John Everett Dolbow

Journal article Advances in Engineering Software · October 1, 2026 Variational approaches to fracture and their regularized counterparts have received great success modeling engineering problems incorporating a wide range of physical phenomena. There is considerable demand for a unified and flexible computational framewor ... Full text Cite

Stochastic modeling of anisotropic strength surfaces from atomistic simulations

Journal article Theoretical and Applied Fracture Mechanics · July 1, 2026 This work develops a unified framework for inferring, representing, and statistically characterizing an anisotropic strength surface directly from molecular dynamics data. Large-scale tensile loading simulations are used to generate failure data across all ... Full text Cite

Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2026 Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of fracture in materials s ... Full text Cite

Examining crack nucleation under spatially uniform stress states with a complete phase-field model for fracture

Journal article Theoretical and Applied Fracture Mechanics · December 1, 2025 This work concerns crack nucleation problems in elastic brittle materials subjected to stress states that are spatially uniform or nearly so. Such conditions arise under a wide range of settings, including standard tests of material strength. This class of ... Full text Cite

Embedded FEM with strongly-enforced interface conditions for incompressible flow with moving boundaries

Journal article Computer Methods in Applied Mechanics and Engineering · October 1, 2025 We present an embedded finite element method for solving the incompressible Navier–Stokes equations on complex or moving domains while using a fixed structured background mesh. The key component of our approach is a ghost node framework that modifies basis ... Full text Cite

A variational phase-field framework for thermal softening and dynamic ductile fracture

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2025 A variational phase field model for dynamic ductile fracture is presented. The model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational ... Full text Cite

Classical variational phase-field models cannot predict fracture nucleation

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2025 Notwithstanding the evidence against them, classical variational phase-field models continue to be used and pursued in an attempt to describe fracture nucleation in elastic brittle materials. In this context, the main objective of this paper is to provide ... Full text Cite

Nucleation of Fracture: The First-Octant Evidence Against Classical Variational Phase-Field Models

Journal article Journal of Applied Mechanics · January 1, 2025 As a companion work to [1], this article 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 materials. The focu ... Full text Cite

A Griffith description of fracture for non-monotonic loading with application to fatigue

Journal article Journal of the Mechanics and Physics of Solids · October 1, 2024 With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids not just under monotonic but under general loading conditions, this paper puts forth a generalization of the ... Full text Cite

A variational formulation of Griffith phase-field fracture with material strength

Journal article International Journal of Fracture · September 1, 2024 In this expository Note, it is shown that the Griffith phase-field theory of fracture accounting for material strength originally introduced by Kumar, Francfort, and Lopez-Pamies (J Mech Phys Solids 112, 523–551, 2018) in the form of PDEs can be recast as ... Full text Cite

A model-based simulation framework for coupled acoustics, elastodynamics, and damage with application to nano-pulse lithotripsy

Journal article International Journal of Solids and Structures · March 1, 2024 We develop a model for solid objects surrounded by a fluid that accounts for the possibility of acoustic pressures giving rise to damage on the surface of the solid. The propagation of an acoustic pressure in the fluid domain is modeled by the acoustic wav ... Full text Open Access Cite

Representing model uncertainties in brittle fracture simulations

Journal article Computer Methods in Applied Mechanics and Engineering · January 5, 2024 This work focuses on the representation of model-form uncertainties in phase-field models of brittle fracture. Such uncertainties can arise from the choice of the degradation function for instance, and their consideration has been unaddressed to date. The ... Full text Cite

The strength of the Brazilian fracture test

Journal article Journal of the Mechanics and Physics of Solids · January 1, 2024 Since its introduction in the 1940s until present times, the so-called Brazilian test has been embraced by practitioners worldwide as a method of choice to indirectly measure the tensile strength of concrete, rocks, and other materials with a large compres ... Full text Cite

A Darcy–Cahn–Hilliard model of multiphase fluid-driven fracture

Journal article Journal of the Mechanics and Physics of Solids · December 1, 2023 A Darcy–Cahn–Hilliard model coupled with damage is developed to describe multiphase-flow and fluid-driven fracturing in porous media. The model is motivated by recent experimental observations in Hele–Shaw cells of the fluid-driven fracturing of a syntheti ... Full text Cite

Shock waves generated by toroidal bubble collapse are imperative for kidney stone dusting during Holmium:YAG laser lithotripsy.

