Rossana Dimitri

A consistency assessment of coupled cohesive zone models for mixed-mode debonding problems

Due to their simplicity, cohesive zone models (CZMs) are very attractive to describe mixed-mode failure and debonding processes of materials and interfaces. Although a large number of coupled CZMs have been proposed, and despite the extensive related literature, little attention has been devoted to ensuring the consistency of these models for mixed-mode conditions, primarily in a thermodynamical sense. A lack of consistency may affect the local or global response of a mechanical system. This contribution deals with the consistency check for some widely used exponential and bilinear mixed-mode CZMs. The coupling effect on stresses and energy dissipation is first investigated and the path-dependance of the mixed-mode debonding work of separation is analitically evaluated. Analytical predictions are also compared with results from numerical implementations, where the interface is described with zero-thickness contact elements. A node-to-segment strategy is here adopted, which incorporates decohesion and contact within a unified framework. A new thermodynamically consistent mixed-mode CZ model based on a reformulation of the Xu-Needleman model as modified by van den Bosch et al. is finally proposed and derived by applying the Coleman and Noll procedure in accordance with the second law of thermodynamics. The model holds monolithically for loading and unloading processes, as well as for decohesion and contact, and its performance is demonstrated through suitable examples.

Isogeometric treatment of large deformation contact and debonding problems with T-splines: a review

Abstract Within a setting where the isogeometric analysis (IGA) has been successful at bringing two different research fields together, i.e. Computer Aided Design (CAD) and numerical analysis, T-spline IGA is applied in this work to frictionless contact and mode-I debonding problems between deformable bodies in the context of large deformations. Based on the concept of IGA, the smooth basis functions are adopted to describe surface geometries and approximate the numerical solutions, leading to higher accuracy in the contact integral evaluation. The isogeometric discretizations are here incorporated into an existing finite element framework by using Bézier extraction, i.e. a linear operator which maps the Bernstein polynomial basis on Bézier elements to the global isogeometric basis. A recently released commercial T-spline plugin for Rhino is herein used to build the analysis models adopted in this study. In such context, the continuum is discretized with cubic T-splines, as well as with Non Uniform Rational B-Splines (NURBS) and Lagrange polynomial elements for comparison purposes, and a Gauss-point-to-surface (GPTS) formulation is combined with the penalty method to treat the contact constraints. The purely geometric enforcement of the non-penetration condition in compression is generalized to encompass both contact and mode-I debonding of interfaces which is approached by means of cohesive zone (CZ) modeling, as commonly done by the scientific community to analyse the progressive damage of materials and interfaces. Based on these models, non-linear relationships between tractions and relative displacements are assumed. These relationships dictate both the work of separation per unit fracture surface and the peak stress that has to be reached for the crack formation. In the generalized GPTS formulation an automatic switching procedure is used to choose between cohesive and contact models, depending on the contact status. Some numerical results are first presented and compared in 2D for varying resolutions of the contact and/or cohesive zone, including frictionless sliding and cohesive debonding, all featuring the competitive accuracy and performance of T-spline IGA. The superior accuracy of T-spline interpolations with respect to NURBS and Lagrange interpolations for a given number of degrees of freedom (Dofs) is always verified. The isogeometric formulation is also extended to 3D bodies, where some examples in large deformations based on T-spline discretizations show an high smoothness of the reaction history curves.

Stabilità dell'Equilibrio Elastico

www.editrice-esculapio.it Il presente manoscritto scaturisce dall’esperienza maturata nel corso di circa dieci anni di studio, di ricerca e di insegnamento su alcuni temi relativi alla stabilita dell’equilibrio elastico. Questi appunti e lezioni rappresentano i temi trattati in alcuni corsi di laurea in Ingegneria, quali: Scienza delle Costruzioni, Scienza delle Costruzioni II, Complementi di Scienza, Teoria delle Strutture, Dinamica delle Strutture, Piastre e Gusci, Costruzioni di Macchine e Elementi delle Macchine. Il titolo, Stabilita dell’Equilibrio Elastico, illustra il tema trattato e la prospettiva seguita nella stesura del volume. Il presente elaborato si pone come obiettivo quello di analizzare il comportamento di strutture soggette a carichi di punta o di compressione. Il libro si articola in tre capitoli, nei quali viene fornita nel dettaglio la teoria relativa ai criteri di stabilita in ambito strutturale e vengono presentati i risultati dell’applicazione di essi ai diversi problemi. Il volume nasce dall’esigenza di avere uno strumento utile ed efficace per intraprendere lo studio di uno dei temi piu affascinanti e importanti della Scienza delle Costruzioni e della Meccanica Applicata in generale. L’obiettivo del presente volume e quello di agevolare gli studenti e i professionisti che intendano impegnarsi nello studio della stabilita dell’equilibrio elastico in ambito strutturale, fornendo un supporto omogeneo, diretto e comprensibile. ta blita d e’equ ilbrio la Sico F. toabene r. d im tri