{"product_id":"handbook-of-peridynamic-modeling-9781482230437","title":"Handbook of Peridynamic Modeling","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on the integration of interactions rather than the spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation\/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage\/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eEditors Bobaru, Foster, Geubelle, and Silling present readers with a collection of academic and research perspectives toward a comprehensive guide to contemporary peridynamic modeling in a variety of applications. The editors have organized the sixteen selections that make up the main body of the text in five parts devoted to the need for nonlocal modeling and introduction toperidynamics; mathematics, numeric’s, and software tools of peridynamics; material models and links to atomsistic models; and other related subjects. Florin Bobaru is a faculty member of the University of Nebraska-Lincoln. John T. Foster is a faculty member of the University of Texas at Austin. Philippe H. Geubelle is a faculty member of the University of Illinois. Stewart A. Silling is with Sandia National Laboratories in New Mexico\u003c\/p\u003e\u003cp\u003e~ProtoView, 2017\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eI The Need for Nonlocal Modeling and Introduction to Peridynamics\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWhy Peridynamics? \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThe mixed blessing of locality \u003c\/p\u003e\u003cp\u003eOrigins of nonlocality in a model\u003c\/p\u003e\u003cp\u003eLong-range forces \u003c\/p\u003e\u003cp\u003eCoarsening a fine-scale material system \u003c\/p\u003e\u003cp\u003eSmoothing of a heterogeneous material system \u003c\/p\u003e\u003cp\u003eNonlocality at the macroscale \u003c\/p\u003e\u003cp\u003eThe mixed blessing of nonlocality\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIntroduction to Peridynamics \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eEquilibrium in terms of integral equations \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eMaterial modeling \u003c\/p\u003e\u003cp\u003eBond based materials\u003c\/p\u003e\u003cp\u003eRelation between bond densities and flux\u003c\/p\u003e\u003cp\u003ePeridynamic states \u003c\/p\u003e\u003cp\u003eOrdinary state based materials \u003c\/p\u003e\u003cp\u003eCorrespondence materials \u003c\/p\u003e\u003cp\u003eDiscrete particles as peridynamic bodies \u003c\/p\u003e\u003cp\u003eSetting the horizon \u003c\/p\u003e\u003cp\u003eLinearized peridynamics \u003c\/p\u003e\u003cp\u003ePlasticity \u003c\/p\u003e\u003cp\u003eBond based microplastic material \u003c\/p\u003e\u003cp\u003eLPS material with plasticity \u003c\/p\u003e\u003cp\u003eDamage and fracture \u003c\/p\u003e\u003cp\u003eDamage in bond based models \u003c\/p\u003e\u003cp\u003eDamage in ordinary state based material models\u003c\/p\u003e\u003cp\u003eDamage in correspondence material models \u003c\/p\u003e\u003cp\u003eNucleation strain \u003c\/p\u003e\u003cp\u003eTreatment of boundaries and interfaces \u003c\/p\u003e\u003cp\u003eBond based materials\u003c\/p\u003e\u003cp\u003eState based materials \u003c\/p\u003e\u003cp\u003eEmu numerical method \u003c\/p\u003e\u003cp\u003e2.7 Conclusions \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eII Mathematics, Numerics, and Software Tools of Peridynamics\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eNonlocal Calculus of Variations and Well-posedness of Peridynamics \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction .\u003c\/p\u003e\u003cp\u003eA brief review of well-posedness results\u003c\/p\u003e\u003cp\u003eNonlocal balance laws and nonlocal vector calculus \u003c\/p\u003e\u003cp\u003eNonlocal calculus of variations - an illustration\u003c\/p\u003e\u003cp\u003eNonlocal calculus of variations - further discussions \u003c\/p\u003e\u003cp\u003eSummary \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eLocal limits and asymptotically compatible discretizations \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eLocal PDE limits of linear peridynamic models \u003c\/p\u003e\u003cp\u003eDiscretization schemes and discrete local limits \u003c\/p\u003e\u003cp\u003eAsymptotically compatible schemes for