Stereo vision is used to measure the strain field of a round tension test specimen in a cylindrical coordinate system. Initially, the displacement fields o
A homogeneous deformation is one where the deformation gradient tensor is independent of the coordinates. From: Continuum Mechanics Modeling of Material Behavior, 2019 About this pageSet alert Discover other topics On this page Definition Chapters and Articles Related Terms Recommended Publications Chapters...
It is also to be noted that the basis vectors {eI}, {ei} and the orthogonal transformations Q and R vary in space in general (as also seen from (9) for the cylindrical basis vectors). In terms of these basis vectors, the deformation gradient F and the undeformed geodesic vector can ...
These models are predicated on the use of a field gradient driving force (work conjugate to the quadrupole density) that is associated with the light beam to predict azobenzene polymer deformation. Such models will break down when simulating bending and twisting of films exposed to uniform light ...
theory of deformation, motion of deformable medium and equations of motion of each moleculedisplacement vector gradient and tensor quantityvolume element rotation and displacement gradientssmall strains' theory and small angles of rotationcompatibility conditions of classical theory of small displacements...
Once the map is obtained, local tissue deformation can be calculated from the deformation gradient tensor \(\tilde{{\boldsymbol{F}}}\) (Fig. 2a and Supplementary Note 2); in particular, quantifying the spatial patterns of area growth rate (the change in the area per given time interval) ...
W. Hutchinson, Strain gradient plasticity: theory and experiment. Acta Metall. Mater.42(2), 475–487 (1994). Article CAS Google Scholar N. A. Fleck, J. W. Hutchinson, A reformulation of strain gradient plasticity. J. Mech. Phys. Solids. 49(10), 2245–2271 (2001). Article Google ...
APPENDIX C: OUT-OF-BALANCE FORCES AND TANGENT STIFFNESS MATRIX We provide here expressions for the gradient and the Hessian of the potential energy. With a view on the implementation, we resort to Voigt's notation for symmetric tensors. To keep the notation clean, depending on the context, ...
If the tensor of the deformation gradient F in Eq. (1) is not constant, then the deformation y(x) is non-homogeneous and therefore a function of the spatial coordinates. In some cases, these non-affine transformations can be expressed in terms of spatial combinations of the previous affine...
This is achieved by confining the material between the walls of the measuring instrument and by setting up a velocity gradient across the thickness of the material, i.e. causing it to flow. This may be by forcing the fluid to flow through a pipe or capillary tube or by moving one wall ...