Inverse problems in elasticity

This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded

Advances in Multiscale and Multifield Solid Material Interfaces

Interfaces play an essential role in determining the mechanical properties and the structural integrity of a wide variety of technological materials. As new manufacturing methods become available, interface engineering and architecture at multiscale length levels in multi-physics materials open up to applications with high innovation potential. This Special Issue is dedicated to recent advances in fundamental and applications of solid material interfaces

The Effect of Cooling Rate on the Microstructure Configuration of Continuously Cast Steel Slabs

This research work is another step for increasing the efficiency and productivity of the steel making process by enhancing both quality and quantity of the steel produced by the Continuous Casting process. When steels cool from a high temperature, austenite transforms into other phase configurations according to the austenite composition and cooling rate. As result of phase transformation, the steel crystal structure and, consequently, both the shape and the lattice parameter of the unit cell, change. These changes may introduce dilatational strains into the microstructure, which result in the creation of residual stress concentration zones within the microstructure. These stress concentration zones are vulnerable regions to the formation of microcracks or growth of the flaws in these regions. The main objective of this dissertation is to develop a method to define the optimum cooling rate for cooling continuously as-cast steel on industrial level. An FEM algorithm developed with the ANSYS codes is introduced in this dissertation to simulate the cooling of as-cast steel from any temperature below the solidification temperature. The algorithm is capable of being customized to simulate the thermodynamic behavior of as-cast steel microstructure with any chemical composition and any casting geometry imposed to desired cooling method. The phase transformation simulations were based on the CCT diagram and, therefore, they were quasi-real models. The models predict, analytically, the generation of the stress concentration regions due to the thermodynamic strains during cooling a sample from the austenite temperature range with different cooling rates. Another series of FEM models presented in this dissertation and post non-destructive tests (NDT) ultrasonic image analysis tests suggested in this work, can be used in the discussion of the effect of the cooling rate on the altering of the soundness of the tested steel. A combination of the suggested FEM algorithm and post image processing of NDT ultrasonic images along with laboratory cooling experiments and microstructural analysis provide a guideline to find the cooling rate for each grade of steel in the casting steel industry. Results of JMATPRO software also are deployed to increase the accuracy of the experimental set up and to obtain the required input data to run the proposed numerical algorithm cooling simulation

A survey on inverse problems for applied sciences

The aim of this paper is to introduce inversion-based engineering applications and to investigate some of the important ones from mathematical point of view. To do this we employ acoustic, electromagnetic, and elastic waves for presenting different types of inverse problems. More specifically, we first study location, shape, and boundary parameter reconstruction algorithms for the inaccessible targets in acoustics. The inverse problems for the time-dependent differential equations of isotropic and anisotropic elasticity are reviewed in the following section of the paper. These problems were the objects of the study by many authors in the last several decades. The physical interpretations for almost all of these problems are given, and the geophysical applications for some of them are described. In our last section, an introduction with many links into the literature is given for modern algorithms which combine techniques from classical inverse problems with stochastic tools into ensemble methods both for data assimilation as well as for forecasting

Numerical modelling techniques for fretting fatigue crack initiation and propagation

status: publishe

Dynamical systems : mathematical and numerical approaches

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science

Identification and analysis of factors affecting thermal shock resistance of ceramic materials in solar receivers

An analysis was conducted of the possible modes of thermal stress failure of brittle ceramics for potential use in point-focussing solar receivers. The pertinent materials properties which control thermal stress resistance were identified for conditions of steady-state and transient heat flow, convective and radiative heat transfer, thermal buckling and thermal fatigue as well as catastrophic crack propagation. Selection rules for materials with optimum thermal stress resistance for a particular thermal environment were identified. Recommendations for materials for particular components were made. The general requirements for a thermal shock testing program quantitatively meaningful for point-focussing solar receivers were outlined. Recommendations for follow-on theoretical analyses were made

