Damage theory: microscopic effects of vanishing macroscopic motions

This paper deals with a mechanical model describing the evolution of damage in elastic and viscoelastic materials. The state variables are macroscopic deformations and a microscopic phase parameter, which is related to the quantity of damaged material. The equilibrium equations are recovered by refining the principle of virtual powers including also microscopic forces. After proving an existence and uniqueness result for a regularized problem, we investigate the behavior of solutions, in the case when a vanishing sequence of external forces is applied. By use of a rigorous asymptotics analysis, we show that macroscopic deformations can disappear at the limit, but their damaging effect remains in the equation describing the evolution of damage at a microscopic level. Moreover, it is proved that the balance of the energy is satisfied at the limit

A vanishing viscosity approach to a rate-independent damage model

We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damage variable and the displacements, solutions may have jumps as a function of time. The latter circumstance makes it necessary to recur to suitable notions of weak solution. However, the by-now classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps. Hence, we consider rate-independent damage models as limits of systems driven by viscous, rate-dependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arc-length reparameterization. In this way, in the limit we obtain a novel formulation for the rate-independent damage model, which highlights the interplay of viscous and rate-independent effects in the jump regime, and provides a better description of the energetic behavior of the system at jump

Quasistatic delamination of sandwich-like Kirchhoff-Love plates

A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguishe

Follow-up and surgical management of Peutz-Jeghers syndrome in children.

BACKGROUND: Peutz-Jeghers syndrome (PJS) is an autosomal dominant syndrome with an increased risk of polyposis complications and intestinal and extraintestinal tumours. METHODS: During the last 15 years, we reviewed a series of 11 children with PJS, with special attention to evolution and follow-up. Diagnosis was based on at least 1 hamartomatous polyp associated with 2 of the 3 following criteria: family record of PJS, polyposis localised on small bowel, and mucocutaneous pigmentation. Diagnosis of PJS also could be raised by a single genetic analysis of STK11 gene. RESULTS: Median age at beginning of symptoms was 6 years old. Seven of the 11 children had genetic tests, which were positive for STK11 gene mutation. Among the 10 children presenting with gastrointestinal complications, 8 were operated on, 6 had at least 1 small bowel resection, and 4 had repeat surgery for recurrent intussusceptions. In case of complications leading to a surgical procedure, we performed intraoperative enteroscopy to remove all large polyps. To prevent any polyposis complications, we suggest a complete check-up of polyposis topography with some of the new endoscopic tools, either double-balloon endoscopy or videocapsule endoscopy. CONCLUSIONS: Children with PJS have a high risk of numerous laparotomies due to polyps\u27 complications. Therefore, a screening of intestinal polyposis by videocapsule endoscopy is recommended, as well as a screening of the most frequent sites of cancers for the patient\u27s whole life. During any abdominal procedure, they should have an intraoperative endoscopy, this management allowing an increased time interval between 2 laparotomies

Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential

A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle \K is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed $n$-dimensional simplex, we prove that the long-time behavior of the solution semigroup associated with this problem can be described in terms of an exponential attractor. In particular, the latter means that the fractal dimension of the associated global attractor is also finite

Numerical approach to a model for quasistatic damage with spatial BV-regularization

We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems

Mechanics of Reversible Unzipping

We study the mechanics of a reversible decohesion (unzipping) of an elastic layer subjected to quasi-static end-point loading. At the micro level the system is simulated by an elastic chain of particles interacting with a rigid foundation through breakable springs. Such system can be viewed as prototypical for the description of a wide range of phenomena from peeling of polymeric tapes, to rolling of cells, working of gecko's fibrillar structures and denaturation of DNA. We construct a rigorous continuum limit of the discrete model which captures both stable and metastable configurations and present a detailed parametric study of the interplay between elastic and cohesive interactions. We show that the model reproduces the experimentally observed abrupt transition from an incremental evolution of the adhesion front to a sudden complete decohesion of a macroscopic segment of the adhesion layer. As the microscopic parameters vary the macroscopic response changes from quasi-ductile to quasi-brittle, with corresponding decrease in the size of the adhesion hysteresis. At the micro-scale this corresponds to a transition from a `localized' to a `diffuse' structure of the decohesion front (domain wall). We obtain an explicit expression for the critical debonding threshold in the limit when the internal length scales are much smaller than the size of the system. The achieved parametric control of the microscopic mechanism can be used in the design of new biological inspired adhesion devices and machines

A comparison of delamination models: Modeling, properties, and applications

This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed