Novel Methods for the Computation of Small-Strain Damping Ratios of Soils from Cyclic Torsional Shear and Free-Vibration Decay Testing

This paper illustrates two novel methods for computing the small-strain hysteretic material damping ratio, λmin, of soils from the cyclic torsional shear (TS) and computing the small-strain viscous material damping ratio, Dmin, from the free-vibration decay (FVD) testing. Both λmin and Dmin are challenging to measure, due to the significant level of ambient noise at small strains (<10−4%). A two-step method is proposed combining the Fourier Transform and a phase-based data fitting method for torsional shear testing, and this method can effectively eliminate the ambient noise at small strains. A Hilbert Transform-based method is proposed for the free-vibration decay testing in order to achieve a more accurate measurement of the viscous material damping ratio, D, at different strain levels, especially at small strains. The improved λmin and Dmin at small strains are compared to data available in the literature. The two novel methods are shown to be accurate in computing the small-strain damping ratios.

Deformation/strain and stress

The necessary vocabulary, fundamentals and definitions for ‘deformation’, ‘strain’ and ‘stress’ are provided. Types of deformation, incremental or progressive, pure shear and simple shear, deformation regimes, flow lines and vorticity number, shortening, extension and strain measurements are explained. The concept of stress acting on a surface, through its normal and shear components is presented, along with their graphical representation using the Mohr diagram. In the elastic domain that characterizes very small strains, the relationship between stress and strain is discussed through the elastic constants among which the shear modulus and Poisson’s coefficient are notable. Finally, the stress–strain relationships for the ductile (plastic) and viscous behaviours, characteristic of large deformations, are discussed. These form the basis of understanding the rheology of the Earth, and hence Tectonics.

A Novel Flow Model of Strain Hardening and Softening for Use in Tensile Testing of a Cylindrical Specimen at Room Temperature

We develop a new flow model based on the Swift method, which is both versatile and accurate when used to describe flow stress in terms of strain hardening and damage softening. A practical issue associated with flow stress at room temperature is discussed in terms of tensile testing of a cylindrical specimen; we deal with both material identification and finite element predictions. The flow model has four major components, namely the stress before, at, and after the necking point and around fracture point. The Swift model has the drawback that not all major points of stress can be covered simultaneously. A term of strain to the third or fourth power (the “second strain hardening exponent”), multiplied and thus controlled by a second strain hardening parameter, can be neglected at small strains. Any effect of the second strain hardening exponent on the identification of the necking point is thus negligible. We use this term to enhance the flexibility and accuracy of our new flow model, which naturally couples flow stress with damage using the same hardening constant as a function of damage. The hardening constant becomes negative when damage exceeds a critical value that causes a drastic drop in flow stress.

Modern Displacement Measuring Systems Used in Geotechnical Laboratories: Advantages and Disadvantages

The paper presents the contemporary displacement measurement systems used in geotechnical laboratories during the determination of soil precise mechanical parameters, e.g., the shear modules G: initial and in the range of small and very small strains. In the laboratory, researchers use standard sensors for measuring deformation, pressure, and force as well as modern measuring systems such as linear variable differential transformers (LVDT), proximity transducers (PT), magnetic encoder sensors with fiber Bragg grating (FBG), or methods based on laser or X-ray measurement. None of the measurements are universal and their use depends on the type of soil (cohesive, non-cohesive), its condition (loose or dense, stiff or very soft), and its characteristic properties (e.g., organic soil, swelling soil). This study points out the interesting equipment solutions and presents the guidelines for selecting appropriate methods of deformation measurement.

RESEARCH OF THE TECHNOLOGY OF OPENING HOLES IN COMPACT AND POWDER MATERIALS

This article is devoted to one of the important problems of mechanical engineering, including processing by cutting and deploying in sintered antifriction powder material in optimal modes with maximum performance. The study was conducted for small diameter cylindrical bushings. Processing of bushings was carried out by reamers from high-speed and carbide tools on materials from porous powder and cast iron. It is established that the temperature of the tools should not exceed the permissible upper limits, for pressing the bushings, it is necessary to use planting with small strains in the cold state. Keywords: engine valve, bushing, powder material, cast iron, reamer, cold pressing.

Analytical Solution and Consolidation Analysis of One-dimensional Large Strain Consolidation Differential Equation

Abstract:: According to the universal one-dimensional consolidation equation introduced by Gibson, the governing equation with the excess pore water pressure as the control variable is derived, and the Fourier series solution under the boundary condition of single-sided drainage is deduced in detail by the standard mathematical physical method. It verifies the correspondence between the analytical solution and the numerical solution from a theoretical point of view. Using this analytical solution, the nonlinear distribution of the excess pore pressure along the depth direction is obtained, and the traditional small strain consolidation is compared in terms of the average consolidation degree and the final settlement. Soft soil foundation, large deformation foundation Derive a consolidation equation for soft soils with large deformations using the super-static pore pressure as the control variable Formula derivation, Example analysis Based on Gibson's general equation of consolidation and its theory, the detailed derivation process of differential equations with excess pore water pressure as the control variable is given. According to the example, the image shows the distribution of excess pore pressure with depth, and comparative analysis of large and small strains, If all other conditions are the same, When mv1=1 MPa-1, it can be calculated according to the large and small strains, but when mv1≥3MPa-1, the two errors are large, The calculation must be considered separately.

Analysis of the Effect of Shape Factor on Cork–Rubber Composites under Small Strain Compression

Like other types of elastomers, different geometries of the same cork–rubber material present different mechanical behaviour when subject to compression between bonded plates. To validate the application of Hooke’s Law on cork–rubber materials, under compression at small strains, a set of experimental and numerical analyses has been conducted. Using finite element analysis, a methodology is described to relate frictionless and frictional compression between a cork–rubber sample and loading plates. Based on that, the performance of square cross-section blocks with other dimensions can be evaluated. The results obtained by this approach showed a good agreement with experimental compression tests and with outputs from other models available in the literature relating Young and apparent compression moduli.

Kinematics

This chapter develops the necessary mathematics for describing general deformations that a solid body may undergo, a topic known as kinematics. Definitions of motion, displacement, velocity, and acceleration which are vectors, and the deformation gradient and displacement gradient which are tensors are given. The mapping of material vectors by the deformation gradient tensor as a basic concept in describing the large deformation kinematics of a deformable body is presented. The powerful polar decomposition theorem is discussed and applied to the deformation gradient tensor to show that it can be decomposed into a stretch followed by a rotation, or a rotation followed by a stretch. Non-linear measures of strain are defined in terms of the stretch tensors. The important case of small deformations, which results in linear measures of strain, is discussed. For small strains the important decomposition of the state of strain that separates a volumetric strain from a non-volumetric or deviatoric strain is presented.