Related papers: Peridynamics for Quasistatic Fracture Modeling
Peridynamics formulates the balance of linear momentum as an integro-differential equation, making it naturally suited for fracture modeling without special treatment of discontinuities. The bond-associated correspondence formulation…
We establish the a-priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models. We consider state based peridynamic models where the force at a material point is due to both the strain between…
A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane…
We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond…
We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the…
Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for dynamic fracture problems in large-scale…
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…
Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…
We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e…
Planar sliding of objects is modeled and analyzed. The model can be used for non-prehensile manipulation of objects lying on a surface. We study possible motions generated by frictional contacts, such as those arising between a soft finger…
A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We formulate a simple one-dimensional model problem and give a…
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…
We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution…
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…
In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with…
Crack-tip stress evaluation has always been a problem in the frame of classical elasticity theory. Peridynamics has been shown to have great advantages in dealing with crack problems. In the present study, we present a peridynamic crack-tip…
This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…
Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based…
Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical bonds. This formulation allows us to model crack initiation, propagation, branching…
We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…