Related papers: Nonlocal elastodynamics and fracture
We consider nonlocal nonlinear potentials and estimate the rate of convergence of time stepping schemes to the peridynamic equation of motion. We begin by establishing the existence of $H^2$ solutions over any finite time interval. Here…
For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…
We derive the irreversibility condition in fracture for the inverse-deformation approach using the second law of thermodynamics. We consider the problem of brittle failure in an elastic bar previously solved in (Rosakis et al 2021). Despite…
In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic…
Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…
The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of…
In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven…
This work models brittle fracture using a linearized surface-substrate theory in which the crack faces possess surface stresses derived from a surface strain-gradient elastic energy. The model incorporates surface stretching, curvature, and…
In this paper, we discussed the non-local derivative on the fractal Cantor set. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and…
A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure inside a microscopic process zone and…
In this paper we derive a new two-dimensional brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small…
The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for…
Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of…
Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results,…
We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects…
We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This…
This paper is intended to serve as a low-hurdle introduction to non-locality for graduate students and researchers with an engineering mechanics or physics background who did not have a formal introduction to the underlying mathematical…