Linear elasticity

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

Reconstructive elasticity imaging for large deformations

Abstract: A method is presented to reconstruct the elastic modulus of soft tissue based on ultrasonic displacement and strain images for comparatively large deformations. If the average deformation is too large to be described with a linear elastic model, nonlinear displacement-strain relations must be used and the mechanical equilibrium equations must include high order spatial derivatives of the displacement. Numerical methods were developed to reduce error propagation in reconstruction algorithms, including these higher order derivatives. Problems arising with the methods, as well as results using ultrasound measurements on gel-based, tissue equivalent phantoms, are given. Comparison to reconstructions using a linear elastic model shows that equivalent image quality can be produced with algorithms appropriate for finite amplitude deformations.

Mechanical behavior of plant tissues as inferred from the theory of pressurized cellular solids

Abstract: The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete "cell" walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive ("cell wall") material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of "cell walls" and the magnitude of internal "cell" pressure. Analyses indicate that two "stiffening" agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or "densifying" material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material. THE MECHANICAL BEHAVIOR of plant tissues varies as a function of turgor pressure and the geometry of their constituent cells. Studies indicate that the elastic modulus of pith parenchyma increases monotonically as turgor pressure increases (Falk, Hertz, and Virgin, 1958; Lin and Pitt, 1986). (The elastic modulus is measured from the slope of the linear portion of a material's stress-strain curve. It measures a specimen's material properties.) A similar relationship has been reported for more anatomically complex structures, such as the leaves of Dubautia and Allium (Robichaux, Holsinger, and Morse, 1986; Niklas and O'Rourke, 1987). In addition to the influence of water content, the elastic modulus of a tissue increases as the ratio of cell wall to protoplasm increases (Niklas, 1989a), while the maximum elastic modulus of algal and higher plant cells decreases as cell size decreases but the cell wall fraction remains relatively constant (Steudle, Zimmermann, and Luttge, 1977; Robichaux I Received for publication 31 May 1988; revision accepted 7 February 1989. et al., 1986). Cell wall composition is another factor that can influence the mechanical properties of tissues. However, data relating to this issue are limited (see Mark, 1967). The influence of turgor pressure and the ratio of cell wall thickness to cell radius on the elastic modulus of pith parenchyma has been modelled by various authors (Nilsson, Hertz, and Falk, 1958; Pitt, 1982, 1984; Gatesetal., 1986; Lin and Pitt, 1986). In all cases, cells are approximated as thin-walled spheres, for which simple shell theory yields the relationship at = Pr/2, where a is the circumferential stress on a cell with a wall-thickness t, radius r, and a turgor pressure of P (see Lin and Pitt, 1986, p. 306). This relationship conforms well to empirical data from pith tissues, since t << r. An underlying assumption to these models is that tissue stiffness increases as the number of cells in a tissue sample increases because increasing cell numbers decrease the capacity for cell-tocell displacements, particularly as turgor pressure increases. This has been experimentally verified (Niklas, 1988). However, for plant tissues other than parenchyma, the assumptions of simple shell theory are violated (cell walls

Permanent deformation in flexible pavements

Abstract: This paper presents a mechanistic-empirical framework for evaluating permanent deformation in flexible pavements. The procedure uses rational material properties and can be used as an analysis tool, as a companion to the design method. The material properties required are (1) the stress dependent modulus of the pavement layers, asphalt concrete and granular base/subbase, and (2) the relation between the accumulated and the resilient strain with the number of load repetitions and stress level. The procedure is a compromise between simple and advanced approaches, between linear elasticity and nonlinear incremental finite element approaches. In addition to this improvement, the proposed procedure uses the “actual” temperature distribution in the asphalt layer at every hour in the whole design period. It is evaluated by computing the rut depth in well-designed pavements. All the results for the pavement response under different conditions are within the expected ranges.