The deviatoric rate of strain tensor
, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is then reduced to:
Furthermore, in order to describe the anisotropic fracture accurately, a non-conjugated anisotropic equivalent plastic strain function is included by operating on a linearly transformation to the strain tensor
The second part of (6) is the system of cinematic equations representing the correlation between the strain tensor
DETERMINING THE STRAIN TENSOR
BASED ON THE RESULTS of geodetic MEASUREMENTS
Green-Lagrange strain tensor
E and Almansi-Euler strain tensor
e, respectively, by the left and right Green deformation tensors B and C derived.
is the trace of the strain tensor
obtained by contraction.
In the MVIB model, the Green strain tensor
is decomposed into spherical and deviatoric parts and the stretch deformation of bonds are decomposed into spherical dilatational deformation and deviatoric deformation to calculate bonds' strain energy.
The cost of designing composite pieces made of alumina--zirconia nanomaterials or even other similar ceramic materials can be easily reduced by using the simulation on thermal behavior and by determining thermal strain tensor
where C and S are the second Piola-Kirchhoff stress tensor and the Cauchy-Green strain tensor
, respectively, and W is the free energy, or strain energy, function.
The analyses made herein regarding tissue deformations in the supported heel only refer to tissue thickness changes between the calcaneal bone edge and supporting surfaces, which, from an engineering point of view, only represents one component of the strain tensor
(that is, compression strain), and does not account for tension and shear strains.
these comes compatible FE ensuring uneven grid area for approximation with some degree of accuracy the stress concentration zones and the development of shear deformation due to the using of finite strain tensor
, that describes the displacements and rotations of FE as a rigid unit (Shimanovsky, Tsyhanovsky 2005).
In general, strain tensor
is composed of elastic and plastic strain tensors
(Jeremic, Yang 2002; Nayak, Zienkiewicz 1972; Zergua, Naimi 2006):