Journal article Ultrasonics sonochemistry · December 2023 Holmium:yttrium-aluminum-garnet (Ho:YAG) laser lithotripsy (LL) has been the treatment of choice for kidney stone disease for more than two decades, yet the mechanisms of action are not completely clear. Besides photothermal ablation, recent evidence sugge ... Full text Cite

A phase-field model for hydraulic fracture nucleation and propagation in porous media

Journal article International Journal for Numerical and Analytical Methods in Geomechanics · November 1, 2023 Many geo-engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field method has gr ... Full text Cite

On formulations for modeling pressurized cracks within phase-field methods for fracture

Journal article Theoretical and Applied Fracture Mechanics · October 1, 2023 Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the effects of pressu ... Full text Cite

Model-based simulations of pulsed laser ablation using an embedded finite element method.

Journal article International journal of heat and mass transfer · May 2023 A model of thermal ablation with application to multi-pulsed laser lithotripsy is presented. The approach is based on a one-sided Stefan-Signorini model for thermal ablation, and relies on a level-set function to represent the moving interface between the ... Full text Cite

Towards validation of crack nucleation criteria from V-notches in quasi-brittle metallic alloys: Energetics or strength?

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2022 We discuss crack nucleation observations from a series of experiments that have proven to be particularly challenging for model validation. In particular, we focus attention on crack nucleation from a series of V-notched specimens of an AISI 4340 steel all ... Full text Cite

A multi-resolution approach to hydraulic fracture simulation

Journal article International Journal of Fracture · September 1, 2022 We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack represe ... Full text Cite

Attaining regularization length insensitivity in phase-field models of ductile failure

Journal article Computer Methods in Applied Mechanics and Engineering · October 1, 2021 A cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, ... Full text Cite

Scale-bridging with the extended/generalized finite element method for linear elastodynamics

Journal article Computational Mechanics · August 1, 2021 This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale pr ... Full text Cite

A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation

Journal article Computer Methods in Applied Mechanics and Engineering · August 15, 2020 We present a new derivation for a phase-field model of cohesive fracture that allows for fully-damaged surfaces to properly transmit tractions under frictionless contact conditions. The model is derived from an energy minimization standpoint, and the gover ... Full text Cite

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

Journal article International Journal for Numerical Methods in Engineering · June 15, 2020 An extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, st ... Full text Cite

Ceramic nuclear fuel fracture modeling with the extended finite element method

Journal article Engineering Fracture Mechanics · January 1, 2020 Ceramic fuel pellets used in nuclear light water reactors experience significant fracture due to the high thermal gradients experienced under normal operating conditions. This has important effects on the performance of the fuel system. Because of this, a ... Full text Cite

Data-driven enhancement of fracture paths in random composites

Journal article Mechanics Research Communications · January 1, 2020 A data-driven framework for the enhancement of fracture paths in random heterogeneous microstructures is presented. The approach relies on the combination of manifold learning, introduced to explore the geometrical structure exhibited by crack patterns and ... Full text Cite

Corrigendum to “A linear complete extended finite element method for dynamic fracture simulation with non-nodal enrichments” [Finite Elem. Anal. Des. 152, 2018](S0168874X18305080)(10.1016/j.finel.2018.09.002)

Journal article Finite Elements in Analysis and Design · May 1, 2019 After manuscript [3] appeared online, previously published work that exhibits similar concepts was brought to the attention of the authors and the Editor-In-Chief. In particular, we mention the IGFEM [1] which introduced the concept of associating enriched ... Full text Cite

A phase-field formulation for dynamic cohesive fracture

Journal article Computer Methods in Applied Mechanics and Engineering · May 1, 2019 We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories o ... Full text Cite

A fully coupled mixed finite element method for surfactants spreading on thin liquid films

Journal article Computer Methods in Applied Mechanics and Engineering · March 1, 2019 A model for the spreading of surfactants over thin liquid films on rough surfaces is presented, along with a novel finite element based discretization. An existing framework for surfactants spreading is first augmented by allowing for the influence of a no ... Full text Cite

