TY - RPRT
T1 - Second-order structured deformations
Y1 - 2016
A1 - Ana Cristina Barroso
A1 - Jose Matias
A1 - Marco Morandotti
A1 - David R. Owen
PB - SISSA
U1 - 35497
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Explicit formulas for relaxed disarrangement densities arising from structured deformations
Y1 - 2015
A1 - Ana Cristina Barroso
A1 - Jose Matias
A1 - Marco Morandotti
A1 - David R. Owen
AB - Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/34492
U1 - 34687
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Homogenization problems in the Calculus of Variations: an overview
Y1 - 2015
A1 - Jose Matias
A1 - Marco Morandotti
AB - In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/34455
N1 - DEDICATED TO PROF. ORLANDO LOPES
U1 - 34598
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Homogenization of functional with linear growth in the context of A-quasiconvexity
Y1 - 2014
A1 - Jose Matias
A1 - Marco Morandotti
A1 - Pedro M. Santos
AB - This work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/7436
U1 - 7528
ER -