Chad M. Landis

Bio: Chad M. Landis is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Constitutive equation & Finite element method. The author has an hindex of 40, co-authored 116 publications receiving 6543 citations. Previous affiliations of Chad M. Landis include Harvard University & Rice University.

A phase-field description of dynamic brittle fracture

Abstract: In contrast to discrete descriptions of fracture, phase-field descriptions do not require numerical tracking of discontinuities in the displacement field. This greatly reduces implementation complexity. In this work, we extend a phase-field model for quasi-static brittle fracture to the dynamic case. We introduce a phase-field approximation to the Lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase-field. We study the behavior of the model in one dimension and show how it influences material properties. For the temporal discretization of the equations of motion, we present both a monolithic and staggered time integration scheme. We study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments. We also introduce a local adaptive refinement strategy and study its performance in the context of locally refined T-splines. We show that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.

A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework

Abstract: Phase-field models based on the variational formulation for brittle fracture have recently been gaining popularity. These models have proven capable of accurately and robustly predicting complex crack behavior in both two and three dimensions. In this work we propose a fourth-order model for the phase-field approximation of the variational formulation for brittle fracture. We derive the thermodynamically consistent governing equations for the fourth-order phase-field model by way of a variational principle based on energy balance assumptions. The resulting model leads to higher regularity in the exact phase-field solution, which can be exploited by the smooth spline function spaces utilized in isogeometric analysis. This increased regularity improves the convergence rate of the numerical solution and opens the door to higher-order convergence rates for fracture problems. We present an analysis of our proposed theory and numerical examples that support this claim. We also demonstrate the robustness of the model in capturing complex three-dimensional crack behavior.

Electrostatic Forces and Stored Energy for Deformable Dielectric Materials

Abstract: An isothermal energy balance is formulated for a system consisting of deformable dielectric bodies, electrodes, and the surrounding space. The formulation in this paper is obtained in the electrostatic limit but with the possibility of arbitrarily large deformations of polarizable material. The energy balance recognizes that charges may be driven onto or off of the electrodes, a process accompanied by external electrical work; mechanical loads may be applied to the bodies, thereby doing work through displacements; energy is stored in the material by such features as elasticity of the lattice, piezoelectricity, and dielectric and electrostatic interactions; and nonlinear reversible material behavior such as electrostriction may occur. Thus the external work is balanced by (I) internal energy consisting of stress doing work on strain increments, (2) the energy associated with permeating free space with an electric field, and (3) by the electric field doing work on increments of electric displacement or, equivalently, polarization. For a conservative system, the internal work is stored reversibly in the body and in the underlying and surrounding space. The resulting work statement for a conservative system is considered in the special cases of isotropic deformable dielectrics and piezoelectric materials. We identify the electrostatic stress, which provides measurable information quantifying the electrostatic effects within the system, and find that it is intimately tied to the constitutive formulation for the material and the associated stored energy and cannot be independent of them. The Maxwell stress, which is related to the force exerted by the electric field on charges in the system, cannot be automatically identified with the electrostatic stress and is difficult to measure. Two well-known and one novel formula for the electrostatic stress are identified and related to specific but differing constitutive assumptions for isotropic materials. The electrostatic stress is then obtained for a specific set of assumptions in regard to a piezoelectric material. An exploration of the behavior of an actuator composed of a deformable, electroactive polymer is presented based on the formulation of the paper.

A constitutive model for ferroelectric polycrystals

Abstract: A constitutive model is developed for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field. It is envisaged that the polycrystal consists of a set of bonded crystals and that each crystal comprises a set of distinct crystal variants. Within each crystal the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation and to a change in the average linear electromechanical properties. It is further assumed that switching is resisted by the dissipative motion of domain walls. The constitutive model for the progressive switching of each crystal draws upon elastic–plastic crystal plasticity theory, and a prescription is given for the tangent moduli of the crystal, for any assumed set of potentially active transformation systems. A self-consistent analysis is used to estimate the macroscopic response of tetragonal crystals (representative of lead titanate) under a variety of loading paths. Also, the evolution of the switching surface in stress-electric field space is calculated. Many of the qualitative features of ferroelectric switching, such as butterfly hysteresis loops, are predicted by the analysis.

