Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

The present paper is intended to show the close interrelationship between non-linear models of solids, produced with additive manufacturing, and models of solids with distributed defects. The common feature of these models is the incompatibility of local deformations. Meanwhile, in contrast with the conventional statement of the problems for solids with defects, the distribution for incompatible local deformations in additively created deformable body is not known a priori, and can be found from the solution of the specific evolutionary problem. The statement of the problem is related to the mechanical and physical peculiarities of the additive process. The specific character of incompatible deformations, evolved in additive manufactured solids, could be completely characterized within a differential-geometric approach by specific affine connection. This approach results in a global definition of the unstressed reference shape in non-Euclidean space. The paper is focused on such a formalism. One more common factor is the dataset which yields a full description of the response of a hyperelastic solid with distributed defects and a similar dataset for the additively manufactured one. In both cases, one can define a triple: elastic potential, gauged at stress-free state, and reference shape, and some specific field of incompatible relaxing distortion, related to the given stressed shape. Optionally, the last element of the triple may be replaced by some geometrical characteristics of the non-Euclidean reference shape, such as torsion, curvature, or, equivalently, as the density of defects. All the mentioned conformities are illustrated in the paper with a non-linear problem for a hyperelastic hollow ball.

Computational program to evaluate local defects type Chalmers Test on a reflective optical surface

A computational tool is developed to measure the local deformations in optical surfaces from the interference patterns obtained by the Chalmers test principle and from the analysis of a reflective optical surface using a commercial Fizeau interferometer of the ZYGO. The tests were made on a concave spherical mirror with a radius of curvature of 60 cm and a diameter of 13 cm. To obtain the measurements of local deformations, a computational tool proposed for the localization of dark fringes is used by evaluating the maximum and minimum of the image obtained in the interference patterns. The results obtained show that the computational tool allows locating fringes within an interference pattern, allowing faster inter-fringe measurements and assigning an error on the surface in terms of wavelength.

Experimental Investigation and Numerical Simulation of a Levy Hinged-Beam Cable Dome

According to existing rigid roofing projects, a new structure called the Levy hinged-beam cable dome is proposed. By replacing the upper flexible cables with hinged beams, rigid plates can be installed overhead. To fulfill the requirements of integral tow-lifting construction, the setting criteria for the temporary hinged joints on ridge beams were presented. An 8-m diameter specimen was manufactured and monitored to investigate the structural configurations during the accumulative traction-hoisting construction process. Finally, the specimen was tested under full-span and half-span loading conditions, while a numerical model was built to verify the experimental values. The results show that in the early stages of traction-hoisting, the structure establishes the overall prestress and finds its internal force balance, while the entire structure is in a shape of “ω”. As the component’s internal force increases during the construction steps, and the local deformations of the hinged beams gradually decrease, with the entire structure changing from “ω” to “m”, and finally reach their designed states. Under full-span loads, large local deformations occurred at the HB-3 hinges, while the bending stresses of these hinged beams were relatively small. Under half-span loads, the loading part exhibits a downward appearance, while the unloading part exhibits upward deflection.

Non-Rigid Liver Registration in Liver Computed Tomography Images Using Elastic Method with Global and Local Deformations

The study of follow-up liver computed tomography (CT) images is required for the early diagnosis and treatment evaluation of liver cancer. Although this requirement has been manually performed by doctors, the demands on computer-aided diagnosis are dramatically growing according to the increased amount of medical image data by the recent development of CT. However, conventional image segmentation, registration, and skeletonization methods cannot be directly applied to clinical data due to the characteristics of liver CT images varying largely by patients and contrast agents. In this paper, we propose non-rigid liver segmentation using elastic method with global and local deformation for follow-up liver CT images. To manage intensity differences between two scans, we extract the liver vessel and parenchyma in each scan. And our method binarizes the segmented liver parenchyma and vessel, and performs the registration to minimize the intensity difference between these binarized images of follow-up CT images. The global movements between follow-up CT images are corrected by rigid registration based on liver surface. The local deformations between follow-up CT images are modeled by non-rigid registration, which aligns images using non-rigid transformation, based on locally deformable model. Our method can model the global and local deformation between follow-up liver CT scans by considering the deformation of both the liver surface and vessel. In experimental results using twenty clinical datasets, our method matches the liver effectively between follow-up portal phase CT images, enabling the accurate assessment of the volume change of the liver cancer. The proposed registration method can be applied to the follow-up study of various organ diseases, including cardiovascular diseases and lung cancer.

The Theoretical and experimental study of the bending of a thin substrate during electrolytic deposition

The present paper is aimed at the theoretical and experimental study of the shape distortion of thin substrates during electrolytic deposition and gaccumulation of residual stresses in them. The theoretical modeling is provided in the framework of the theory of solids with variable material composition. The result of the deposition process is modeled with a continuous family of elastic bodies, which local deformations are incompatible. These deformations act as internal sources for stresses. Formally they are equivalent to the field of distributed defects. Unlike the classical approach adopted in nonlinear elasticity, the elements of the family which present a body with a variable material composition don’t have a global reference natural (free of stresses) form. Instead we used the continuous family being only locally free from stresses. To formulate the boundary value problem, continuous families of reference, intermediate and actual forms and corresponding families of deformations are defined. The deformations, belonging to these families, locally represent implants (local deformations of reference forms into intermediate ones) and deformations that bring intermediate forms into actual ones. Relations for stresses and strains in such bodies are obtained under the assumption that the displacement gradients are small with respect to unity and satisfy the kinematic hypothesis of the technical plate theory. Under these assumptions the equilibrium equations are derived. They include specific terms which determine formal loading that is caused by incompatible deformations. Axisymmetric problems for a circular substrate under various types of fixing and tension on the boundary, which characterize the conditions of the experiment, are obtained. The theoretical distribution for displacements of the substrate surface is formulated upon the obtained solution. They are intended to identify incompatible deformations that cause bending during the deposition process. The experimental measuring setup is constructed according to a holographic scheme of displacement measurements in real time. The deposition process is carried out in a cylindrical chamber with flange fastening of the cathode. The electrochemical process is implemented in sulphate electrolyte. As a result of comparing the theoretically obtained relations for bending surfaces of the substrate with the experimental results, the parameters that characterize the substrate shrinkage and tension are estimated.

Junction conditions and local spacetimes in general relativity

In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. This framework is used to show that two Lorentzian manifolds can be matched by considering local deformations of the associated spacetime metrics. Based on the fact that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local spacetimes in general relativity. Furthermore, it is shown that said approach not only extends the conventional thin shell formalism, but also allows the treatment of geometric problems that cannot be treated with standard gluing techniques.

The role of U(1)’s in 5d theories, Higgs branches, and geometry

We explore the Higgs branches of five-dimensional $$ \mathcal{N} $$ N = 1 quiver gauge theories at finite coupling from the paradigm of M-theory on local Calabi-Yau threefolds described as ℂ∗-fibrations over local K3’s. By properly counting local deformations of singularities, we find results compatible with unitary as opposed to special unitary gauge groups. We interpret these results by dualizing to both IIA on local K3’s with D6-branes, and to IIB with 5-branes. Finally, we find that, by compactifying the ℂ∗-fibers to tori, a well-known Stückelberg mechanism eliminates Abelian factors, and provides missing Higgs branch moduli in a very interesting way. This is also explained from the dual IIA and IIB viewpoints.