This book pursues optimal design from the perspective of mechanical
properties and resistance to failure caused by cracks and fatigue.
The book abandons the scale separation hypothesis and takes up
phase-field modeling, which is at the cutting edge of research and
is of high industrial and practical relevance. Part 1 starts by
testing the limits of the homogenization-based approach when the
size of the representative volume element is non-negligible
compared to the structure. The book then introduces a non-local
homogenization scheme to take into account the strain gradient
effects. Using a phase field method, Part 2 offers three
significant contributions concerning optimal placement of the
inclusion phases. Respectively, these contributions take into
account fractures in quasi-brittle materials, interface cracks and
periodic composites. The topology optimization proposed has
significantly increased the fracture resistance of the composites
studied.
General
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