Dislocation generation due to differences between the coefficients of thermal expansion

Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Multiscale Methods for Composites: A Review

Computational plasticity for composite structures based on mathematical homogenization: Theory and practice

https://hal.archives-ouvertes.fr/hal-00088331/document

Nonuniform transformation field analysis

It is 100 years since the well-know Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.

Advances in strength theories for materials under complex stress state in the 20th Century

Initial yield surfaces were constructed for the boron-aluminum com posite under arbitrary combinations of applied composite stresses and tem perature changes, by means of a finite element analysis of a regular hexa gonal array model.The results suggest that with regard to initial yielding, the macroscopic transverse isotropy of the composite is approximately retained on the microscale. Therefore, the general isothermal yield surface can be con structed as a function of four composite stresses. Yielding in the transverse plane is controlled mainly by matrix properties, whereas yielding under normal composite stresses applied in the fiber direction is controlled by the ratio Ef/Em of the Young's moduli of the constituents. In general, high magnitudes of this ratio, as well as higher fiber volume fractions make yielding more difficult.It was found that yielding takes place both under hydrostatic composite stresses, and as a consequence of uniform temperature changes. Therefore, these effects must be accounte...

M. S. M. Rao

Papers

Yielding in Unidirectional Composites Under External Loads and Temperature Changes

Axisymmetric plasticity theory of fibrous composites

Generalized Initial Yield Surfaces for Unidirectional Composites

Shakedown of unidirectional composites