Related papers: A local variational principle for fracture
In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…
Modeling microstructural evolution at large strains requires mechanical formulations that remain thermodynamically consistent while capturing significant lattice rotations and transformation-induced stresses. However, most existing…
This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and…
Simulation of frictional contact and shear failure of fractures in fractured media is of paramount important in computational mechanics. In this work, a preconditioned mixed-finite element (FE) scheme with Lagrange multipliers is proposed…
Phase-field models are a leading approach for realistic fracture problems. They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. This…
The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…
We examine the incorporation of gauge symmetries in the modern effective field theory (EFT) matching paradigm with a particular focus on spontaneously broken symmetries. The presence of gauge symmetries entails the introduction of…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
A rigorous theoretical framework is developed for a generalized local frame transformation theory (GLFT). The GLFT is applicable to the following systems: to Rydberg atoms or molecules in an electric field, or to negative ions in any…
Fracture is a very challenging and complicated problem with various applications in engineering and physics. Although it has been extensively studied within the context of mesh-based numerical techniques, such as the finite element method…
A field theory is presented for predicting damage and fracture in quasi brittle materials incorporating effects of irreversible (plastic) deformation as well as elastic moduli that soften with damage. The new observation made here is that…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…
Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft…
Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Within the PUM global-local enrichment scheme [1, 2] different physical models can exist to…
We compare two widespread formulations of the mean-field approximation, based on minimizing an appropriately built mean-field free energy. We use the example of the antiferromagnetic Ising model to show that one of these formulations does…
A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues. Such tissues consist of one or more solid and fluid phases and can demonstrate nonlinear…
Variational phase field fracture models are now widely used to simulate crack propagation in structures. A critical aspect of these simulations is the correct determination of the propagation threshold of pre-existing cracks, as it highly…
Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the…
A new gradient-based formulation for predicting fracture in elastic-plastic solids is presented. Damage is captured by means of a phase field model that considers both the elastic and plastic works as driving forces for fracture. Material…
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…