Models and simulations of surfactant-driven fracture in particle rafts

Journal article International Journal of Solids and Structures · January 1, 2019 A continuum-based model for the surfactant-driven fracture of closely-packed particle rafts is extended to examine the influence of micro-scale density variability. The model treats the particle monolayer as an elastic sheet endowed with a critical fractur ... Full text Cite

An optimization-based phase-field method for continuous-discontinuous crack propagation

Journal article International Journal for Numerical Methods in Engineering · October 5, 2018 A new continuous-discontinuous strategy for the computational modeling of crack propagation within the context of phase-field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage ba ... Full text Cite

A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data

Journal article Computational Mechanics · August 1, 2018 We present a strategy for the numerical integration of partial elements with the eXtended finite element method (X-FEM). The new strategy is specifically designed for problems with propagating cracks through a bulk material that exhibits inelasticity. Foll ... Full text Cite

Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers.

Journal article Soft matter · September 2017 A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as t ... Full text Cite

Remeshing strategies for large deformation problems with frictional contact and nearly incompressible materials

Journal article International Journal for Numerical Methods in Engineering · March 2, 2017 We present a framework to efficiently solve large deformation contact problems with nearly incompressible materials by implementing adaptive remeshing. Specifically, nodally integrated elements are employed to avoid mesh locking when linear triangular or t ... Full text Cite

The Thick Level-Set model for dynamic fragmentation

Journal article Engineering Fracture Mechanics · March 1, 2017 The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function ... Full text Cite

A robust Nitsche's formulation for interface problems with spline-based finite elements

Journal article International Journal for Numerical Methods in Engineering · November 16, 2015 The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving embedded interface problems. With a few exceptions, the X-FEM has mostly been used in conjunction with piecewise-linear shape functions and an associated pie ... Full text Cite

Special Issue: Advances in Embedded Interface Methods

Journal article International Journal for Numerical Methods in Engineering · November 16, 2015 Full text Cite

Extended finite element method in computational fracture mechanics: a retrospective examination

Journal article International Journal of Fracture · November 1, 2015 In this paper, we provide a retrospective examination of the developments and applications of the extended finite element method (X-FEM) in computational fracture mechanics. Our main attention is placed on the modeling of cracks (strong discontinuities) fo ... Full text Cite

Design of stiff, tough and stretchy hydrogel composites via nanoscale hybrid crosslinking and macroscale fiber reinforcement.

Journal article Soft matter · October 2014 Hydrogels' applications are usually limited by their weak mechanical properties. Despite recent great progress in developing tough hydrogels, it is still challenging to achieve high values of , toughness and modulus all together in synthetic hydrogels. In ... Full text Cite

A narrow-band gradient-augmented level set method for multiphase incompressible flow

Journal article Journal of Computational Physics · September 15, 2014 A finite-difference based numerical method for the simulation of multiphase incompressible flows is presented. The proposed algorithm adapts the gradient-augmented level set method of Nave et al. [25] for use in multiphase fluid simulations by interpolatin ... Full text Cite

Toward robust and accurate contact solvers for large deformation applications: A remapping/adaptivity framework for mortar-based methods

Journal article Computational Mechanics · July 1, 2014 In recent years, the mortar method has proven to be an effective spatial discretization strategy for large deformation contact problems, particularly when such problems feature deformable-to-deformable contact. The mortar approach has been shown to greatly ... Full text Cite

A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: Single interface

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2014 We investigate a finite element method for frictional sliding along embedded interfaces within a weighted Nitsche framework. For such problems, the proposed Nitsche stabilized approach combines the attractive features of two traditionally used approaches: ... Full text Cite

Toward robust and accurate contact solvers for large deformation applications: a remapping/adaptivity framework for mortar-based methods

Journal article Computational Mechanics · 2014 Cite

Going to new lengths: Studying the Navier-Stokes-αβ equations using the strained spiral vortex model

Journal article Discrete and Continuous Dynamical Systems Series B · January 1, 2014 We study the effect of the length scales α and β on the performance of the Navier-Stokes-αβ equations for numerical simulations of turbulence over coarse discretizations. To this end, we rely on the strained spiral vortex model and take advantage of the di ... Full text Cite

Adaptive refinement of hierarchical B-spline finite elements with an efficient data transfer algorithm

Journal article International Journal for Numerical Methods in Engineering · January 1, 2014 We present an adaptive B-spline FEM that employs hierarchical refinement and coarsening techniques. Hierarchical B-spline refinement augments the approximation space through the use of finer, more compactly supported B-splines. With this approach compatibi ... Full text Cite

A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: Intersecting interfaces

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2013 We extend the weighted Nitsche's method proposed in the first part of this study to include multiple intersecting embedded interfaces. These intersections arise either inside a computational domain - where two internal interfaces intersect; or on the bound ... Full text Cite

Microdomain evolution on giant unilamellar vesicles.