peridynamics \u003c\/p\u003e\u003cp\u003eSummary\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eRoadmap for Software Implementation \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eEvaluating the internal force density \u003c\/p\u003e\u003cp\u003eBond damage and failure\u003c\/p\u003e\u003cp\u003eThe tangent stiffness matrix \u003c\/p\u003e\u003cp\u003eModeling contact \u003c\/p\u003e\u003cp\u003eMeshfree discretizations for peridynamics \u003c\/p\u003e\u003cp\u003eProximity search for identification of pairwise interactions \u003c\/p\u003e\u003cp\u003eTime integration\u003c\/p\u003e\u003cp\u003eExplicit time integration for transient dynamics \u003c\/p\u003e\u003cp\u003eEstimating the maximum stable time step \u003c\/p\u003e\u003cp\u003eImplicit time integration for quasi-statics \u003c\/p\u003e\u003cp\u003eExample simulations \u003c\/p\u003e\u003cp\u003eFragmentation of a brittle disk resulting from impact \u003c\/p\u003e\u003cp\u003eQuasi-static simulation of a tensile test\u003c\/p\u003e\u003cp\u003eSummary\u003cstrong\u003e \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIII Material Models and Links to Atomistic Models\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eConstitutive Modeling in Peridynamics \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eKinematics, momentum conservation, and terminology\u003c\/p\u003e\u003cp\u003eLinear peridynamic isotropic solid \u003c\/p\u003e\u003cp\u003ePlane elasticity\u003c\/p\u003e\u003cp\u003ePlane stress \u003c\/p\u003e\u003cp\u003ePlane strain \u003c\/p\u003e\u003cp\u003e\"Bond-based” theories as a special case\u003c\/p\u003e\u003cp\u003eOn the role of the influence function \u003c\/p\u003e\u003cp\u003eFinite Deformations \u003c\/p\u003e\u003cp\u003eInvariants of peridynamic scalar-states\u003c\/p\u003e\u003cp\u003eCorrespondence models\u003c\/p\u003e\u003cp\u003eNon-ordinary correspondence models for solid mechanics \u003c\/p\u003e\u003cp\u003eOrdinary correspondence models for solid mechanics \u003c\/p\u003e\u003cp\u003ePlasticity \u003c\/p\u003e\u003cp\u003eYield surface and flow rule \u003c\/p\u003e\u003cp\u003eLoading\/unloading and consistency\u003c\/p\u003e\u003cp\u003eNon-ordinary models \u003c\/p\u003e\u003cp\u003eA non-ordinary beam model\u003c\/p\u003e\u003cp\u003eA non-ordinary plate\/shell model \u003c\/p\u003e\u003cp\u003eOther non-ordinary models\u003c\/p\u003e\u003cp\u003eFinal Comments\u003cstrong\u003e \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eLinks between Peridynamic and Atomistic Models \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eMolecular dynamics\u003c\/p\u003e\u003cp\u003eMeshfree discretization of peridynamic models\u003c\/p\u003e\u003cp\u003eUpscaling molecular dynamics to peridynamics \u003c\/p\u003e\u003cp\u003eA one-dimensional nonlocal linear springs model \u003c\/p\u003e\u003cp\u003eA three-dimensional embedded-atom model \u003c\/p\u003e\u003cp\u003eComputational speedup through upscaling\u003c\/p\u003e\u003cp\u003eConcluding remarks \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAbsorbing Boundary Conditions with Verification \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eA PML for State-based Peridynamics \u003c\/p\u003e\u003cp\u003eTwo-dimensional (2D), State-based Peridynamics Review \u003c\/p\u003e\u003cp\u003eAuxiliary Field Formulation and PML Application\u003c\/p\u003e\u003cp\u003eNumerical Examples\u003c\/p\u003e\u003cp\u003eVerification of Cone and Center Crack Problems\u003c\/p\u003e\u003cp\u003eDimensional Analysis of Hertzian Cone Crack Development\u003c\/p\u003e\u003cp\u003ein Brittle Elastic Solids\u003c\/p\u003e\u003cp\u003eState-based Verification of a Cone Crack \u003c\/p\u003e\u003cp\u003eBond-based Verification of a Center Crack \u003c\/p\u003e\u003cp\u003eVerification of an Axisymmetric Indentation Problem \u003c\/p\u003e\u003cp\u003eFormulation \u003c\/p\u003e\u003cp\u003eAnalytical Verification \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIV Modeling Material Failure and Damage \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eDynamic brittle fracture as an upscaling of unstable mesoscopic dynamic\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eThe macroscopic evolution of brittle fracture as a small horizon