Elastocapillary Phenomena in Soft Elastic Solids

Soft elastic solids play an important role in a wide range of applications such as in tissue scaffolds to grow artificial organs, in wearable contact lenses, as adhesives, in soft robotics and even as prototypical models to understand the mechanics of growth and morphology of organs. For a soft elastic material like hydrogel with its shear modulus in the range of tens of pascals, its surface tension also contributes to the mechanics of its deformation in addition to its elasticity. As opposed to a hard solid that is very difficult to deform, for the case of these soft solids, even a weak force like gravity can bring about significant deformation. Many of these aspects of the deformation and behavior of these ultrasoft materials are still not very well understood. Thus, the objectives of this dissertation were to understand the role of elastocapillarity (i.e, joint roles of solid surface tension and elasticity) and elastobuoyancy (i.e, joint roles of gravity and elasticity) that manifest in such solids. In this dissertation, we studied the role elastocapillarity in adhesion-induced instability in thin elastic films bonded to rigid substrates and also in surface oscillation modes of soft gel spheres set to vibration; the elastobuoyancy effect; elasticity mediated interaction of particles in soft solids as well as on thin films supported over a pool of liquid. We also presented some new results on how soft spherical gels undergo restricted spreading on rigid substrates with varying surface energies. In the first section, we studied how a thin confined layer of a soft elastic film loses adhesion from a rigid substrate by forming interfacial instabilities when a tensile stress is applied to it. We performed experiments to quantify the characteristic lengthscale of the patterns formed and found that they were significantly larger than the wavelengths of purely elastic instabilities. A linear stability analysis of the elastic field equations by taking into account the role of surface tension showed that the amplification of the wavelength is due to the role of elastocapillarity where the surface tension, elasticity, and film thickness contribute jointly in a non-trivial way. In addition, we found experimentally as well as theoretically that the stress required to adhesively fracture these films is much larger than Griffith’s fracture stress for stiffer elastic films, which is also due to the effect of elastocapillarity. We also studied the surface fluctuation of sessile hydrogel spheres subjected to mechanically-induced Gaussian white noise to understand the role of elastocapillarity in their oscillation modes. An important finding of this study is that they give a direct evidence that the surface tension of these elastic hydrogels is almost like that of water, which is the integral solvent in the swollen network of the polymeric gel. In the subsequent section, we introduced the new phenomenon of Elastobuoyancy. When a rigid sphere is placed on the surface of an ultrasoft hydrogel, it plunges into the soft substrate to an equilibrium depth where the elastic strain energy of the surrounding medium balances its weight. We refer to this state of the sphere as ‘Elastobuoyant’. By performing systematic experiments where we varied the sphere size and the elasticity of the substrate, we obtained scaling laws of the depth as a function of the radii, elastic modulus and the spheres buoyant weight, which were also supported by asymptotic analyses of the same. Following the section on elastobuoyancy, we reported a new set of principles to design self-assembly of particles by using the combined roles of surface tension, elasticity, and gravity in soft substrates. We used three different systems to study this elastic interaction macroscopically: (i) elastobuoyant assembly of particles suspended inside a soft elastic gel, (ii) elastocapillary assembly of particles floating on the surface of soft gels analogous to capillary attraction of objects on the surface of liquids, and (iii) assembly of particles on the surface of thin elastic membranes supported over a viscous liquid. In the second last chapter in this thesis, we presented some results on how soft elastic gel spheres spread on rigid substrates with different surface energies. Our observations indicate that their contact angles are slightly greater than those of equivalent liquid drops on similar substrates. The contact angles of these gel spheres increase as a function of elasticity and decrease when surface energy increases. We derived an expression for the excess elastic tension in the gel spheres at the crack tip by using an approach that is similar to estimating the viscous dissipation at the contact line during spreading of liquids. By using a general constitutive law where the elastic energy is not limited to the square of the strains, the singularity at the crack tip is artificially removed thereby forcing the gel to assume a liquid-like behavior. Our experimental results agreed reasonably well with the model. In the last chapter, we summarized the doctoral research and presented suggestions for future investigations. There are several appendices in this thesis that have interesting observations from partially completed projects that need additional research and analysis in the future

Cracking in asphalt materials

This chapter provides a comprehensive review of both laboratory characterization and modelling of bulk material fracture in asphalt mixtures. For the purpose of organization, this chapter is divided into a section on laboratory tests and a section on models. The laboratory characterization section is further subdivided on the basis of predominant loading conditions (monotonic vs. cyclic). The section on constitutive models is subdivided into two sections, the first one containing fracture mechanics based models for crack initiation and propagation that do not include material degradation due to cyclic loading conditions. The second section discusses phenomenological models that have been developed for crack growth through the use of dissipated energy and damage accumulation concepts. These latter models have the capability to simulate degradation of material capacity upon exceeding a threshold number of loading cycles.Peer ReviewedPostprint (author's final draft

Effects of near-surface thawing on elastic properties and signatures of seismic surface waves

The ongoing temperature rise in the Arctic may have severe effects on large areas of today’s permanently frozen ground. Therefore, it is important to establish robust systems that can monitor permafrost changes with time. Surface wave methods are useful for mapping seismic structures in permafrost because they do not require abrupt velocity contrasts or normal velocity gradients (i.e., increasing velocity with depth). Rock physics models can be used to calculate how the stiffness and density of permafrost change with the degree of freezing, and they can be helpful when interpreting real seismic data from repeated acquisitions. I have tested several rock physics models and parameters of layered subsurface models to investigate their effects on elastic properties and surface wave propagation in permafrost. Changes in the dispersion characteristic of Rayleigh waves can be seen in the frequency-velocity spectra of the waves and depend on the distribution of the layer velocities and thicknesses. The seismic velocities depend on the ice saturation and the geometrical ice distribution in the pore space. However, other factors such as pore saturation, porosity, and sand properties also affect the seismic velocities and must be considered in analyses.Masteroppgave i geovitenskapGEOV399MAMN-GEO