Journal article Biomechanics and modeling in mechanobiology · June 2013 A chemo-mechanical model is used to capture the formation and evolution of microdomains on the deforming surface of giant unilamellar vesicles. The model is intended for the regime of vesicle dynamics characterized by a distinct difference in time scales b ... Full text Cite

Numerical study of the grain-size dependent Young's modulus and Poisson's ratio of bulk nanocrystalline materials

Journal article International Journal of Solids and Structures · December 15, 2012 We present a numerical study of the elastic properties of bulk nanocrystalline materials based on a continuum theory, introduced by Fried and Gurtin (2009), for nanoscale polycrystalline elasticity that captures length-scale effects and accounts for intera ... Full text Cite

Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods

Journal article International Journal for Numerical Methods in Engineering · October 12, 2012 We investigate various strategies to enforce the kinematics at an embedded interface for transient problems within the extended finite element method. In particular, we focus on explicit time integration of the semi-discrete equations of motion and extend ... Full text Cite

A robust Nitsche's formulation for interface problems

Journal article Computer Methods in Applied Mechanics and Engineering · June 15, 2012 In this work, we propose a novel weighting for the interfacial consistency terms arising in a Nitsche variational form. We demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearin ... Full text Cite

Robust imposition of Dirichlet boundary conditions on embedded surfaces

Journal article International Journal for Numerical Methods in Engineering · April 6, 2012 We develop both stable and stabilized methods for imposing Dirichlet constraints on embedded, three-dimensional surfaces in finite elements. The stable method makes use of the vital vertex algorithm to develop a stable space for the Lagrange multipliers to ... Full text Cite

Erratum: An efficient finite element method for embedded interface problems

Journal article International Journal for Numerical Methods in Engineering · December 23, 2011 Full text Cite

A new method for simulating rigid body motion in incompressible two-phase flow

Journal article International Journal for Numerical Methods in Fluids · October 30, 2011 Computational treatment of immersed rigid bodies, especially in the presence of free surfaces and/or breaking waves, poses several modeling challenges. A motivating example where these systems are of interest is found in offshore wave energy harvesting sys ... Full text Cite

The Navier-Stokes-αβ equations as a platform for a spectral multigrid method to solve the Navier-Stokes equations

Journal article Computers and Fluids · May 1, 2011 This paper describes a spectral multigrid method for spatially periodic homogeneous and isotropic turbulent flows. The method uses the Navier-Stokes- αβ equations to accelerate convergence toward solutions of the Navier-Stokes equations. The Navier-Stokes- ... Full text Cite

Imposing dirichlet boundary conditions with Nitsche's method and spline-based finite elements

Journal article International Journal for Numerical Methods in Engineering · August 13, 2010 A key challenge while employing non-interpolatory basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. The current work studies the weak enforcement of such conditions for B-spline basis functions, with appli ... Full text Cite

Phase separation in biological membranes: integration of theory and experiment.

Journal article Annual review of biophysics · January 2010 Lipid bilayer model membranes that contain a single lipid species can undergo transitions between ordered and disordered phases, and membranes that contain a mixture of lipid species can undergo phase separations. Studies of these transformations are of in ... Full text Cite

Analysis of an efficient finite element method for embedded interface problems

Journal article Computational Mechanics · January 1, 2010 A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems, in which the finite element mesh need not be aligned with the interface geometry. We ... Full text Cite

From contact mechanics to fluid/structure interaction: Recent developments in interface discretization and stabilization

Journal article Computational Plasticity X Fundamentals and Applications · December 1, 2009 Cite

An edge-bubble stabilized finite element method for fourth-order parabolic problems

