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Third Medium Contact
The third medium contact (TMC) is an implicit formulation used in contact mechanics. Contacting bodies are embedded in a highly compliant medium (the third medium), which becomes increasingly stiff under compression. The stiffening of the third medium allows tractions to be transferred between the contacting bodies when the third medium between the bodies is compressed. In itself, the method is inexact; however, in contrast to most other contact methods, the third medium approach is continuous and differentiable, which makes it applicable to applications such as topology optimization. History The method was first proposed in 2013 by , Jörg Schröder, and Alexander Schwarz, where a St. Venant-Kirchhoff material was used to model the third medium. This approach required explicit treatment of surface normals and continued to be used until 2017, when Bog et al. simplified the method by applying a Hencky material with the inherent property of becoming rigid under ultimate compressi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Third Medium Sliding Contact Example
Third or 3rd may refer to: Numbers * 3rd, the ordinal form of the cardinal number 3 * , a fraction of one third * Second#Sexagesimal divisions of calendar time and day, 1⁄60 of a ''second'', i.e., the third in a series of fractional parts in a sexagesimal number system Places * 3rd Street (other) * Third Avenue (other) * Highway 3 Music Music theory *Interval number of three in a musical interval **Major third, a third spanning four semitones **Minor third, a third encompassing three half steps, or semitones **Neutral third, wider than a minor third but narrower than a major third **Augmented third, an interval of five semitones **Diminished third, produced by narrowing a minor third by a chromatic semitone *Third (chord), chord member a third above the root *Degree (music), three away from tonic **Mediant, third degree of the diatonic scale **Submediant, sixth degree of the diatonic scale – three steps below the tonic **Chromatic mediant, chromatic relati ... [...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 Elasticity (physics), 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 (unit), pascal (Pa), although it is usually expressed in Pascal (unit), gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional analysis, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Topology Optimization With Third Medium Contact
3D, 3-D, 3d, or Three D may refer to: Science, technology, and mathematics * A three-dimensional space in mathematics Relating to three-dimensionality * 3D computer graphics, computer graphics that use a three-dimensional representation of geometric data * 3D display, a type of information display that conveys depth to the viewer * 3D film, a motion picture that gives the illusion of three-dimensional perception * 3D modeling, developing a representation of any three-dimensional surface or object * 3D printing, making a three-dimensional solid object of a shape from a digital model * 3D television, television that conveys depth perception to the viewer * 3D projection * 3D rendering * 3D scanning, making a digital representation of three-dimensional objects * Video game graphics#3D, 3D video game * Stereoscopy, any technique capable of recording three-dimensional visual information or creating the illusion of depth in an image * Three-dimensional space Other uses in science and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Plasticity
Crystal plasticity is a mesoscale computational technique that takes into account crystallographic anisotropy in modelling the mechanical behaviour of polycrystalline materials. The technique has typically been used to study deformation through the process of slip, however, there are some flavors of crystal plasticity that can incorporate other deformation mechanisms like twinning and phase transformations. Crystal plasticity is used to obtain the relationship between stress and strain that also captures the underlying physics at the crystal level. Hence, it can be used to predict not just the stress-strain response of a material, but also the texture evolution, micromechanical field distributions, and regions of strain localisation. The two widely used formulations of crystal plasticity are the one based on the finite element method known as Crystal Plasticity Finite Element Method (CPFEM), which is developed based on the finite strain formulation for the mechanics, and a sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TMC Friction Model Example
TMC may stand for: Companies and brands *Thinking Machines Corporation, a defunct supercomputer company *Toyota Motor Corporation, a Japanese automobile manufacturer *Toshiba Memory Corporation * Trans Mountain Corporation *Transportation Management Center, a division of American shipping company C.H. Robinson *Transportation Manufacturing Corporation, a defunct bus manufacturer based in Roswell, New Mexico *Triumph Motor Company, a defunct British automotive manufacturer Educational and medical institutions *Texas Medical Center, a medical institution * Texas Military College, a private junior college, high school, and primary school located in Terrell, Texas that operated from 1915 to 1949 * Thanjavur Medical College, a golden jubilee college in Tamil Nadu, India *Thomson Medical Centre, a private hospital in Novena, Singapore *Thurgood Marshall College, a college within University of California, San Diego * Thursday Morning Club, a not-for-profit organization in Madison, New Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sliding Bulge Problem
Sliding may refer to: *Sliding (dance), also floating or gliding, a group of footwork-oriented dance techniques *Slide (baseball), an attempt by a baseball runner to avoid getting tagged out *Sliding (motion) See also *Slide (other) Slide or Slides may refer to: Places * Slide, California, former name of Fortuna, California Arts, entertainment, and media Music Albums * ''Slide'' (Lisa Germano album), 1998 * ''Slide'' (George Clanton album), 2018 *''Slide'', by Patrick Glee ... * Slider (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deformation Gradient Tensor
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 field Deformation gradient tensor The deformation gradient tensor \mathbf F(\mathbf X,t) = F_ \mathbf e_j \otimes \mathbf I_K is related to both the reference and current configuration, as seen by the unit vectors \mathbf e_j and \mathbf I_K\,\!, therefore it is a ''two-point tensor''. Two types of deformation gradient tensor may be defined. Due to the assumption of continuity of \chi(\mathbf X,t)\,\!, \mathbf F has the inverse \mathbf H = \mathbf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trace (linear Algebra)
In linear algebra, the trace of a square matrix , denoted , is the sum of the elements on its main diagonal, a_ + a_ + \dots + a_. It is only defined for a square matrix (). The trace of a matrix is the sum of its eigenvalues (counted with multiplicities). Also, for any matrices and of the same size. Thus, similar matrices have the same trace. As a consequence, one can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect to a basis are similar. The trace is related to the derivative of the determinant (see Jacobi's formula). Definition The trace of an square matrix is defined as \operatorname(\mathbf) = \sum_^n a_ = a_ + a_ + \dots + a_ where denotes the entry on the row and column of . The entries of can be real numbers, complex numbers, or more generally elements of a field . The trace is not defined for non-square matrices. Example Let be a matrix, with \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a Scalar field, scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the Del, nabla operator), or \Delta. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical coordinates, cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian of a function at a point measures by how much the average value of over small spheres or balls centered at deviates from . The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distributio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
