Stress, Strain, and the Basic Equations of Solid Mechanics

2016 ◽  
pp. 21-61
Author(s):  
C. K. H. Dharan ◽  
B. S. Kang ◽  
Iain Finnie
Keyword(s):  
Solid Mechanics ◽  
Stress Strain ◽  
Basic Equations

Introduction to the Basics of Stress

2020 ◽  
pp. 1-21
Author(s):  
Karthik Selva Kumar Karuppasamy ◽  
Niranjan Sahoo ◽  
Balaji Selvaraj
Keyword(s):  
Body Force ◽  
The Body ◽  
External Loading ◽  
Stress System ◽  
Stress Equation ◽  
Stress Strain ◽  
Basic Concepts ◽  
Stress States ◽  
Basic Equations ◽  
New Machine

For the design and development of new machine components, the researchers and engineers must have an extreme understanding of the stress, strain, and the basic equations/laws relating the stress to the strain. In this chapter, the authors show the basic concepts of stress developed in a component concerning the external loading and the loading concerning the body force. In this chapter, the following aspects were proposed to be briefly discussed: type of stresses, introduction to stress at particular node, stress equation relates the equilibrium of body, laws related to transformation of stress, states of stress, and sample solved problems related to the simple state of the stress system.

scholarly journals Evaluation of a Simple UQ Approach to Compensate for Sparse Stress-Strain Curve Data in Solid Mechanics Applications

2017 ◽  
Author(s):  
Vicente J. Romero ◽  
J. F. Dampsey ◽  
Ben Schroeder ◽  
John Lewis ◽  
Nicole Breivik ◽  
...  
Keyword(s):  
Solid Mechanics ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain

Teaching Stress Transformation Through Laboratory Experiments

2013 ◽  
Author(s):  
O. Aluko
Keyword(s):  
Student Performance ◽  
Solid Mechanics ◽  
Teaching Strategy ◽  
Independent Study ◽  
Test Facility ◽  
Normal Strain ◽  
Stress Strain ◽  
Principal Coordinates ◽  
Strain Transformation ◽  
Hands On

This paper describes a hands-on laboratory solid mechanics project which was supervised as an independent study. The experimental study and analysis were focused on strain and stress transformation on cantilever beam subjected to bending within elastic range. A combination of five different metals and two types strain rosette arrangements were used in the experimentation. The project involves the design and construction of test facility and experimental analysis of tested piece. The samples of measured data and analysis are reported in this paper. The strains in rectangular and principal coordinates which were computed from measured strains enabled the stress in both coordinates to be determined. This analysis enables the students to determine experimentally, that the sum of normal strain and stresses are invariant. The teaching strategy employed to integrate fundamental theories with hands-on experiences is described. The effectiveness of the laboratory project in enhancing student learning of stress-strain transformation and project management skill was demonstrated by monitoring student performance improvements over the duration of the project. The success of this project leads to an experiment for teaching students stress-strain transformation in mechanics of materials laboratory.

scholarly journals Derivation of analytical dependencies for determining stiffness parameters of vibration isolators of vibratory machine

2020 ◽  
Vol 6 (3-4) ◽  
pp. 1-8
Author(s):  
Oleksii Lanets ◽  
◽  
Oleksandr Kachur ◽  
Vitaliy Korendiy ◽  
◽  
...  
Keyword(s):  
Computer Simulation ◽  
Large Scale ◽  
Strain State ◽  
Vibration Isolation ◽  
Solid Mechanics ◽  
Machine Building ◽  
Stress Strain ◽  
Vibration Isolators ◽  
Stress Strain State ◽  
Vibratory Equipment

Problem statement. While designing vibration isolators, the essential attention should be paid to the safety factors such as the levels of vibration and noise, as well as to the material and the structure of isolators. In major vibratory technological equipment, there are used full-metal vibration isolators, which can be designed in the form of coil (cylindrical, conical, helico-spiral) or flat (leaf-type, disc-type) springs. The problems of stress-strain analysis of metal springs used for vibration isolation of various vibratory equipment are of urgent interest among the designers and researcher. The engineering techniques of step-by-step calculation of full-metal vibration isolators of different types of vibratory technological machines are not thoroughly presented in the modern information resources. Purpose. The present paper is aimed at developing and implementing the detailed algorithm of determining the stiffness parameters of the metal coil springs used for vibration isolation of large-scale vibratory machines. Methodology. The investigations are carried out using the basic laws and principles of solid mechanics and theory of vibrations. The calculations were conducted using MathCAD software; the computer simulation of the spring’s stress-strain state was performed using SolidWorks software. Findings (results) and originality (novelty). The improved design of the vibratory conveyer-separator is considered. The engineering technique of calculating the passive vibration isolators of various vibratory equipment designed in the form of metal coil springs is developed. The proposed technique is implemented while designing the vibration isolation system of the vibratory conveyer-separator. The system’s operational characteristics are determined, and the computer simulation of the springs stress-strain state is carried out. Practical value. The proposed design of the vibratory conveyer-separator can be implemented in various industries (machine-building, chemical, pharmaceutical, food-processing, construction, mining, metallurgy, textile industries etc.) for conveying different loose, bulky and piecewise products, and separating them into fractions of different sizes. Scopes of further investigations. While carrying out further investigations, it is necessary to analyse the influence of the proposed design of vibratory conveyer-separator on the foundation during its operation, and to consider the necessary of applying the additional fixation systems.