Journal article Finite Elements in Analysis and Design · June 1, 2009 We develop an edge-bubble stabilized finite element method for fourth-order parabolic problems. The method begins with a non-conforming approach, in which C0 basis functions are used to approximate the coarse scale of the bulk field. Continuity ... Full text Cite

On methods for stabilizing constraints over enriched interfaces in elasticity

Journal article International Journal for Numerical Methods in Engineering · May 28, 2009 Enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non-smooth problems. Internal features such as boundaries. Enriched finite element approaches such as the exte ... Full text Cite

An efficient finite element method for embedded interface problems

Journal article International Journal for Numerical Methods in Engineering · April 9, 2009 A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems. We consider cases in which the jump of a field across the interface is given, as well ... Full text Cite

Computational modeling of surface phenomena in soft-wet materials

Journal article International Journal of Solids and Structures · March 15, 2009 We consider the problem of extracting tribological information from experimental observations of contact with soft-wet materials. Particular attention is placed on simulating the response of two rotating cylinders of soft specimens placed in frictional con ... Full text Cite

The Melosh competition

Journal article Finite Elements in Analysis and Design · March 1, 2009 Full text Cite

Impact of the inherent separation of scales in the Navier-Stokes-αβ equations

Journal article Physical Review E · 2009 Cite

Residual-free bubbles for embedded Dirichlet problems

Journal article Computer Methods in Applied Mechanics and Engineering · August 15, 2008 We examine a stabilized method employing residual-free bubbles for enforcing Dirichlet constraints on embedded finite element interfaces. In particular, we focus attention on problems where the underlying mesh is not explicitly "fitted" to the geometry of ... Full text Cite

The Melosh Competition

Journal article Finite Elements in Analysis and Design · March 1, 2008 Full text Cite

Coupling volume-of-fluid based interface reconstructions with the extended finite element method

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2008 We examine the coupling of the patterned-interface-reconstruction (PIR) algorithm with the extended finite element method (X-FEM) for general multi-material problems over structured and unstructured meshes. The coupled method offers the advantages of allow ... Full text Cite

A stabilized treatment of arbitrarily oriented interfaces

Journal article Computational Plasticity Fundamentals and Applications Complas Ix · December 1, 2007 This work demonstrates novel methods for the stabilized enforcement of constraints associated with un-gridded interfaces, using enriched finite element methods for mechanics problems. Traditional methods such as penalty enforcement can be shown to yield os ... Cite

A theory of amorphous viscoelastic solids undergoing finite deformations with application to hydrogels

Journal article International Journal of Solids and Structures · June 1, 2007 We consider a hydrogel in the framework of a continuum theory for the viscoelastic deformation of amorphous solids developed by Anand and Gurtin [Anand, L., Gurtin, M., 2003. A theory of amorphous solids undergoing large deformations, with application to p ... Full text Cite

A numerical method for a second-gradient theory of incompressible fluid flow

Journal article Journal of Computational Physics · May 1, 2007 This work concerns the development of a finite-element method for discretizing a recent second-gradient theory for the flow of incompressible fluids. The new theory gives rise to a flow equation involving higher-order gradients of the velocity field and in ... Full text Cite

The Melosh Competition

Journal article Finite Elements in Analysis and Design · March 1, 2007 Full text Cite

A mortared finite element method for frictional contact on arbitrary interfaces

Journal article Computational Mechanics · February 2007 This work concerns finite-element algorithms for imposing frictional contact constraints on intra-element, or embedded surfaces. Existing techniques typically rely on the underlying bulk mesh to implicitly partition the surface, a strategy that can give ri ... Cite

A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces

Journal article International Journal for Numerical Methods in Engineering · January 22, 2007 We examine a bubble-stabilized finite element method for enforcing Dirichlet constraints on embedded interfaces. By 'embedded' we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mes ... Full text Cite

Switchable friction of stimulus-responsive hydrogels.

