Related papers: Data-driven fracture mechanics
A new generation of experiments on dry macroscopic friction has revealed that the transition from static to dynamic friction is essentially a spatially and temporally non-uniform process, initiated by a rupture-like detachment front. We…
The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics `purely brittle' model of Savkoor and Briggs, models have…
The modeling of cracks is an important topic - both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometry of the crack is not known beforehand, but part of the…
This study presents a novel physics informed, data-driven modeling framework for capturing the strongly nonlinear thermo-viscoelastic behavior of soft materials exhibiting stress softening, with emphasis on the Mullins effect. Unlike…
We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and…
A universal particle velocity based algorithm for simulating hydraulic fracture with leak-off, previously demonstrated for the PKN and KGD models, is extended to obtain solutions for a penny-shaped crack. The numerical scheme is capable of…
As a companion work to [1], this Note presents a series of simple formulae and explicit results that illustrate and highlight why classical variational phase-field models cannot possibly predict fracture nucleation in elastic brittle…
This paper presents a computational framework for quasi-static brittle fracture in three dimensional solids. The paper set outs the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of…
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…
Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a…
This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volumetric-based…
We propose and analyze an adaptive finite element method for a phase-field model of dynamic brittle fracture. The model couples a second-order hyperbolic equation for elastodynamics with the Ambrosio-Tortorelli regularization of the…
We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute…
Fractured metal fragments with rough and irregular surfaces are often found at crime scenes. Current forensic practice visually inspects the complex jagged trajectory of fractured surfaces to recognize a ``match'' using comparative…
We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown…
This work presents a two-stage physics-informed, data-driven constitutive modeling framework for hyperelastic soft materials undergoing progressive damage and failure. The framework is grounded in the concept of hyperelasticity with energy…
Fracture produces new mesh fragments that introduce additional degrees of freedom in the system dynamics. Existing finite element method (FEM) based solutions suffer from an explosion in computational cost as the system matrix size…
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models…
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…