WebA strain is a normalized measure of deformation representing the displacement between particles in the body relative to a reference length.The concept of strain is used to … The concept of strain is used to evaluate how much a given displacement differs locally from a rigid body displacement. One of such strains for large deformations is the Lagrangian finite strain tensor, also called the Green-Lagrangian strain tensor or Green – St-Venant strain tensor, defined as or as a function of … See more 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 … See more The deformation gradient tensor $${\displaystyle \mathbf {F} (\mathbf {X} ,t)=F_{jK}\mathbf {e} _{j}\otimes \mathbf {I} _{K}}$$ is … See more A representation of deformation tensors in curvilinear coordinates is useful for many problems in continuum mechanics such as nonlinear shell theories and large plastic deformations. Let See more • Infinitesimal strain • Compatibility (mechanics) • Curvilinear coordinates See more The displacement of a body has two components: a rigid-body displacement and a deformation. • A rigid-body displacement consists of a simultaneous translation and rotation of the body without changing its shape or size. • Deformation … See more Several rotation-independent deformation tensors are used in mechanics. In solid mechanics, the most popular of these are the right and left … See more The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on bodies. These allowable conditions leave the body … See more
Finite strain theory - Wikipedia
WebIn physics and continuum mechanics, deformation is the transformation of a body from a reference configuration to a current configuration. [1] A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, [2] intrinsic activity (e.g. muscle contraction ), body forces (such as ... WebThe Lagrange description of strain is similar to the Cauchy-Green description of the quadratic strain (Equation 9). It only uses a different definition of the quadratic … how many half steps are in a major third
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WebComparing the minimum thickness strain for each foil thickness (see Fig. 17.18), there is no correlation between the minimum thickness strain and the mean normal plastic anisotropy of the foil.Although the highest plastic anisotropy was obtained for the 50 µm-thick foil, the thickness reduction at the cup corner was larger than that for the 300 µm … WebThe Lagrangian finite strain tensor, also known as the Green-Lagrangian strain tensor, is a finite strain measure which includes higher order displacement terms; it defines gradients in terms of the original configuration. This measure is commonly used for materials undergoing large strains such as elastomers. Please note that at large strains ... WebMathematically, an elastic material is one for which a strain energy function can be defined. The scalar strain energy function is usually defined using a W. The strain energy … how many half steps are in an octave