Journal article Langmuir : the ACS journal of surfaces and colloids · January 2007 Poly(N-isopropylacrylamide) (pNIPAAm) gels are stimulus-responsive hydrogels that exhibit large reversible changes in their volume and surface physicochemical properties near the lower critical solution temperature (LCST) in response to external stimuli, s ... Full text Cite

Kinetics of thermally induced swelling of hydrogels

Journal article International Journal of Solids and Structures · April 1, 2006 We present a continuum model for thermally induced volume transitions in stimulus-responsive hydrogels (SRHs). The framework views the transition as proceeding via the motion of a sharp interface separating swollen and collapsed phases of the underlying po ... Full text Cite

The Melosh Competition

Journal article Finite Elements in Analysis and Design · April 1, 2006 Full text Cite

An assumed-gradient finite element method for the level set equation

Journal article International Journal for Numerical Methods in Engineering · October 28, 2005 The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set e ... Full text Cite

A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels

Journal article Computer Methods in Applied Mechanics and Engineering · October 15, 2005 We present a strategy for obtaining numerical solutions to a system of non-linear, coupled evolution equations describing volume transitions in stimulus-responsive hydrogels (SRHs). The theory underlying our sharp-interface model of phase transitions in SR ... Full text Cite

Point defects in nematic gels: The case for hedgehogs

Journal article Archive for Rational Mechanics and Analysis · July 1, 2005 We address the question of whether a nematic gel is capable of sustaining a radially-symmetric point defect (or, hedgehog). We consider the special case of a gel cross-linked in a state where the mesogens are randomly aligned, and study the behavior of a s ... Full text Cite

The Melosh competition

Journal article Finite Elements in Analysis and Design · April 1, 2005 Full text Cite

On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method

Journal article International Journal for Numerical Methods in Engineering · December 14, 2004 We consider a problem stemming from recent models of phase transitions in stimulus-responsive hydrogels, wherein a sharp interface separates swelled and collapsed phases. Extended finite element methods that approximate the local solution with an enriched ... Full text Cite

Enrichment of enhanced assumed strain approximations for representing strong discontinuities: Addressing volumetric incompressibility and the discontinuous patch test

Journal article International Journal for Numerical Methods in Engineering · January 7, 2004 We present a geometrically non-linear assumed strain method that allows for the presence of arbitrary, intra-finite element discontinuities in the deformation map. Special attention is placed on the coarse-mesh accuracy of these methods and their ability t ... Full text Cite

Chemically induced swelling of hydrogels

Journal article Journal of the Mechanics and Physics of Solids · January 1, 2004 We consider a continuum model for chemically induced volume transitions in hydrogels. Consistent with experimental observations, the model allows for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer c ... Full text Cite

A note on enrichment functions for modelling crack nucleation

Journal article Communications in Numerical Methods in Engineering · December 1, 2003 For particular discretizations and crack configurations, the enhanced approximations of the eXtended finite-element method (X-FEM) cannot accurately represent the discontinuities in the near-tip displacement fields. In this note, we focus on the particular ... Full text Cite

On the use of effective properties for the fracture analysis of microstructured materials

Journal article Engineering Fracture Mechanics · September 1, 2002 This paper addresses some fundamental theoretical and numerical issues concerning the application of effective properties for the failure analysis of microstructured materials, with a focus on functionally graded materials. An edge-cracked square region is ... Full text Cite

A hybrid extended finite element/level set method for modeling phase transformations

Journal article International Journal for Numerical Methods in Engineering · July 20, 2002 A hybrid numerical method for modelling the evolution of sharp phase interfaces on fixed grids is presented. We focus attention on two-dimensional solidification problems, where the temperature field evolves according to classical heat conduction in two su ... Full text Cite

On the computation of mixed mode stress intensity factors in functionally graded materials

Journal article International Journal of Solids and Structures · April 30, 2002 A new interaction energy integral method for the computation of mixed-mode stress intensity factors at the tips of arbitrarily oriented cracks in functionally graded materials is described. In the method, interaction energy contour integrals are defined an ... Full text Cite

Solving thermal and phase change problems with the eXtended finite element method

Journal article Computational Mechanics · January 1, 2002 The application of the eXtended finite element method (X-FEM) to thermal problems with moving heat sources and phase boundaries is presented. Of particular interest is the ability of the method to capture the highly localized, transient solution in the vic ... Full text Cite

An extended finite element method for modeling crack growth with frictional contact

Journal article Computer Methods in Applied Mechanics and Engineering · October 26, 2001 A new technique for the finite element modeling of crack growth with frictional contact on the crack faces is presented. The extended Finite Element Method (X-FEM) is used to discretize the equations, allowing for the modeling of cracks whose geometry are ... Full text Cite

