shear deformationshear flow/ simple shear decompositiondeformation gradientm-dimensional homogeneous deformationuniform dilatationrotationm-1 simple shearsEvery m -dimensional ( m ≥2) homogeneous deformation is shown to consist in a succession of a uniform dilatation, a rotation, and m 1 simple shears....
A simple shear deformation is always accompanied by a rigid body rotation, because the displacement gradient tensor is not symmetrical. Since plastic deformation in metallic materials proceeds by simple shear mechanisms (dislocation glide, mechanical twinning) the grains in a polycrystal change their orie...
Some efforts have been made to quantify the deformation gradient at the atomic scale. Kruyt and Rothenburg developed a simple expression for an average displacement gradient tensor (∂u∂X=F-1) for two-dimensional regions in the simulation of granular materials (Kruyt and Rothenburg, 1996). ...
This paper examines a condition for the existence and uniqueness of a finite deformation field whenever a Gram–Schmidt (QR) factorization of the deformation gradient $${\\mathbf {F}}$$ is used. First, a compatibility condition is derived, provided that a right Cauchy–Green tensor $${\\...
Deformation Gradient
as the length-scale of the deformation induced by the simple shear scales with the down-dip length of the subduction zone interface (e.g. see ref.51), which is of the order 100–200 km. As such, the simple shear at the subduction boundaries is not significant for the large-scale (...
Fig. 1: Structure of InSb and shear stress response. aThe structure of InSb with sketch map of double face centered cubic (fcc) lattice, the red atoms are In and the blue atoms are Sb.bThe shear stress–strain curve of seven different slip systems. The shear stress–strain curve of the...
Another caution regarding the usage is the effect of rotation or the gradient of the fingertip while the participants tried to maintain the posture of their finger during the exploration in our experiments. The acceleration at the finger side is also affected by gravity, which should not be confu...
A simpleshear deformationis always accompanied by a rigid-body rotation, because thedisplacement gradienttensor is not symmetrical. Sinceplastic deformationin metallic materials proceeds by simple shear mechanisms (dislocation glide, mechanical twinning), the grains in apolycrystalchange theircrystallographic ...
Along the direction of shear marked by an arrow, a displacement, u1, takes place. Its gradient, du1/dx2, is determined by the slope which is denoted as: Sign in to download full-size image Figure 1.2.5. Small (a) and large (b) deformations in simple shear. [1.2.31]γ=tanα=du...