Integral-gradient formulae for structured deformations

1995 ◽  
Vol 131 (2) ◽  
pp. 121-138 ◽  
Author(s):  
Gianpietro del Piero ◽  
David R. Owen
Keyword(s):  
Structured Deformations

scholarly journals Dimension Reduction in the Context of Structured Deformations

2018 ◽  
Vol 133 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Graça Carita ◽  
José Matias ◽  
Marco Morandotti ◽  
David R. Owen
Keyword(s):  
Dimension Reduction ◽  
Structured Deformations

A relaxation result in the framework of structured deformations in a bounded variation setting

2012 ◽  
Vol 142 (2) ◽  
pp. 239-271 ◽  
Author(s):  
Margarida Baía ◽  
José Matias ◽  
Pedro Miguel Santos
Keyword(s):  
Integral Representation ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Crystalline Structures ◽  
Structured Deformations ◽  
Asymptotic Models

We obtain an integral representation of an energy for structured deformations of continua in the space of functions of bounded variation, as a first step to the study of asymptotic models for thin defective crystalline structures, where phenomena as slips, vacancies and dislocations prevent the effectiveness of classical theories.

scholarly journals Upscaling and spatial localization of non-local energies with applications to crystal plasticity

2020 ◽  
pp. 108128652097324
Author(s):  
José Matias ◽  
Marco Morandotti ◽  
David R. Owen ◽  
Elvira Zappale
Keyword(s):  
Single Crystals ◽  
Crystal Plasticity ◽  
Weighting Function ◽  
Spatial Localization ◽  
Localization Formula ◽  
Weighted Averages ◽  
Structured Deformations ◽  
Energy Formula ◽  
Non Local

We describe multiscale geometrical changes via structured deformations [Formula: see text] and the non-local energetic response at a point x via a function [Formula: see text] of the weighted averages of the jumps [Formula: see text] of microlevel deformations [Formula: see text] at points y within a distance r of x. The deformations [Formula: see text] are chosen so that [Formula: see text] and [Formula: see text]. We provide conditions on [Formula: see text] under which the upscaling “[Formula: see text]” results in a macroscale energy that depends through [Formula: see text] on (1) the jumps [Formula: see text] of g and the “disarrangement field”[Formula: see text], (2) the “horizon” r, and (3) the weighting function [Formula: see text] for microlevel averaging of [Formula: see text]. We also study the upscaling “[Formula: see text]” followed by spatial localization “[Formula: see text]” and show that this succession of processes results in a purely local macroscale energy [Formula: see text] that depends through [Formula: see text] upon the jumps [Formula: see text] of g and the “disarrangement field”[Formula: see text] alone. In special settings, such macroscale energies [Formula: see text] have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity of single crystals.

Structured deformations of continua

1993 ◽  
Vol 124 (2) ◽  
pp. 99-155 ◽  
Author(s):  
Gianpietro Del Piero ◽  
David R. Owen
Keyword(s):  
Structured Deformations

scholarly journals A survey on structured deformations

2011 ◽  
Vol 5 (2) ◽  
pp. 185 ◽  
Author(s):  
M. Baía ◽  
J. Matias ◽  
P. M. Santos
Keyword(s):  
Structured Deformations
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