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Reduced-order models are developed to model the evolution of microstructure described by an orientation distribution function using a finite element discretization of the orientation space.
The model results to be a nonlinear hyperelastic 1D second gradient continuum, endowed with an internal microstructure described by seven scalar kinematic parameters.
Hence, the aims of the study were 1) to assess the brain microstructure described by DTI in brain areas involved in the visceral sensory processing in healthy control subjects and in patients with long-standing DM and gastrointestinal symptoms and 2) to correlate the findings with the clinical parameters in patients.
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In this phase space, the microstructure is described by dislocation orientation distribution functions (DODF) ρ r,φ).
The numerical approach is based on the finite element method with the microstructure being described by a periodic Voronoi tessellation with randomly oriented grains.
The microstructure is described by voids of arbitrary ellipsoidal shapes and orientations and as a result the material exhibits deformation-induced (or morphological) anisotropy at finite deformations.
In this model, a polycrystalline microstructure is described by many orientation field variables whose temporal and spatial evolutions can be obtained by solving the time-dependent Ginzburg-Landau (TDGL) equations.
In this model, a two-phase microstructure is described by non-conserved field variables which represent crystallographic orientations of grains in each phase and by a conserved composition field variable which distinguishes the compositional difference between the two phases.
Transverse plane histological slides were made and viewed with polarizing and reflectance microscopy and the microstructure described [50].
The state of the microstructure withineachcell is described by an additional field that may be discontinuous or highly oscillating.
The transducer function relating the changes at the surface to the changes in the conductivity of a ceramic microstructure is also described by an example.
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