We propose a method for deriving equivalent one-dimensional models slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, rotations, arbitrary cross-sections shapes, inhomogeneous elastic properties across the cross-section, constitutive laws (possibly with low symmetry) distributions of pre-strain, including pre-strain. It ...

The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell cult...

It is the aim to compute efficiently the deformations of the mechanical structures that are excited or damped by piezoelectric actuators. They are treated as 3D structures to have much flexibility. Special design of the finite element concept is required since the structures are thin walled and locking effects have to be avoided. Although the computations are performed in the framework of 3-dim...

We summarize some recent results of the authors and their collaborators, regarding the derivation of thin elastic shell models (for shells with mid-surface of arbitrary geometry) from the variational theory of 3d nonlinear elasticity. We also formulate a conjecture on the form and validity of infinitely many limiting 2d models, each corresponding to its proper scaling range of the body forces i...

We propose a method to automatically tune a patient-based virtual environment training simulator for abdominal needle insertion. The key attributes to be customized in our framework are the elasticity of soft-tissues and the respiratory model parameters. The estimation is based on two 3D Computed Tomography (CT) scans of the same patient at two different time steps. Results are presented on fou...

This paper describes the concurrent multi-frontal direct solver algorithm for a multi-physics Finite Element Method (FEM). The multi-physics FEM utilizes different element sizes as well as polynomial orders of approximation over element edges, faces, and interiors (element nodes). The solver is based on the concept of a node, and management of unknowns is realized at the level of nodes. The sol...

Starting form 3D elasticity, we deduce the variational limit of the string and of the membrane on the space of one and two-dimensional gradient Young measures, respectively. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account in the string model. The rate at which the energy density blows up characterizes the effective domain of the l...

Abstract In this work, the $$\varvec{J}$$ J -, M - and $$\varvec{L}$$ L -integrals of two line charges forces in generalized plane strain are derived framework three-dimensional (3D) electrostatics compatible linear elasticity, respectively, order to study interaction b...