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Simple Shear
Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other. In fluid mechanics In fluid mechanics, simple shear is a special case of deformation where only one component of velocity vectors has a non-zero value: :V_x=f(x,y) :V_y=V_z=0 And the gradient of velocity is constant and perpendicular to the velocity itself: :\frac = \dot \gamma , where \dot \gamma is the shear rate and: :\frac = \frac = 0 The displacement gradient tensor Γ for this deformation has only one nonzero term: :\Gamma = \begin 0 & & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end Simple shear with the rate \dot \gamma is the combination of pure shear strain with the rate of \dot \gamma and rotation with the rate of \dot \gamma: :\Gamma = \begin \underbrace \begin 0 & & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end \\ \mbox\end = \begin \underbrace \begin 0 & & 0 \\ & 0 & 0 \\ 0 & 0 & 0 \end \\ \mbox \end + \b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Shear
Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other. In fluid mechanics In fluid mechanics, simple shear is a special case of deformation where only one component of velocity vectors has a non-zero value: :V_x=f(x,y) :V_y=V_z=0 And the gradient of velocity is constant and perpendicular to the velocity itself: :\frac = \dot \gamma , where \dot \gamma is the shear rate and: :\frac = \frac = 0 The displacement gradient tensor Γ for this deformation has only one nonzero term: :\Gamma = \begin 0 & & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end Simple shear with the rate \dot \gamma is the combination of pure shear strain with the rate of \dot \gamma and rotation with the rate of \dot \gamma: :\Gamma = \begin \underbrace \begin 0 & & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end \\ \mbox\end = \begin \underbrace \begin 0 & & 0 \\ & 0 & 0 \\ 0 & 0 & 0 \end \\ \mbox \end + \b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base Isolation
Seismic base isolation, also known as base isolation, or base isolation system, is one of the most popular means of protecting a structure against earthquake forces. It is a collection of structural elements which should substantially decouple a superstructure from its substructure that is in turn resting on the shaking ground, thus protecting a building or non-building structure's integrity. Base isolation is one of the most powerful tools of earthquake engineering pertaining to the passive structural vibration control technologies. The isolation can be obtained by the use of various techniques like rubber bearings, friction bearings, ball bearings, spring systems and other means. It is meant to enable a building or non-building structure to survive a potentially devastating seismic impact through a proper initial design or subsequent modifications. In some cases, application of base isolation can raise both a structure's seismic performance and its seismic sustainability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Shear
In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body. It is an example of irrotational strain in which body is elongated in one direction while being shortened perpendicularly. For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyperelastic and fracture mechanical behaviour. Pure shear is differentiated from simple shear in that pure shear involves no rigid body rotation. The deformation gradient for pure shear is given by: F = \begin1&\gamma&0 \\\gamma&1&0\\0&0&1\end Note that this gives a Green-Lagrange strain of: E = \frac\begin\gamma^2&2\gamma&0\\2\gamma&\gamma^2&0\\0&0&0\end Here there is no rotation occurring, which can be seen from the equal off-diagonal components of the strain tensor. The linear approximation to the Green-Lagrange strain shows that the small strain tensor is: \epsilon = \frac\begin0&2\gamma&0\\2\gamma&0&0\\0&0&0\end which has only shearing components. See ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Strain Theory
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. Displacement The displacement of a body has two components: a rigid-body displacement and a deformation. * A rigid-body displacement consists of a simultaneous translation (physics) and rotation of the body without changing its shape or size. * Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration \kappa_0(\mathcal B) to a current or deformed configuration \kappa_t(\mathcal B) (Figure 1). A change in the confi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal Strain Theory
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation. With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made. The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson's Ratio
In materials science and solid mechanics, Poisson's ratio \nu ( nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, \nu is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. For soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression. Many typical solids have Poisson's ratios in the range of 0.2–0.3. The ratio is named after the French mathematician and physicist Siméon Poisson. Origin Poisson's ratio is a measure of the Poisson effect, the phenomenon in which ... [...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] |
Shear Modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackrel\ \frac = \frac = \frac where :\tau_ = F/A \, = shear stress :F is the force which acts :A is the area on which the force acts :\gamma_ = shear strain. In engineering :=\Delta x/l = \tan \theta , elsewhere := \theta :\Delta x is the transverse displacement :l is the initial length of the area. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M1L−1T−2, replacing ''force'' by ''mass'' times ''acceleration''. Explanation The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: * Young's modulus ''E'' describes the ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Strain
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of ''relative'' displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the temperature field of the body. The relati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Stress
Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. General shear stress The formula to calculate average shear stress is force per unit area.: : \tau = , where: : = the shear stress; : = the force applied; : = the cross-sectional area of material with area parallel to the applied force vector. Other forms Wall shear stress Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as: \tau_w:=\mu\left(\frac\right)_ Where \mu is the dynamic viscosity, u the flow velocity and y the distance from the wall. It is used, for example, in the description of arterial blood flow in which case which t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Shear
In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body. It is an example of irrotational strain in which body is elongated in one direction while being shortened perpendicularly. For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyperelastic and fracture mechanical behaviour. Pure shear is differentiated from simple shear in that pure shear involves no rigid body rotation. The deformation gradient for pure shear is given by: F = \begin1&\gamma&0 \\\gamma&1&0\\0&0&1\end Note that this gives a Green-Lagrange strain of: E = \frac\begin\gamma^2&2\gamma&0\\2\gamma&\gamma^2&0\\0&0&0\end Here there is no rotation occurring, which can be seen from the equal off-diagonal components of the strain tensor. The linear approximation to the Green-Lagrange strain shows that the small strain tensor is: \epsilon = \frac\begin0&2\gamma&0\\2\gamma&0&0\\0&0&0\end which has only shearing components. See ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vibration Control
In earthquake engineering, vibration control is a set of technical means aimed to mitigate seismic impacts in building and non-building structures. All seismic vibration control devices may be classified as ''passive'', ''active'' or ''hybrid'' where: * ''passive control devices'' have no feedback capability between them, structural elements and the ground; * ''active control devices'' incorporate real-time recording instrumentation on the ground integrated with earthquake input processing equipment and actuators within the structure; * ''hybrid control devices'' have combined features of active and passive control systems. When ground seismic waves reach up and start to penetrate a base of a building, their energy flow density, due to reflections, reduces dramatically: usually, up to 90%. However, the remaining portions of the incident waves during a major earthquake still bear a huge devastating potential. After the seismic waves enter a superstructure, there is a number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
