Volumetric strain

• v • t • e In infinitesimal strain theory is a mathematical approach to the description of the 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 The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the Infinitesimal strain tensor [ ] For infinitesimal deformations of a ‖ ∇ u ‖ ≪ 1 . In such a linearization, the non-linear or second-order terms of the finite strain tensor are neglected. Thus we have E = 1 2 ( ∇ X u + ( ∇ X u ) T + ( ∇ X u ) T ∇ X u ) ≈ 1 2 ( ∇ X u + ( ∇ X u ) T ) or E K L = 1 2 ( ∂ U K ∂ X L + ∂ U L ∂ X K + ∂ U M ∂ X K ∂ U M ∂ X L ) ≈ 1 2 ( ∂ U K ∂ X L + ∂ U L ∂ X K ) and e = 1 2 ( ∇ x u + ( ∇ x u ) T − ∇ x u ( ∇ x u ) T ) ≈ 1 2 ( ∇ x u + ( ∇ x u ) T ) or e r s = 1 2 ( ∂ u r ∂ x s + ∂ u s ∂ x r − ∂ u k ∂ x r ∂ u k ∂ x s ) ≈ 1 2 ( ∂ u r ∂ x s + ∂ u s ∂ x r ) This linearization implies that the Lagrangian description and the Eulerian description are approximately the same as there is little difference in the material and spatial coordinates of a given material point in the continuum. Therefore, the material displacement gradient components and the spatial displacement gradient components are approximately equal. Thus we have E K L ≈ e r s ≈ ε i j = 1 2 ( u i , j + u j , i ) , also called Cauchy's strain tensor, linear strain ten...

Volumetric Strain \[\text\] Instructions to use calculator • Enter the scientific value in exponent format, for example if you have value as 0.0000012 you can enter this as 1.2e-6 • Please use the mathematical deterministic number in field to perform the calculation for example if you entered x greater than 1 in the equation \[y=\sqrt \right)\] to calculate r (which cannot be expressed explicitly in terms of a,n) enter some arbitrary value of r in the first iteration along with the values of a and n and in the next iteration adjust the value of a and n to get correct value of r • You should reset calculator for new calculation however result of last field can be recalculated without reset the calculator, you just need to change the value of other fields. • If you find something wrong please report us through report icon or write us through

Hi all, Volumetric strain is occurred due to the volume change in the soil body due to the compressive stresses. Please explain the following items to learn 01. What is meant by deviatoric strain (please don't explain in the scientific way, just simply explain)? 02. How deviatoric strain explain the failure surface in the soil in Plaxis? 03. What is the different between total deviatoric strain and total cartesian strain? 04. Out of 2 (mentioned in 2), which one is going to define failure surface and the reason? Sorry for asking these questions, i searched in net but couldn't find and reference manual has no any explanations along that i keen to learn these items, that's why asking. Thanks. Nitha, You're asking super generalized questions, so it's impossible to give detailed questions. For discussion purpose I will add: 01. The google answer which I like is" Deviatoric strain is what's left after subtracting out the hydrostatic strain". In other words deviatoric strain is what I think of as shear strain. 02. Most all materials fail when the deviatoric stress (related to strain) reaches a limiting value. The deviatoric stress/strain relationship and the limiting value of deviatoric stress are determined by the constitutive model in Plaxis. 03. deviatoric strain is a shear strain and cartesian strains are axial strains (i.e changing in length). Axial strains are defined in a direction, the cartesian axial strains are aligned with the coordinate system. The "total" word in Pl...

Yet, absolute displacements are not enough to determine stresses. A solid may translate or rotate in space without development of any internal stresses required to equilibrate external actions (imagine a cookie “floating” in zero gravity within the International Space Station Let's look at Figure • (LEFT) A solid is stretched on its face 1 (perpendicular to ) in direction 1 only. This type of deformation produces a change of volume of the solid and therefore contributes to volumetric strain. The resulting deformation or strain (change of length divided original length) is ( 3. 5) • (RIGHT) The solid is now distorted. Notice that the faces do not make a right angle anymore. The change of volume is negligible for small deformations. The resulting distortion or shear strain is proportional to the change in angle between faces 1 and 2. Hence the change of angle is . The shear strain is 1/2 of the total change of the angle and therefore (for small changes ) Strains do not quantify the absolute value of displacements, but its variation in space (derivative with respect to ). All other strains are found with similar equations in the 3D case. Similarly to the stress tensor, strains can be organized in a tensor where elements in the diagonal contribute to volumetric strain, and off-diagonal elements are shear strains.