Robert Lipton
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View article: Quasi-Brittle Fracture: The Blended Approach
Quasi-Brittle Fracture: The Blended Approach Open
A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement …
View article: Fracture as an Emergent Phenomenon
Fracture as an Emergent Phenomenon Open
The mechanics of fracture propagation provides essential knowledge for the risk tolerance design of devices, structures, and vehicles. Techniques of free energy minimization provide guidance, but have limited applicability to material syst…
View article: A multiscale fracture model using peridynamic enrichment of finite elements within an adaptive partition of unity: Experimental validation
A multiscale fracture model using peridynamic enrichment of finite elements within an adaptive partition of unity: Experimental validation Open
Partition of unity methods (PUM) are of domain decomposition type and provide\nthe opportunity for multiscale and multiphysics numerical modeling. Within the\nPUM global-local enrichment scheme [1, 2] different physical models can exist\nt…
View article: Nodal finite element approximation of peridynamics
Nodal finite element approximation of peridynamics Open
This work considers the nodal finite element approximation of peridynamics, in which the nodal displacements satisfy the peridynamics equation at each mesh node. For the nonlinear bond-based peridynamics model, it is shown that, under the …
View article: Energy balance and damage for dynamic brittle fracture from a nonlocal formulation
Energy balance and damage for dynamic brittle fracture from a nonlocal formulation Open
A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and uniq…
View article: Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials
Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials Open
Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfac…
View article: Quasistatic fracture evolution
Quasistatic fracture evolution Open
Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fractur…
View article: Bloch waves in high contrast electromagnetic crystals
Bloch waves in high contrast electromagnetic crystals Open
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the i…
View article: Quasistatic Evolution with Unstable Forces
Quasistatic Evolution with Unstable Forces Open
We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating …
View article: A comparative review of peridynamics and phase-field models for engineering fracture mechanics
A comparative review of peridynamics and phase-field models for engineering fracture mechanics Open
Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models appl…
View article: Lorentz resonance in the homogenization of plasmonic crystals
Lorentz resonance in the homogenization of plasmonic crystals Open
We explain the Lorentz resonances in plasmonic crystals that consist of two-dimensional nano-dielectric inclusions as the interaction between resonant material properties and geometric resonances of electrostatic nature. One example of suc…
View article: Peridynamics for Quasistatic Fracture Modeling
Peridynamics for Quasistatic Fracture Modeling Open
Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the perspect…
View article: Bloch Waves in High Contrast Electromagnetic Crystals
Bloch Waves in High Contrast Electromagnetic Crystals Open
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the i…
View article: Bloch Spectra for High Contrast Elastic Media
Bloch Spectra for High Contrast Elastic Media Open
Analytic representation formulas and power series are developed to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent th…
View article: Quasistatic Fracture using Nonlinear-Nonlocal Elastostatics with Explicit Tangent Stiffness Matrix
Quasistatic Fracture using Nonlinear-Nonlocal Elastostatics with Explicit Tangent Stiffness Matrix Open
We apply a nonlinear-nonlocal field theory for numerical calculation of quasistatic fracture. The model is given by a regularized nonlinear pairwise (RNP) potential in a peridynamic formulation. The potential function is given by an explic…
View article: Simulating grain shape effects and damage in granular media using PeriDEM
Simulating grain shape effects and damage in granular media using PeriDEM Open
We provide a numerical platform for the analysis of particle shape and topology effect on the macroscopic behavior of granular media. We work within a Discrete Element Method (DEM) framework and apply a peridynamic model for deformable par…
View article: A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method
A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method Open
Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of l…
View article: A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method: Part I.
A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method: Part I. Open
Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of l…
View article: A comparative review of peridynamics and phase-field models for engineering fracture mechanics
A comparative review of peridynamics and phase-field models for engineering fracture mechanics Open
Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models appl…
View article: Nonlocal elastodynamics and fracture
Nonlocal elastodynamics and fracture Open
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 el…
View article: Peridynamics-based discrete element method (PeriDEM) model of granular\n systems involving breakage of arbitrarily shaped particles
Peridynamics-based discrete element method (PeriDEM) model of granular\n systems involving breakage of arbitrarily shaped particles Open
Usage, manipulation, transport, delivery, and mixing of granular or\nparticulate media, comprised of spherical or polyhedral particles, is commonly\nencountered in industrial sectors of construction (cement and rock fragments),\npharmaceut…
View article: Finite element approximation of nonlocal dynamic fracture models
Finite element approximation of nonlocal dynamic fracture models Open
In this work we estimate the convergence rate for time stepping schemes applied to nonlocal dynamic fracture modeling. Here we use the nonlocal formulation given by the bond based peridynamic equation of motion. We begin by establishing th…
View article: Nonlocal elastodynamics and fracture
Nonlocal elastodynamics and fracture Open
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 el…
View article: Classic dynamic fracture recovered as the limit of a nonlocal peridynamic model: The single edge notch in tension
Classic dynamic fracture recovered as the limit of a nonlocal peridynamic model: The single edge notch in tension Open
A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The fracture evolution is shown to converge in the limit of vanishing nonlocality to classic plane elastodynamics with a running crack. The kinetic re…