<p>Continuum mechanics is used to model the mechanical behaviour of concrete structures subjected to high rates of loading in defence applications. Large deformation theory is used and an isotropic elastic-plastic constitutive equation with isotropic hardening, damage and strain rate dependent loading surface. The hydrostatic pressure is governed by an equation of state. Numerical analysis is performed using the finite element method and the central difference method for the time integration.</p><p>Projectile penetration is studied and it is concluded that it is not suitable to use material description of the motion of both the target and the projectile together with an erosion criterion. Instead, the material description should be used only for the projectile and the spatial description for the target. In this way the need for an erosion criterion is eliminated. Also, in the constitutive model used it is necessary to introduce a scaling of the softening phase in relation to the finite element size, in order to avoid strain localization.</p><p>Drop weight testing of reinforced concrete beams are analysed, where a regularisation is introduced that renders mesh objectivity regarding fracture energy release. The resulting model can accurately reproduce results from material testing but the regularisation is not sufficient to avoid strain localization when applied to an impact loaded structure. It is finally proposed that a non-local measure of deformation could be a solution to attain convergence.</p><p>The third study presents the behaviour of a concrete constitutive model in a splitting test and a simplified non-local theory applied in a tensile test. The splitting test model exhibits mesh dependency due to a singularity. In the tensile test the non-local theory is shown to give a convergent solution. The report https://www.diva-portal.org/liu/webform/form.jsp#paper0is concluded with a discussion on how to better model concrete materials.</p>

The continuum theory provides a framework in which the growth of a plant root as a dynamic process involving interactions among transport of water and solute, cell division, and the subsequent cell elongation can be described. A plant root is modeled as a one-dimensional, multi-phase, mathematical continuum. The network of cell walls constitute the solid phase of the system. The symplast and the apoplast pathways reside in this network of cell walls. Water and carbohydrates move in opposite directions through the apoplast and symplast pathways within the deforming network of cell walls. The division and elongation of cells depends on the mechanical stress imposed on the cell walls, the rate of metabolic stress relaxation process, and the physical properties of the cell walls. The model consists of five systems of differential equations. The kinematic equations are derived which allow, specifically, the different roles of cell division and elongation in root growth to be considered. These provide the reference system of the model. Equations of water transport in the coupled system of apoplast and symplast pathways are derived from considerations of theories of transport in the porous media and the cellular and membrane properties of the plant root. Equations of solute transport are derived by considering, specifically, the mechanisms involved in solute transport both at the membranes separating individual cells and within the cytoplasm. The rate of cell elongation is described as a function of the mechanical stress in the cell walls, the viscoelastic properties of the cell walls, and a metabolically controlled strain energy relaxation process. Growth in the meristem is modeled as the result of continuous cell elongation and division. The equations of water and solute transport, cell elongation, and meristem growth are solved simultaneously under the reference system provided by the kinematic theory. The model is used to examine the effects of soil water stress, soil resistance to root penetration, and temperature, as well as the carbohydrate supply from the upper part of the plant on the dynamic process of root elongation. The close correspondence between the material coordinate system and the underlying cellular structure of the root allows the comparison between the continuum theory and the results of cell growth studies. Agreement of the model predictions of the pattern of growth along the root axis, as well as the effects of temperature and soil water stress on root growth, with the experimental measurements reported in the literature provides the justification for the theories. / Graduation date: 1991

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 110-120). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 110-120). Also available on the Internet.

No description available.

This dissertation focuses on a novel approach for characterizing the mechanical behavior of an elastic body. In particular, we develop a mathematical tool for the estimation of residual stress field in an elastic body that has mechanical properties similar to that of the arterial wall, by making use of intravascular ultrasound (IVUS) imaging techniques. This study is a preliminary step towards understanding the progression of a cardiovascular disease called atherosclerosis using ultrasound technology. It is known that residual stresses play a significant role in determining the overall stress distribution in soft tissues. The main part of this work deals with developing a nonlinear inverse spectral technique that allows one to accurately compute the residual stresses in soft tissues. Unlike most conventional experimental, both in vivo and in vitro, and theoretical techniques to characterize residual stresses in soft tissues, the proposed method makes fundamental use of the finite strain non- linear response of the material to a quasi-static harmonic loading. The arterial wall is modeled as a nonlinear, isotropic, slightly compressible elastic body. A boundary value problem is formulated for the residually stressed arterial wall, the boundary of which is subjected to a constant blood pressure, and then an idealized model for the IVUS interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on large deformations via an asymptotic construction of its solution. We then use a semi-inverse approach to study the model for a specific class of deformations. The analysis leads us to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, we then develop several inverse spectral algorithms to approximate the residual stress distribution in the arterial wall, given the first few eigenfrequencies of several induced blood pressures.

Thesis (Ph.D.) - James Cook University, 2003. / Typescript (photocopy). Appendices: leaves 156-172. Bibliiography: leaves 149-155.

Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Jianmin Qu; Committee Member: David McDowell; Committee Member: Elisa Riedo; Committee Member: Min Zhou; Committee Member: Mo Li.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1971. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1959. / Typescript. Abstracted in Dissertation abstracts, v. 20 (1959) no. 2, p. 614-615. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 166-171).