Arbitrary branched and intersecting cracks with the extended finite element method

Journal article International Journal for Numerical Methods in Engineering · August 30, 2000 Extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended finite element method (X-FEM) allows the representation of crack discontinuities an ... Full text Cite

Discontinuous enrichment in finite elements with a partition of unity method

Journal article Finite Elements in Analysis and Design · January 1, 2000 A technique is presented to model arbitrary discontinuities in the finite element framework by locally enriching a displacement-based approximation through a partition of unity method. This technique allows discontinuities to be represented independently o ... Full text Cite

Modeling fracture in Mindlin-Reissner plates with the extended finite element method

Journal article International Journal of Solids and Structures · January 1, 2000 A technique for the modeling of cracks and crack growth in plates using the extended finite element method (X-FEM) is presented. Beginning with a plate formulation which does not exhibit shear locking, the finite element approximation is enriched with both ... Full text Cite

Volumetric locking in the element free Galerkin method

Journal article International Journal for Numerical Methods in Engineering · October 30, 1999 A new formulation of the Element Free Galerkin (EFG) method is developed for the modelling of incompressible materials. Beginning with a mixed variational principle, a selective reduced integration procedure is developed by implementing nodal quadrature. N ... Full text Cite

A finite element method for crack growth without remeshing

Journal article International Journal for Numerical Methods in Engineering · September 10, 1999 An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through ... Full text Cite

A finite element method for crack growth without remeshing

Numerical integration of the Galerkin weak form in meshfree methods

Journal article Computational Mechanics · January 1, 1999 The numerical integration of Galerkin weak forms for meshfree methods is investigated and some improvements are presented. The character of the shape functions in meshfree methods is reviewed and compared to those used in the Finite Element Method (FEM). E ... Full text Cite

On the completeness of meshfree particle methods

Journal article International Journal for Numerical Methods in Engineering · 1998 The completeness of Smooth Particle Hydrodynamics (SPH) and its modifications is investigated. Completeness, or the reproducing conditions, in Galerkin approximations play the same role as consistency in finite-difference approximations. Several techniques ... Full text Cite

On the completeness of meshfree particle methods

Journal article Int. J. Numer. Methods Eng. (UK) · 1998 The completeness of smooth particle hydrodynamics (SPH) and its modifications is investigated. Completeness, or the reproducing conditions, in Galerkin approximations play the same role as consistency in finite-difference approximations. Several techniques ... Full text Link to item Cite

Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks

Journal article International Journal of Solids and Structures · January 1, 1998 New domain integrals for extracting mixed-mode stress intensity factors along curved, three-dimensional bimaterial interface cracks are derived. In the derivation, the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are im ... Full text Cite

Effect of out-of-plane properties of a polyimide film on the stress fields in microelectronic structures

Journal article Mechanics of Materials · January 1, 1996 The detailed modeling of microelectronic structures involving thin polyimide films is difficult due to the limited amount of information available on the out-of-plane polyimide properties. In the present analysis, we treat the out-of-plane mechanical prope ... Full text Cite

Interaction integral formulation for computing stress intensity factors along curved bimaterial interface cracks

Journal article American Society of Mechanical Engineers, Aerospace Division (Publication) AD · 1996 Domain integrals for extracting mixed-mode stress intensity factors along curved, three-dimensional bimaterial interface cracks are derived. In the derivation, the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are impose ... Cite

AN INTERACTION INTEGRAL FORMULATION FOR COMPUTING STRESS INTENSITY FACTORS ALONG CURVED BIMATERIAL INTERFACE CRACKS

Journal article ASME International Mechanical Engineering Congress and Exposition Proceedings Imece · January 1, 1996 Domain integrals for extracting mixed-mode stress intensity factors along curved, three-dimensional bimaterial interface cracks are derived. In the derivation, the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are impose ... Full text Cite

Influence of out-of-plane insulator properties on the interfacial stresses in periodic electronic structures

Journal article American Society of Mechanical Engineers Paper · December 1, 1995 While the in-plane properties of thin polyimide films can be measured using standard thermal-mechanical testing procedures, the experimental characterization of the out-of-plane properties (elastic constants and coefficient of thermal expansion) is very di ... Cite

A Variational Phase-Field Model For Ductile Fracture with Coalescence Dissipation

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