On thermoelastic deformation of a transversally isotropic medium in 3D construction printing

A three-dimensional dynamic model of a thermoelastic transversely isotropic medium is used to describe the thermoelastic deformation of materials with anisotropy of elastic properties with a selected direction of anisotropy. Such materials are layered and composite materials used in construction, mechanical engineering, aircraft and shipbuilding, soils in permafrost conditions, glaciers, as well as rocks (basalt, sandstone, marble, limestone, shale, and others). The study of this model, in particular, is relevant in connection with the use of 3D printers in construction. This is due to the fact that it is necessary to select the heating mode of the 3D printer head, in which cracks will not form during the cooling of the polystyrene concrete layers.We study this model using the group analysis methods, which is one of the most powerful and effective tools for obtaining exact solutions. The group stratification of the system of second-order differential equations defining this model is carried out. A system of first-order differential equations is obtained, which is equivalent to the equations of the original model. The solution describing a traveling wave for this system is obtained, that depends on arbitrary elements: parameters and function. For the specific sets of these elements, we study a deformation of a sphere and cube located inside a thermoelastic transversely isotropic medium with increasing time is found. The corresponding graphs are given.

Isotropic and anisotropic elastic scatterers of underwater sound

Object and purpose of research. This paper discusses diffraction parameters of isotropic and anisotropic elastic scatterers, demonstrating that transversally isotropic bodies with a certain orientation of their planes of isotropy might be regarded as isotropic scatterers with similar size, shape and physical parameters. Materials and methods. Diffraction theory methods in solution of boundary problems and equations of dynamic elasticity theory for isotropic and anisotropic bodies. Main results. Calculation of moduli for angular parameters, as well as of relative back-scattering sections for isotropic and anisotropic scatterers of various shapes. Conclusion. The studies demonstrated that if transversally isotropic bodies of various shapes have a certain orientation of their planes of isotropy and a certain vector of a plane wave falling onto them, their reflection parameters, like relative backscattering sections and angular scattering characteristic of an anisotropic body are the same as those for isotropic bodies of similar size, shape and elasticity.

Identifying Elastic Constants for PPS Technical Material When Designing and Printing Parts Using FDM Technology

This paper introduces a methodology to study the anisotropic elastic constants of technical phenylene polysulfide thermoplastic (PPS), printed using fused deposition modeling (FDM) in order to provide designers with a guide to achieve the required mechanical properties in a printed part. The properties given by the manufacturer are usually taken from injected samples and these are not the real properties for printed parts. Compared to other plastic materials, PPS offers higher mechanical and thermal resistance, lower moisture absorption, higher dimensional stability, is highly resistant to chemical attacks and environmental aging, and its fireproof performance is good. One of the main difficulties presented when calculating and designing for FDM printing is that printed parts present anisotropic behavior i.e., they do not have the same properties in different directions. Haltera-type samples were printed in the three manufacturing directions according to optimum parameters for material printing, aimed at calculating the anisotropic matrix of the material. The samples were tested in order to meet standards and values for elastic modulus, shear modulus and tensile strength were obtained, using Digital Image Correlation System to measure the deformations. An approximated transversally isotropic matrix was defined using the obtained values. The fracture was analyzed using SEM microscopy to check whether the piece was printed correctly. Finally, the obtained matrix was validated by a flexural test and a finite element simulation.

THEORETICAL SUBSTANTIATION OF THE MECHANISM PATTERNS OF THE MANMADE BASE “STRUCTURAL GEOTECHNICAL SOLID”

When building on weak water-saturated soils, manmade base in the form of a "structural geotechnical solid" are increasingly used. The article provides a theoretical substantiation for the use of a model of a transversally isotropic material with the given deformation characteristics for the design of such structures. The problem of determining the radius of a rigid cylindrical element during its formation in an elastic-plastic porous medium under normal pressure of jet-grouting of soil is considered. A method is proposed for determining the effective modulus of deformation of a "structural geotechnical solid" with the allocation of a representative volume - a periodicity cell, within which the geometric averaging of deformation characteristics is performed depending on the volume contribution of its components. Analysis of the results of modeling the joint operation of the base-building system using the proposed base model showed the effectiveness of its application.

Numerical Modeling of the Process of Thermoplastic Deformation of Transversally Isotropic Parallelepipeds

The paper proposes a modified version of the iterative method for numerically solving a three-dimensional uncoupled boundary-value problem that describes the process of thermoplastic deformations of a transversely isotropic parallelepiped. A discrete analogue of the boundary value problem is compiled on the basis of the finite-difference method. A recurrent finite-difference relation is written which allows one to find the desired components of the displacement vector in combination with the iterative method. It is assumed that, at a first approximation, the values of the sought displacements in the internal nodes are trivial. The essence of the method is demonstrated by solving the thermoplastic boundary-value problem for a transversely isotropic parallelepiped. The proposed method can be applied to solve related problems of dynamic thermoplasticity.

Effective Characteristics of the Multi-Modular Composites under Transverse Stretching

In this article is determined the ratio between effective elastic characteristics of the fibrous transversally isotropic material. Fibrous uniaxial material, which consists of the isotropic elastic matrix and fiber, is in the focus of attention. It is assumed that mechanical properties of components under stretching and compression are different, notably matrix material and fiber material are multi-modular. Transverse stretching and transverse compression of composite cell are considered. Two problems for each type of strain are solved. In the first problem stresses and displacements of matrix and fiber under conditions of their common axisymmetrical deformation are determined. Subsequently similar characteristics for the cell deformation of the homogeneous transversally isotropic material as a composite are determined. Ratio between effective composite’s characteristics is solved from the conditions of equality of the axial displacements of the composite’s cell and radial displacements on its surface. The relation of the calculated ratio from volume fraction of fiber in a composite is analyzed.