Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Mathematical Methods in Elasticity Imaging

Abstract: This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

On the determination of elastic moduli of cells by AFM based indentation

Abstract: The atomic force microscopy (AFM) has been widely used to measure the mechanical properties of biological cells through indentations. In most of existing studies, the cell is supposed to be linear elastic within the small strain regime when analyzing the AFM indentation data. However, in experimental situations, the roles of large deformation and surface tension of cells should be taken into consideration. Here, we use the neo-Hookean model to describe the hyperelastic behavior of cells and investigate the influence of surface tension through finite element simulations. At large deformation, a correction factor, depending on the geometric ratio of indenter radius to cell radius, is introduced to modify the force-indent depth relation of classical Hertzian model. Moreover, when the indent depth is comparable with an intrinsic length defined as the ratio of surface tension to elastic modulus, the surface tension evidently affects the indentation response, indicating an overestimation of elastic modulus by the Hertzian model. The dimensionless-analysis-based theoretical predictions, which include both large deformation and surface tension, are in good agreement with our finite element simulation data. This study provides a novel method to more accurately measure the mechanical properties of biological cells and soft materials in AFM indentation experiments.

Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties

Abstract: In this paper a three-dimensional Voronoi cell finite element model is developed for analyzing heterogeneous materials containing a dispersion of ellipsoidal inclusions or voids in the matrix. The paper starts with a description of 3D tessellation of a domain with ellipsoidal heterogeneities, to yield a 3D mesh of Voronoi cells containing the heterogeneities. A surface based tessellation algorithm is developed to account for the shape and size of the ellipsoids in point based tessellation methods. The 3D Voronoi cell finite element model, using the assumed stress hybrid formulation, is developed for determining stresses and displacements in a linear elastic material domain. Special stress functions that introduce classical Lame functions in ellipsoidal coordinates are implemented to enhance solution convergence. Numerical methods for implementation of algorithms and yielding stable solutions are discussed. Numerical examples are conducted with inclusions and voids to demonstrate the effectiveness of the model.

Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone

Abstract: The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g, introduced in the strain energy, and (b) the micro-inertia term h, in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h=10−4 m and h=10−5 m. For each case, three subcases for g were assumed, namely, g>h, g

Toward a Micromechanics-Based Procedure to Characterize Fatigue Performance of Asphalt Concrete

Abstract: A lattice-based micromechanics approach is proposed to characterize the cracking performance of asphalt concrete. A random truss lattice model was introduced and investigated for simulating the following: (a) linear elastic and viscoelastic deformation of homogeneous materials in axial compression and shear loading experiments, (b) linear elastic deformation and the stress field in heterogeneous materials in an axial compression loading experiment, and (c) damage evolution in elastic solids under an indirect tensile test. The simulation results match well with the theoretical solutions and show excellent promise in predicting cracking patterns in the indirect tensile test. A brief discussion about ongoing work is also presented.