Modeling long-term creep rupture by debonding in unidirectional fibre-reinforced composites

Delayed fracture due to debonding can be observed in many unidirectional fibre-reinforced composites when the fibre/matrix interface experiences creep. The aim of this work is to describe such a phenomenon within the recently proposed modeling framework of transverse isotropy that allows for a neat decomposition of the mechanical behavior into fibre-directional, transverse, and pure shear parts. Specifically, debonding is here chosen to be governed by the tension transverse to the fibres. One can then speak of a mode-I debonding if use is made of the terminology adopted in fracture mechanics. On another hand, the time-dependent response is attributed to the matrix constituent. As the role of this latter is to deform and support stresses primarily in shear, a viscoelastic behavior is introduced that affects solely the pure shear part of the behavior. We show that both characteristics can be easily embedded into the aforementioned formulation. Among others, the occurrence of tertiary creep is made possible to predict. It is otherwise found that the predicted debonding path always propagates along the direction of the fibres in agreement with many experimental observations found in the literature. On the numerical side, the algorithmic treatment of debonding is independent of the one for viscoelasticity. This renders the implementation within the context of the finite element method very easy.     

Local modal participation analysis of nonlinear systems using Poincaré linearization

Nonlinear Dynamics - This study proposes a modified recurrence quantification analysis, called global recurrence quantification analysis (GRQA). It is well known that the recurrence threshold is an...     

A note on kernel methods for multiscale systems with critical transitions

We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast‐slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near fast subsystem bifurcation points can be computed to leading order. This leading order approximation shows that the MMD depends intricately on the fast‐slow systems parameters, which can influence the detection of potential early‐warning signs before critical transitions. However, the MMD turns out to be an excellent binary classifier to detect the change‐point location induced by the critical transition. We cross‐validate our results by numerical simulations for a van der Pol‐type model.     

Some remarks on elliptic problems with critical growth in the gradient

In this work we analyze existence, nonexistence, multiplicity and regularity of solution to problem

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Competition reaction-absorption in some elliptic and parabolic problems related to the Caffarelli-Kohn-Nirenberg inequalities

We consider the following elliptic problem:

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Prototropie et synthèses nouvelles dans la série des dihydro-5,6 hydroxy-4 pyrones-2 et pyridones-2

The multistep catalytic reduction of 6-methyl-4-hydroxy-2-pyrone allows isolation of two intermediate compounds: the biologically active parasorbic acid ( 5 ) and the 6-methyl-5,6-dihydro-4-hydroxy-2-pyrone ( 2 ). The desmotropic keto-enol equilibrium lies on the enol side, with the 4rhydroxy structure. Primary arylamines readily react with 2 , leading to corresponding 2-pyridones 8 ; with methylamine, the aliphatic intermediate 7 resulting from ring attack at the 2 position can be isolated. Also further functionnalization of both dihydropyrone and 2-pyridone is possible by selective bromination at position 3.