Browsing by Subject "residual stress"
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Item Recovery of the Shear Modulus and Residual Stress of Hyperelastic Soft Tissues by Inverse Spectral Techniques(2012-11-15) Gou, Kun 1981-Inverse spectral techniques are developed in this dissertation for recovering the shear modulus and residual stress of soft tissues. Shear modulus is one of several quantities for measuring the stiffness of a material, and hence estimating it accurately is an important factor in tissue characterization. Residual stress is a stress that can exist in a body in the absence of externally applied loads, and beneficial for biological growth and remodeling. It is a challenge to recover the two quantities in soft tissues both theoretically and experimentally. The current inverse spectral techniques recover the two unknowns invasively, and are theoretically based on a novel use of the intravascular ultrasound technology (IVUS) by obtaining several natural frequencies of the vessel wall material. As the IVUS is interrogating inside the artery, it produces small amplitude, high frequency time harmonic vibrations superimposed on the quasistatic deformation of the blood pressure pre-stressed and residually stressed artery. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body for computational convenience. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflexive of the response due to imposed blood pressures. Subsequently, a boundary value problem is developed from intravascular ultrasound interrogation generating small amplitude, high frequency time harmonic vibrations superimposed on the quasistatic finite deformations via an asymptotic construction of the solutions. This leads to a system of second order ordinary Sturm-Liouville problems (SLP) with the natural eigenfrequencies from IVUS implementation as eigenvalues of the SLP. They are then employed to reconstruct the shear modulus and residual stress in a nonlinear approach by inverse spectral techniques. The shear modulus is recovered by a multidimensional secant method (MSM). The MSM avoids computing the Jacobian matrix of the equations and is shown to be convenient for manipulation. Residual stress is recovered via an optimization approach (OA) instead of the traditional equation-solving method. The OA increases the robustness of the algorithms by overdetermination of the problem, and comprehensive tests are performed to guarantee the accuracy of the solution. Numerical examples are displayed to show the viability of these techniques.Item Residual stress measurement using X-ray diffraction(Texas A&M University, 2005-02-17) Anderoglu, OsmanThis paper briefly describes the theory and methods of x-ray residual stress measurements. Residual stresses can be defined as the stresses which remain in a material in the absence of any external forces. There are many stress determination methods. Some of those methods are destructive and some are nondestructive. X-ray residual stress measurement is considered as a nondestructive method. X-ray diffraction together with the other diffraction techniques of residual stress measurement uses the distance between crystallographic planes as a strain gage. The deformations cause changes in the spacing of the lattice planes from their stress free value to a new value that corresponds to the magnitude of the residual stress. Because of Poisson?s ratio effect, if a tensile stress is applied, the lattice spacing will increase for planes perpendicular to the stress direction, and decrease for planes parallel to the stress direction. This new spacing will be the same in any similarly oriented planes, with respect to the applied stress. Therefore the method can only be applied to crystalline, polycrystalline and semi-crystalline materials. The diffraction angle, 2θ, is measured experimentally and then the lattice spacing is calculated from the diffraction angle, and the known x-ray wavelength using Bragg's Law. Once the d-spacing values are known, they can be plotted versus 2 sin ψ, ( ψ is the tilt angle). In this paper, stress measurement of the samples that exhibit a linear behavior as in the case of a homogenous isotropic sample in a biaxial stress state is included. The plot of d vs. 2 sin ψ is a straight line which slope is proportional to stress. On the other hand, the second set of samples showed oscillatory d vs. 2 sin ψ behavior. The oscillatory behavior indicates the presence of inhomogeneous stress distribution. In this case the xray elastic constants must be used instead of E and ν values. These constants can be obtained from the literature for a given material and reflection combination. It is also possible to obtain these values experimentally. Calculation of the residual stresses for these samples is beyond the scope of this paper and will not be discussed here.