A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects

Abstract: Phase-field models have been a topic of much research in recent years. Results have shown that these models are able to produce complex crack patterns in both two and three dimensions. A number of extensions from brittle to ductile materials have been proposed and results are promising. To date, however, these extensions have not accurately represented strains after crack initiation or included important aspects of ductile fracture such as stress triaxiality. This work introduces a number of contributions to further develop phase-field models for fracture in ductile materials. These contributions include: a cubic degradation function that provides a stress–strain response prior to crack initiation that more closely approximates linear elastic behavior, a derivation of the governing equations in terms of a general energy potential from balance laws that describe the kinematics of both the body and phase-field, introduction of a yield surface degradation function that provides a mechanism for plastic softening and corrects the non-physical elastic deformations after crack initiation, a proposed mechanism for including a measure of stress triaxiality as a driving force for crack initiation and propagation, and a correction to an error in the configuration update of an elastoplastic return-mapping algorithm for J 2 flow theory. We also present a heuristic time stepping scheme that facilitates computations that require a relatively long load time prior to crack initiation. A number of numerical results will be presented that demonstrate the effects of these contributions.

Perspective on the Development of Lead-free Piezoceramics

Abstract: A large body of work has been reported in the last 5 years on the development of lead-free piezoceramics in the quest to replace lead–zirconate–titanate (PZT) as the main material for electromechanical devices such as actuators, sensors, and transducers. In specific but narrow application ranges the new materials appear adequate, but are not yet suited to replace PZT on a broader basis. In this paper, general guidelines for the development of lead-free piezoelectric ceramics are presented. Suitable chemical elements are selected first on the basis of cost and toxicity as well as ionic polarizability. Different crystal structures with these elements are then considered based on simple concepts, and a variety of phase diagrams are described with attractive morphotropic phase boundaries, yielding good piezoelectric properties. Finally, lessons from density functional theory are reviewed and used to adjust our understanding based on the simpler concepts. Equipped with these guidelines ranging from atom to phase diagram, the current development stage in lead-free piezoceramics is then critically assessed.

Carbon nanotubes and nanofibers in catalysis

Abstract: This review analyses the literature from the early 1990s until the beginning of 2003 and covers the use of carbon nanotubes (CNT) and nanofibers as catalysts and catalysts supports. The article is composed of three sections, the first one explains why these materials can be suitable for these applications, the second describes the different preparation methods for supporting metallic catalysts on these supports, and the last one details the catalytic results obtained with nanotubes or nanofibers based catalysts. When possible, the results were compared to those obtained on classical carbonaceous supports and explanations are proposed to clarify the different behaviors observed.

A review on phase-field models of brittle fracture and a new fast hybrid formulation

Abstract: In this contribution we address the issue of efficient finite element treatment for phase-field modeling of brittle fracture. We start by providing an overview of the existing quasi-static and dynamic phase-field fracture formulations from the physics and the mechanics communities. Within the formulations stemming from Griffith's theory, we focus on quasi-static models featuring a tension-compression split, which prevent cracking in compression and interpenetration of the crack faces upon closure, and on the staggered algorithmic implementation due to its proved robustness. In this paper, we establish an appropriate stopping criterion for the staggered scheme. Moreover, we propose and test the so-called hybrid formulation, which leads within a staggered implementation to an incrementally linear problem. This enables a significant reduction of computational cost--about one order of magnitude--with respect to the available (non-linear) models. The conceptual and structural similarities of the hybrid formulation to gradient-enhanced continuum damage mechanics are outlined as well. Several benchmark problems are solved, including one with own experimental verification.

Theory of dielectric elastomers

Abstract: In response to a stimulus, a soft material deforms, and the deformation provides a function. We call such a material a soft active material (SAM). This review focuses on one class of soft active materials: dielectric elastomers. When a membrane of a dielectric elastomer is subject to a voltage through its thickness, the membrane reduces thickness and expands area, possibly straining over 100%. The dielectric elastomers are being developed as transducers for broad applications, including soft robots, adaptive optics, Braille displays, and electric generators. This paper reviews the theory of dielectric elastomers, developed within continuum mechanics and thermodynamics, and motivated by molecular pictures and empirical observations. The theory couples large deformation and electric potential, and describes nonlinear and nonequilibrium behavior, such as electromechanical instability and viscoelasticity. The theory enables the finite element method to simulate transducers of realistic configurations, predicts the efficiency of electromechanical energy conversion, and suggests alternative routes to achieve giant voltage-induced deformation. It is hoped that the theory will aid in the creation of materials and devices.