WebDeformation Stretch and Strain Tensors (Part II) — Lesson 6 Continuing the discussion of stretch and strain tensors, in this lesson we discuss the mathematical properties of the Right Cauchy-Green stretch tensor and the Lagrange strain tensor. Answers to Frequently Asked Questions In this video we will answer the following question: Is it possible to … WebLecture 11 part 4
Finite strain theory - Wikipedia
WebApr 13, 2024 · Here is a picture of the deformation and the reference coordinate system. the deformation is given by x = X+0.5Z ,y=Y ,z=Z. The questions ask us to transform between … In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation tensor or Green's deformation tensor, defined as: C = F T F = U 2 or C I J = F k I F k J = ∂ x k ∂ X I ∂ x k ∂ X J . {\displaystyle \mathbf {C} =\mathbf {F} ^{T}\mathbf {F} =\mathbf {U} ^{2}\qquad … 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 related to both the reference and current configuration, as seen by the unit vectors $${\displaystyle \mathbf {e} _{j}}$$ See more 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 … 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 The displacement of a body has two components: a rigid-body displacement and a deformation. • A rigid-body displacement consists of a simultaneous See more Several rotation-independent deformation tensors are used in mechanics. In solid mechanics, the most popular of these are the right and left Cauchy–Green deformation tensors. Since a pure rotation should not induce any strains in a … See more A representation of deformation tensors in curvilinear coordinates is useful for many problems in continuum mechanics such as nonlinear shell … See more lam 002a
Analysis of Deformation in Solid Mechanics - COMSOL …
WebThe Right Cauchy-Green Deformation Tensor The tensor is termed the right Cauchy-Green deformation tensor. As shown above, it is a positive definite symmetric matrix, thus, it has three positive real eigenvalues and three perpendicular eigenvectors. WebIn terms of the basis of , it is straightfoward to verify that Here, are the components of the right Cauchy-Green tensor, and is the Kronecker delta symbol. The diagonal component fields are called axial , or tensile strains, while the off-diagonal component fields , with are called shear strains. WebThe right Cauchy-Green tensor C ̲ = F ̲ T F ̲ and left Cauchy-Green tensor b ̲ = F ̲ F ̲ T describe the strain in the reference and the current configuration, respectively. In contrast to the multiplicative split of F ̲, the stress state of the generalized Maxwell model in the reference configuration is described by the second Piola ... jeong lizardi p.c