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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 FE 2 ) 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.

The paper proposes a modified formalism of continuum damage mechanics in order to describe plastic compressibility in the context of ductile damage. The model uses two damage state variables, one of them playing role of porosity in micromechanics based approaches like Gurson's model. Various versions of the model are determined and compared with Gurson's model, in terms of the constitutive responses for various loading conditions, as well as for simple structural examples like a free and a clamped plate under plane strain, and an axisymmetric notched bar under tension. The classical CDM is also applied and some advantages of the proposed approach are underlined.

Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014 ) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in ∼ 0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods.

The paper considers two classes of approaches for the numerical analysis of composite systems: the first one discretizes the assumed interphase (between matrix and fibre) as volumic elements and uses material models that degenerate from Continuum Damage Mechanics. The second one introduces interface elements that relate non linearly the normal and tangential tractions to the corresponding displacement discontinuities, incorporating a progressive decohesion, following the lines of Needleman (1987) and Tvergaard (1990).The respective capabilities of these two approaches are discussed on the basis of some numerical results obtained for a unidirectional metal matrix composite system. When the models are consistently adjusted they are able to reproduce the same kind of results. The advantages of the second class of method is underlined and two new versions of interface models are proposed that guarantee the continuity and the monotonicity of the shear stiffness between the progressive decohesion phase and the subsequent contact/friction law that plays role under compressive shear after complete separation.

Contributed by world-renowned specialists on the occasion of Paul Germain's 80th birthday, this unique book reflects the foundational works and the intellectual influence of this author.It presents the realm of modern thermomechanics with its extraordinary wealth of applications to the behaviour of materials, whether solid or fluid.

Many aspects related to the thermoelastic viscoplastic constitutive equations are considered. The discussion is mainly based on the macroscopic constitutive models that have been experienced for a long time at ONERA, for applications in several domains, in the framework of life prediction methods for components working at high temperature, such as gas turbine components (aeroengines) and nuclear plants. Materials cited include IN100, 316, 316L, 17-12 SPH, 304 and 2024 (Al).

The thermodynamics of irreversible processes, using the notion of local state and internal state variables, is used for developing consistent constitutive and damage equations. The Generalized Standard Models are recalled and some of the induced limitations are discussed, both for non linear kinematic hardening in viscoplasticity and for elasto-plastic damage couplings. In order to release some of these constraints, a pseudo-standard approach is formulated and discussed, that allows us to recover most of the classically used constitutive equations and damage models.