For small deformation, the Jacobin of elastic deformation gradient is equivalent to (ɛre + 1)(ɛθe + 1). Consequently, the following expression could be obtained based on small deformation. (12.52)lnJe≈
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...
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 ...
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, ...
The diffu- sion and drift of jet partons propagating in a nonuniform QGP medium have lead to the study of gradient tomography of jet quenching. Also the results from the leading corrections to jet momentum broadening and medium-induced branching, arising from the velocity of a moving medium ...
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) ...
Applying the surface gradient to both sides of (7) then yields where is the surface gradient of \(\tilde{z}^{i}\) and \(\boldsymbol{I}\) is the identity tensor in the tangent space \({\mathcal {D}}^{\text{tan}}\) of \({\mathcal {D}}\). Thus, it follows that (8)...
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...
CYLINDRICAL MICROSHELLSA first-order shear deformation (FOSD) free-form microshell model described in general curvilinear coordinates was developed within the complete framework of Mindlin's form II linear isotropic strain-gradient theory (SGT), considering both strain-gradient and micro-inertia effects....
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...