The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. The Preconditioned Conjugate Gradient iterative method is used for solving of the large-scale linear algebraic systems arising after the Finite Eleme...

For the numerical simulation in continuum mechanics the Composite Finite Element (CFE) method allows an effective treatment of problems where material parameters are discontinuous across geometrically complicated interfaces. Instead of complicated and computationally expensive tetrahedral meshing, specialized CFE basis functions are constructed on a uniform hexahedral grid. This is a convenient...

In this paper we consider numerical solution of 3D linear elasticity equations described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. Preconditioned Conjugate Gradient iterative method is used for solving large-scale linear algebraic systems arising after the Finite Element Method (FEM) dis...

With recent advances in instrumentation and experimental methodology, noncontact atomic force microscopy is now being frequently used to measure the atomic-scale interactions acting between a sharp probe tip and surfaces of interest as a function of three spatial dimensions, via the method of three-dimensional atomic force microscopy (3D-AFM). In this chapter, we discuss the different data coll...

In-situ homogeneous dispersion of noble metals in three-dimensional graphene sheets is a key tactic for producing macroscopic architecture, which is desirable for practical applications, such as electromagnetic interference shielding and catalyst. We report a one-step greener approach for developing porous architecture of 3D-graphene/noble metal (Pt and Ag) nanocomposite monoliths. The resultin...

In biological tissue, an increase in elasticity is often a marker of abnormalities. Techniques such as quasi-static ultrasound elastography have been developed to assess the strain distribution in soft tissues in two dimensions using a quasi-static compression. However, as abnormalities can exhibit very heterogeneous shapes, a three dimensional approach would be necessary to accurately measure ...

complex shape variability evident in intersubject ̄ oanatomies can be accommodated using GrenanGlobal Shape models. Following the approach of :, 3, 4], we construct a digitized textbook containall of the information currently available about a :al neuroanatomy on a fixed 3D coordinate system. textbook contains anatomical information (mag: resonance images, cryosection blockfaces, etc...) symboli...

Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus can increase by up to three orders of magnitude while the networks withstand relatively large stresses without rupturing. Here, we perform an analytical and numerical study on model networ...

Medical imaging is vital to modern clinical practice, enabling clinicians to examine tissues inside the human body non-invasively. Its value depends on accuracy, resolution, and the imaged property (e.g., density). Various new scanning techniques are aimed at producing elasticity images related to mechanical properties (e.g., stiffness) to which conventional forms of ultrasound, X-ray and magne...

A 3D distinct lattice spring model (DLSM) is proposed where matter is discretized into individual particles linked by springs. The presented model is different from the conventional lattice spring models where a shear spring is introduced to model the multibody force by evaluating the spring deformation from the local strain rather than the particle displacement. By doing this, the proposed mod...