The variational approach to fracture
At the risk of being unfair, we credit first and foremost AA Griffith for develo** the field of
brittle fracture. His views were that cracks are the macroscopic manifestation of putative …
brittle fracture. His views were that cracks are the macroscopic manifestation of putative …
Minimum energy multiple crack propagation. Part I: Theory and state of the art review
The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic
solid under quasi-static conditions. The principle of minimum total energy, ie the sum of the …
solid under quasi-static conditions. The principle of minimum total energy, ie the sum of the …
Rate-independent systems
Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …
material models for shape-memory alloys that are flexible enough to encompass nonlinear …
Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives
Since the first studies dedicated to the mechanics of deformable bodies (by Euler,
D'Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to …
D'Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to …
Concentration of transformation-induced plasticity in pseudoelastic NiTi shape memory alloys: Insight from austenite–martensite interface instability
Transformation-induced plasticity (TRIP) in pseudoelastic polycrystalline NiTi shape memory
alloys (SMAs) is investigated through tensile tests combined with in-situ infrared and digital …
alloys (SMAs) is investigated through tensile tests combined with in-situ infrared and digital …
A vanishing viscosity approach to a rate-independent damage model
D Knees, R Rossi, C Zanini - Mathematical Models and Methods in …, 2013 - World Scientific
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 …
quantities are a stored energy functional and a dissipation functional, which is assumed to …
BV solutions and viscosity approximations of rate-independent systems∗
In the nonconvex case, solutions of rate-independent systems may develop jumps as a
function of time. To model such jumps, we adopt the philosophy that rate-independence …
function of time. To model such jumps, we adopt the philosophy that rate-independence …
Damage and fracture evolution in brittle materials by shape optimization methods
This paper is devoted to a numerical implementation of the Francfort–Marigo model of
damage evolution in brittle materials. This quasi-static model is based, at each time step, on …
damage evolution in brittle materials. This quasi-static model is based, at each time step, on …
On the inviscid limit of a model for crack propagation
D Knees, A Mielke, C Zanini - Mathematical Models and Methods in …, 2008 - World Scientific
We study the evolution of a single crack in an elastic body and assume that the crack path is
known in advance. The motion of the crack tip is modeled as a rate-independent process on …
known in advance. The motion of the crack tip is modeled as a rate-independent process on …
Damage of nonlinearly elastic materials at small strain–Existence and regularity results–
M Thomas, A Mielke - ZAMM‐Journal of Applied Mathematics …, 2010 - Wiley Online Library
This paper discusses an existence result for energetic solutions of rate‐independent
damage processes and the temporal regularity of the solution. The authors consider a body …
damage processes and the temporal regularity of the solution. The authors consider a body …