Methodology for the Experimental Assessment of True Stress-Strain Curves After Necking Employing Cylindrical Tensile Specimens: Experiments and Parameters Calibration

2013 ◽  
Author(s):  
Gustavo Henrique B. Donato ◽  
Grace Kelly Q. Ganharul
Keyword(s):  
Real Time ◽  
Cross Sections ◽  
Solid Mechanics ◽  
Structural Integrity ◽  
Equivalent Stress ◽  
Tensile Tests ◽  
Plastic Instability ◽  
True Stress ◽  
Stress Strain ◽  
Physical Measurements

Simulations and structural integrity evaluations including severe plasticity have undergone significant expansion during recent years (e.g. fracture mechanics FE models including ductile tearing and/or generalized yielding), which demand accurate true stress-strain data until fracture. This is a consequence of the use of high toughness ductile materials subjected to severe loadings and high levels of operational efficiency and optimization. However, tensile tests present one inconvenience when providing such data, since the occurrence of plastic instability (necking) complicates the direct assessment of true stress-strain curves until final fracture. Two main difficulties can be pointed out: i) the nonuniform geometry assumed by the cross sections along its length and; ii) the imposition of a complex triaxial stress state. The first occurrence can only be overcome by real-time physical measurements. The second occurrence demands a correction model to provide an equivalent stress including triaxial effects. Current authors recently demonstrated that even the well-known Bridgman’s correction presents limitations, particularly for strains greater than ∼ 0.50–0.60, which motivated proposals to better describe the geometrical evolution of necking minimizing the need for real-time physical measurements [1]. As a new step in this direction, this work presents three key contributions: i) first, experiments regarding the geometrical evolution of necking were largely extended incorporating 10 materials to corroborate the validity of the recently proposed model (including Carbon, stainless steels and copper); ii) second, and for the same materials, the necking region was investigated in more details to verify to which extent an osculating circle well describes the high deformation region. A new model could be proposed to better support future solid mechanics analyses regarding equilibrium and stress/strain fields; iii) finally, a modified Bridgman’s model is proposed, followed by recommended practices for testing. The results provide further support to σ-ε assessment considering severe plasticity and demanding less physical measurements.

scholarly journals Pore pressure when compacting two-phase soil

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Elefhan Agakhanov ◽  
Murad Agakhanov
Keyword(s):  
Pore Pressure ◽  
Strain State ◽  
Solid Mechanics ◽  
Water Pressure ◽  
Deformable Solid ◽  
Stress Strain ◽  
Two Phase ◽  
Tangential Stresses ◽  
Stress Strain State ◽  
Special Cases

In modern conditions, in relation to the total amount of accumulated professional knowledge, the volume of active information resources increases, and construction practice is constantly enriched with new experimentally-theoretically based accurate knowledge. Therefore, various programs are widely used when solving problems in ground bases. Despite the fact that modern numerical methods allow solving problems of any complexity, it should be noted that experimental and analytical methods are still relevant, and it is an effective combination of methods that leads to the development of mechanics, an organic combination of experimental research methods with the enormous computational capabilities of modern supercomputers. Methods for modeling the action of bulk forces are widely used in problems of deformable solid mechanics. Many known solutions have limitations and are given for special cases. The authors present the theoretical foundations of the elastic analogy method for modeling the effect of pore pressure on the soil. When posing the question, the following assumption is made that the liquid filling the pores of the soil does not perceive shear deformation. Tangential stresses that occur in the ground are only perceived by the ground skeleton. The water that fills the pores does not resist tangential stresses. In this case, the deformation of the soil skeleton from the action of hydrostatic water pressure, respectively, is a volumetric deformation. In this case, the components of the ball stress tensor are equal to the pore pressure. The article considers the use of the theory of volume forces in modeling the effect of pore pressure in the process of compaction of two-phase soil. In this case, we consider a one-dimensional problem for the case of deformation (compaction) of a two-phase soil layer thickness under the action of a distributed load of constant intensity. We believe that the consolidated layer lies on a rocky undeformable base. The authors consider various drainage conditions for the surfaces of the consolidated layer. Expressions are given for determining stresses and precipitation with creep, for the instantaneous stress-strain state and the final stress-strain state.

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