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Strain Energy Release Rate
In fracture mechanics, the energy release rate, G, is the rate at which energy is transformed as a material undergoes fracture. Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, and is thus expressed in terms of energy per unit area. Various energy balances can be constructed relating the energy released during fracture to the energy of the resulting new surface, as well as other dissipative processes such as plasticity and heat generation. The energy release rate is central to the field of fracture mechanics when solving problems and estimating material properties related to fracture and fatigue. Definition The energy release rate G is defined as the instantaneous loss of total potential energy \Pi per unit crack growth area s, : G \equiv -\frac , where the total potential energy is written in terms of the total strain energy \Omega, surface traction \mathbf, displacement \mathbf, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fracture Mechanics
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip. A number of different parameters have been developed. When the plastic zone at the tip of the crack is small relative to the crack length the stress state at the crack tip is the result of elastic forces within the material and is termed linear elastic fracture mechanics (LEFM) and can be characterised using the stress intensity factor K. Although the load on a crack can be arbitrary, in 1957 G. Irwin fou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress \sigma (force per unit area) and axial strain \varepsilon (proportional deformation) in the linear elastic region of a material and is determined using the formula: E = \frac Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa). Example: * Silly Putty (increasing pressure: length increases quickly, meaning tiny E) * Aluminum (increasing pressure: length increases slowly, meaning high E) Higher Young's modulus corresponds to greater (lengthwise) stiffness. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain Energy Release Rate
In fracture mechanics, the energy release rate, G, is the rate at which energy is transformed as a material undergoes fracture. Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, and is thus expressed in terms of energy per unit area. Various energy balances can be constructed relating the energy released during fracture to the energy of the resulting new surface, as well as other dissipative processes such as plasticity and heat generation. The energy release rate is central to the field of fracture mechanics when solving problems and estimating material properties related to fracture and fatigue. Definition The energy release rate G is defined as the instantaneous loss of total potential energy \Pi per unit crack growth area s, : G \equiv -\frac , where the total potential energy is written in terms of the total strain energy \Omega, surface traction \mathbf, displacement \mathbf, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nodal Release Debounded
Nodal homolog is a secretory protein that in humans is encoded by the ''NODAL'' gene which is located on chromosome 10q22.1. It belongs to the transforming growth factor beta superfamily (TGF-β superfamily). Like many other members of this superfamily it is involved in cell differentiation in early embryogenesis, playing a key role in signal transfer from the primitive node, in the anterior primitive streak, to lateral plate mesoderm (LPM). Nodal signaling is important very early in development for mesoderm and endoderm formation and subsequent organization of left-right axial structures. In addition, Nodal seems to have important functions in neural patterning, stem cell maintenance and many other developmental processes, including left/right handedness. Signaling Nodal can bind type I and type II serine/threonine kinase receptors, with Cripto-1 acting as its co-receptor. Signaling through SMAD 2/3 and subsequent translocation of SMAD 4 to the nucleus promotes the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain Energy Release Rate
In fracture mechanics, the energy release rate, G, is the rate at which energy is transformed as a material undergoes fracture. Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, and is thus expressed in terms of energy per unit area. Various energy balances can be constructed relating the energy released during fracture to the energy of the resulting new surface, as well as other dissipative processes such as plasticity and heat generation. The energy release rate is central to the field of fracture mechanics when solving problems and estimating material properties related to fracture and fatigue. Definition The energy release rate G is defined as the instantaneous loss of total potential energy \Pi per unit crack growth area s, : G \equiv -\frac , where the total potential energy is written in terms of the total strain energy \Omega, surface traction \mathbf, displacement \mathbf, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simpl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DCB Specimen Path
DCB may stand for: * Dame Commander of the Order of the Bath * Development Credit Bank, a private-sector bank in India * David Campbell Bannerman (born 1960), a British politician * David Crowder Band, a Christian rock band * ''Dictionary of Canadian Biography'' * Dead cat bounce, a figurative term used by traders in the finance industry * Dulwich College Beijing, a British international school in Beijing, China In science and technology * Disconnecting circuit breaker, a high-voltage circuit breaker with disconnectors integrated into the breaking chamber * Data center bridging, in computer networking * Data Control Block, a data structure for accessing data sets on IBM mainframes * Double Cantilever Beam, a test specimen in fracture mechanics * Dichlorobenzene * Digital Control Bus, a proprietary MIDI-like interface by Roland Corporation * Direct Copper Bonding, also Direct Bonding Copper, a type of power electronic substrate * Direct Carrier Billing, a method of doing digit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integral'' is used as well, although that is typically reserved for line integrals in the complex plane. The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on intervals. Many simple formulae in physics, such as the definition of work as W=\mathbf\cdot\mathbf, have natural continuous analogues in terms of line integrals, in this case \textstyle W = \int_L \mathbf(\mathbf)\cdot d\mathbf, which computes the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
J-integral
The J-integral represents a way to calculate the strain energy release rate, or work ( energy) per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov and independently in 1968 by James R. Rice,J. R. Rice, ''A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks'', Journal of Applied Mechanics, 35, 1968, pp. 379–386. who showed that an energetic contour path integral (called ''J'') was independent of the path around a crack. Experimental methods were developed using the integral that allowed the measurement of critical fracture properties in sample sizes that are too small for Linear Elastic Fracture Mechanics (LEFM) to be valid. Lee, R. F., & Donovan, J. A. (1987). J-integral and crack opening displacement as crack initiation criteria in natural rubber in pure shear and tensile specimens. Rubber chemistry and technology, 60(4), 674–688/ref> These experiments ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphical Illustration Of G Under Fixed Displacement And Fixed Load Conditions
Graphics () are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain. In contemporary usage, it includes a pictorial representation of data, as in design and manufacture, in typesetting and the graphic arts, and in educational and recreational software. Images that are generated by a computer are called computer graphics. Examples are photographs, drawings, line art, mathematical graphs, line graphs, charts, diagrams, typography, numbers, symbols, geometric designs, maps, engineering drawings, or other images. Graphics often combine text, illustration, and color. Graphic design may consist of the deliberate selection, creation, or arrangement of typography alone, as in a brochure, flyer, poster, web site, or book without any other element. The objective can be clarity or effective communication, association with other cultural elements, or merely the creation of a distinctive style. Graphics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DCB Specimen
DCB may stand for: * Dame Commander of the Order of the Bath * Development Credit Bank, a private-sector bank in India * David Campbell Bannerman (born 1960), a British politician * David Crowder Band, a Christian rock band * ''Dictionary of Canadian Biography'' * Dead cat bounce, a figurative term used by traders in the finance industry * Dulwich College Beijing, a British international school in Beijing, China In science and technology * Disconnecting circuit breaker, a high-voltage circuit breaker with disconnectors integrated into the breaking chamber * Data center bridging, in computer networking * Data Control Block, a data structure for accessing data sets on IBM mainframes * Double Cantilever Beam, a test specimen in fracture mechanics * Dichlorobenzene * Digital Control Bus, a proprietary MIDI-like interface by Roland Corporation * Direct Copper Bonding, also Direct Bonding Copper, a type of power electronic substrate * Direct Carrier Billing, a method of doing digit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
