相关论文: Damage-driven fracture with low-order potentials: …

We prove a $\Gamma$-convergence result for space dependent weak membrane energies, that is for 'truncated quadratic potentials', that are quadratic below some threshold (depending on the pair of points that we are considering) and constant…

We report results on the interrelation between driving force, roughness exponent, branching and crack speed in a finite element model. We show that for low applied loadings the crack speed reaches the values measured in the experiments, and…

Loss of circulation while drilling is a challenging problem that may interrupt operations, reduce efficiency, and may contaminate the subsurface. When a drilled borehole intercepts conductive faults or fractures, lost circulation manifests…

Drawing a direct analogy with the well-studied vibration or elastic modes, we introduce an object's fracture modes, which constitute its preferred or most natural ways of breaking. We formulate a sparsified eigenvalue problem, which we…

On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a perimeter term. Our scaling allows low-energy states to be…

We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the micro-structure of the material and the complex…

In this work we present a model reduction procedure to derive a hybrid-dimensional framework for the mathematical modeling of reactive transport in fractured porous media. Fractures are essential pathways in the underground which allow fast…

We investigate analytically the motion of underdamped particles subject to a deterministic periodic potential and a periodic temperature. Despite the fact that an underamped particle experiences the temperature oscillation many times in its…

Using a simple and generic molecular dynamics model, we study the damage in a disc of interacting particles as the disc fragments upon impact with a wall. The damage, defined as the ratio of the number of bonds broken by the impact to the…

We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…

In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the…

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the…

The effect of geometrical shape of eroding absolutely rigid particles on the threshold rate of failure has been studied. The Shtaerman-Kilchevsky theory of quasi-static blunt impact, which generalizes Hertz's classical impact theory, is…

Material failure is mediated by the propagation of cracks, which in realistic 3D materials typically involve multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures,…

The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The $\Gamma$-limit of a suitable rescaling of the renormalized energy is characterized in the space of probability measures. This…

We establish the $\Gamma$-convergence of some energy functionals describing nonlocal attractive interactions in bounded domains. The interaction potential solves an elliptic equation (local or nonlocal) in the bounded domain and the primary…

We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…

Picking up, laying down, colliding, rolling, and peeling are partial-contact interactions involving moving discontinuities. We examine the balances of momentum and energy across a moving discontinuity in a string, with allowance for…

We propose models in nonlinear elasticity for nonsimple materials that include surface energy terms. Additionally, we also discuss living surface loads on the boundary. We establish corresponding linearized models and show their…

Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions.…