Special Issue "Numerical Simulation of Discontinuities in Mechanics"

Guest Editor
Dr. Stefano Mariani
Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, Italy
Website: http://www.stru.polimi.it
E-Mail:
Interests: MEMS; structural sensors; kalman filtering

Guest Editor
Dr. Paolo Maria Mariano
Università di Firenze, DICeA, Via Santa Marta 3, 50139 Firenze, Italy
Website: http://www.dicea.unifi.it/paolo.mariano/
E-Mail:
Interests: mechanics and thermodynamics of continua; computational methods; statistical mechanics

Guest Editor
Dr. Paolo Venini
Università di Pavia, Dipartimento di Meccanica Strutturale, Via Ferrata 1, 27100 Pavia, Italy
Website: http://www-1.unipv.it/venini/
E-Mail:
Interests: nonlinear computational mechanics; wavelet methods for strain localization problems; analysis and optimization of uncertain structures; dual mixed methods for plane elastoplasticity; active structural control with neural networks

Submission

All papers should be submitted to algorithms@mdpi.org. To be published continuously until the deadline and papers will be listed together at the special issue website.

Submitted papers should not have been published nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors is available on the Instructions for Authors page. Algorithms is an international peer-reviewed quarterly journal published by Molecular Diversity Preservation International.

Article Processing Charges (APC) will be waived for well prepared manuscripts of invited papers. For the first three volumes of this new journal the APC are of 300 CHF (or 550 CHF per paper for those papers that require extensive additional formatting and/or English corrections) for papers submitted before 31 December 2010.

• solid mechanics
• fluid mechanics
• weak and strong discontinuities
• complex bodies
• multi-scale methods

Title: Numerical relaxation of nonconvex functionals in solid mechanics
Author: Antonio Orlando
Affiliation: School of Engineering, Swansea University, UK
Abstract: The occurrence of microstructures in solid mechanics can be attributed to a loss of the convexity characteristics of the underlying energy potentials. Specific model problems include, for instance, phase transitions in crystalline solids, material instabilities in finite strain plasticity, and material deteroriation due to damage processes. While the material deforms macroscopically, structures in the form of shear bands, cracks or laminates can be formed on microscopic scales. The numerical simulation of these problems through energy minimization poses, how- ever a very challenging task because of the enforced high oscillatory character of the developed microstructure and of the clustering of a large number of local minimizers around some global finite element approximation. Macroscopic properties of the resulting microstructure can, nevertheless, be recovered by replacing the underlying potential with its quasiconvex hull. The latter is a nonlocal notion and extremely difficult to analyse in theory and computation. Therefore, one introduces weaker or stronger notions, like rank-one convexity and polyconvexity, which are more amenable to numerical treatment. In this paper, we illustrate the effects of nonconvexity and describe relaxation theory from calculus of variations in the scalar and vector case using two model examples: the Young-Tartar problem and the modeling of the elastoplastic behavior of single crystals in finite strain.

Title: Algorithms of the Heterogeneous Cohesive Model for Fracture Simulation
Authors: Keqiang Hu, X. Frank Xu¹; Zhenjun Yang²
Affiliations: ¹: Stevens Institute of Technology, Hoboken, NJ 07030, USA; ²: The University of Liverpool, Liverpool L69 3GH, UK
Abstract: Stochastic fracture modeling is challenging especially due to unresolved puzzles on crack resolution or fractals. Research effort in this area is needed to address emerging technologies in MEMS and biosystems. By generalizing the conventional Griffith energy-balance concept to heterogeneous materials, a heterogeneous cohesive (HC) crack model is proposed in (Yang & Xu, 2008) to predict macroscopic strength of materials based on meso-scale random fields of fracture properties. A new stress-based criterion is proposed to determine the crack growth direction by taking into account both crack-tip stress state and heterogeneity of tensile strength. In this paper the algorithms developed and employed in the HC model are presented. Particularly the algorithms for simulation of Weibull random fields using classical Monte Carlo and Sparse Grid methods are introduced in detail.