Finite Element Based Tracking of Deforming Surfaces

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object's surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.Comment: additional experiment

Correlating low energy impact damage with changes in modal parameters: diagnosis tools and FE validation

This paper presents a basic experimental technique and simplified FE based models for the detection, localization and quantification of impact damage in composite beams around the BVID level. Detection of damage is carried out by shift in modal parameters. Localization of damage is done by a topology optimization tool which showed that correct damage locations can be found rather efficiently for low-level damage. The novelty of this paper is that we develop an All In One (AIO) package dedicated to impact identification by modal analysis. The damaged zones in the FE models are updated by reducing the most sensitive material property in order to improve the experimental/numerical correlation of the frequency response functions. These approximate damage models(in term of equivalent rigidity) give us a simple degradation factor that can serve as a warning regarding structure safety

Shakedown analysis for rolling and sliding contact problems

There is a range of problems where repeated rolling or sliding contact occurs. For such problems shakedown and limit analyses provides significant advantages over other forms of analysis when a global understanding of deformation behaviour is required. In this paper, a recently developed numerical method. Ponter and Engelhardt (2000) and Chen and Ponter (2001), for 3-D shakedown analyses is used to solve the rolling and sliding point contact problem previously considered by Ponter, Hearle and Johnson (1985) for a moving Herzian contact, with friction, over a half space. The method is an upper bound programming method, the Linear Matching Method, which provides a sequence of reducing upper bounds that converges to the least upper bound associated with a finite element mesh and may be implemented within a standard commercial finite element code. The solutions given in Ponter, Hearle and Johnson (1985) for circular contacts are reproduced and extended to the case when the frictional contact stresses are at an angle to the direction of travel. Solutions for the case where the contact region is elliptic are also given

Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates

This paper studies mathematical models of biopolymer supramolecular aggregates that are formed by the self-assembly of single monomers. We develop a new multiscale numerical approach to model the structural properties of such aggregates. This theoretical approach establishes micro-macro relations between the geometrical and mechanical properties of the monomers and supramolecular aggregates. Most atomistic-to-continuum methods are constrained by a crystalline order or a periodic setting and therefore cannot be directly applied to modeling of soft matter. By contrast, the energy matching method developed in this paper does not require crystalline order and, therefore, can be applied to general microstructures with strongly variable spatial correlations. In this paper we use this method to compute the shape and the bending stiffness of their supramolecular aggregates from known chiral and amphiphilic properties of the short chain peptide monomers. Numerical implementation of our approach demonstrates consistency with results obtained by molecular dynamics simulations

Measuring cellular traction forces on non-planar substrates

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have been established before mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a worksflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite element method (FEM). Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with a L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.Comment: 34 pages, 9 figure