrix using simple line springs. A new algorithm is developed, which enables the selection of constituent springs based on their positions and directions. The constraining space of the line springs is then investigated. It is shown that an isotropic stiffness matrix, in general, can be split into the sum of two rank-3 stiffness matri...

We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs on point surfaces. This discretization is based on the local assembly of PDE-specific mass and s...

In some qualification such as damage detection, a more detailed representation including mass, stiffness, and damping property matrices plays a more pivotal role than an equivalent state-space model. In practice, estimating the modal parameters of the dominant modes in the signal records is superior to directly identifying the mass, stiffness, and damping matrices. In this paper, a novel techni...

We investigate the problem of computing the inverses of stiffness matrices resulting from the finite element discretization of elliptic partial differential equations. Since the solution operators are non-local, the inverse matrices will in general be dense, therefore they cannot be represented by standard techniques. In this paper, we prove that these matrices can be approximated by Hand H2-ma...

Stiffness matrices of beams with stochastic distributed parameters modelled by random fields are considered. In finite element analysis, deterministic shape functions traditionally employed to derive stiffness using the variational principle. Such not exact because derived from solution governing partial differential equation relevant boundary conditions. This paper proposes an analytical metho...

In this study, the natural frequencies and mode shapes of beams without cracks and cracked Timoshenko beams is calculated with different boundary conditions using finite element method. The energy method is used to solve the equations. Hardness and softness matrices for Timoshenko beam without crack are obtained by solving the potential and kinetic energy equations. Then for investigation of cr...