Related papers: A non incremental variational principle for brittl…
Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation…
We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of…
This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state.…
Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length…
We study a class of models for brittle fracture: elastic theory models which allow for cracks but not for plastic flow. We show that these models exhibit, at all finite temperatures, a transition to fracture under applied load similar to…
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…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
The classical variational approach to brittle fracture propagation does not distinguish between strain energy accumulation in tension versus compression and consequently results in physically unrealistic cracking under compression. A…
The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On…
The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology,…
In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the…
The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss…
Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to large components or systems crucial for real applications…
Irreversible evolution is one of the central concepts as well as implementation challenges of both the variational approach to fracture by Francfort and Marigo (1998) and its regularized counterpart by Bourdin, Francfort and Marigo (2000,…
We address brittle fracture in anisotropic materials featuring two-fold and four-fold symmetric fracture toughness. For these two classes, we develop two variational phase-field models based on the family of regularizations proposed by…
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…
Crack growth is the basic mechanism leading to the failure of brittle materials. Engineering addresses this problem within the framework of continuum mechanics, which links deterministically the crack motion to the applied loading. Such an…
A novel phase-field for ductile fracture model is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling…
We discuss a weighted variational integral approach for nonlocal linear diffusion models with forcing term, providing a selection principle for solutions of elliptic in time regularizations.
We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as…