Gradient theory from the thermomechanics point of view

Problem of Thermoelasticity for an Orthotropic Plate-Strip of Variable Thickness with Regard for Transverse Shear

“…In numerous works, the Ritz and Bubnov-Galerkin methods, as well as the methods of finite differences and finite and boundary elements are extensively used and rapidly developed [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Effect of dissipative processes on the near-surface inhomogeneity of a hollow cylinder

“…In the scientific literature, the near-surface inhomogeneity is often described by nonlocal theories based on the assumption that the local thermodynamic state of a body at a given point depends on the state of neighboring points. This dependence is taken into account either by functional defining relations of the space type [18][19][20][21] or by the addition of higher-order gradients of the strain tensor to the space of state parameters [1,22,[25][26][27][28][29][30]. Within the framework of continual approach, these nonlocal (gradient) models describe the near-surface inhomogeneity of the stress and strain distributions.…”

A thermodynamic approach to non-local damage modelling of concrete

“…On the other hand, the thermodynamic aspects of constitutive modelling using non-local theories have been discussed by several researchers (Maugin, 1990;Santaoja, 2004;Nedjar, 2001;Borino et al, 1999;Benvenuti et al, 2002;Nilsson, 1997;Jirásek and Rolshoven, 2003;Peerlings et al, 2004;Voyiadjis and Dorgan, 2004;Makowski et al, 2006). In thermodynamic approaches, non-local or gradient terms can appear in the expressions of the first or second law of thermodynamics.…”

“…In some thermodynamic approaches (Nedjar, 2001;Santaoja, 2004;Voyiadjis and Dorgan, 2004;Makowski et al, 2006), non-local or gradient terms of internal variables appear in the expressions of the energy potential, as independent internal variables. The corresponding associated thermodynamic forces are then defined on those gradient terms.…”

“…However, inconsistencies in the definition of those thermodynamic forces between some approaches can be seen (e.g. in Santaoja, 2004 andVoyiadjis andDorgan, 2004). In Santaoja (2004), a scalar damage variable and its gradient form are associated with two corresponding thermodynamic forces, both of which are of scalar form and subjected to a constraint.…”