limit\u003c\/p\u003e\u003cp\u003eof mesoscopic dynamics \u003c\/p\u003e\u003cp\u003eDynamic instability and fracture initiation \u003c\/p\u003e\u003cp\u003eLocalization of dynamic instability in the small horizon-macroscopic limit\u003c\/p\u003e\u003cp\u003eFree crack propagation in the small horizon-macroscopic limit \u003c\/p\u003e\u003cp\u003eSummary\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCrack Branching in Dynamic Brittle Fracture \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eA brief review of literature on crack branching \u003c\/p\u003e\u003cp\u003eTheoretical models and experimental results on dynamic\u003c\/p\u003e\u003cp\u003ebrittle fracture and crack branching \u003c\/p\u003e\u003cp\u003eComputations of dynamic brittle fracture based on FEM \u003c\/p\u003e\u003cp\u003eDynamic brittle fracture results based on atomistic modeling \u003c\/p\u003e\u003cp\u003e Dynamic brittle fracture based on particle and lattice-based methods \u003c\/p\u003e\u003cp\u003ePhase-field models in dynamic fracture \u003c\/p\u003e\u003cp\u003eResults on dynamic brittle fracture from peridynamic models\u003c\/p\u003e\u003cp\u003eBrief Review of the bond-based Peridynamic model\u003c\/p\u003e\u003cp\u003eAn accurate and efficient quadrature scheme\u003c\/p\u003e\u003cp\u003ePeridynamic results for dynamic fracture and crack branching \u003c\/p\u003e\u003cp\u003eCrack branching in soda-lime glass \u003c\/p\u003e\u003cp\u003eLoad case 1: stress on boundaries \u003c\/p\u003e\u003cp\u003eLoad case 2: stress on pre-crack surfaces \u003c\/p\u003e\u003cp\u003eLoad case 3: velocity boundary conditions \u003c\/p\u003e\u003cp\u003eCrack branching in Homalite \u003c\/p\u003e\u003cp\u003eLoad case 1: stress on boundaries\u003c\/p\u003e\u003cp\u003eLoad case 2: stress on pre-crack surfaces \u003c\/p\u003e\u003cp\u003eLoad case 3: velocity boundary conditions \u003c\/p\u003e\u003cp\u003eInfluence of sample geometry\u003c\/p\u003e\u003cp\u003e10.5.3.1 Load case 1: stress on boundaries \u003c\/p\u003e\u003cp\u003eLoad case 2: stress on pre-crack surfaces \u003c\/p\u003e\u003cp\u003eLoad case 3: velocity boundary conditions \u003c\/p\u003e\u003cp\u003eDiscussion of crack branching results \u003c\/p\u003e\u003cp\u003eWhy do cracks branch? \u003c\/p\u003e\u003cp\u003eThe importance of nonlocal modeling in crack branching \u003c\/p\u003e\u003cp\u003eConclusions \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eRelations Between Peridynamic and Classical Cohesive Models \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction\u003c\/p\u003e\u003cp\u003eAnalytical PD-based normal cohesive law\u003c\/p\u003e\u003cp\u003eCase 1 – No bonds have reached critical stretch \u003c\/p\u003e\u003cp\u003eCase 2 – Bonds have exceeded the critical stretch \u003c\/p\u003e\u003cp\u003eNumerical approximation of PD-based cohesive law \u003c\/p\u003e\u003cp\u003ePD-based tangential cohesive law\u003c\/p\u003e\u003cp\u003eCase 1 – No bonds have reached critical stretch\u003c\/p\u003e\u003cp\u003eCase 2 – Bonds have exceeded the critical stretch \u003c\/p\u003e\u003cp\u003ePD-based mixed-mode cohesive law\u003c\/p\u003e\u003cp\u003eConclusion\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePeridynamic modeling of fiber-reinforced composites\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003ePeridynamic analysis of a lamina \u003c\/p\u003e\u003cp\u003ePeridynamic analysis of a laminate \u003c\/p\u003e\u003cp\u003eNumerical results \u003c\/p\u003e\u003cp\u003eConclusions \u003c\/p\u003e\u003cp\u003eAppendix A: PD material constants of a lamina \u003c\/p\u003e\u003cp\u003eSimple shear \u003c\/p\u003e\u003cp\u003eUniaxial stretch in the fiber direction\u003c\/p\u003e\u003cp\u003eUniaxial stretch in the transverse direction \u003c\/p\u003e\u003cp\u003eBiaxial stretch \u003c\/p\u003e\u003cp\u003eAppendix B: Surface correction factors for a composite lamina \u003c\/p\u003e\u003cp\u003eAppendix C: PD interlayer and shear bond constants of a laminate \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePeridynamic Modeling of Impact and Fragmentation \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eConvergence studies and damage models that influence the damage\u003c\/p\u003e\u003cp\u003ebehavior \u003c\/p\u003e\u003cp\u003eDamage-dependent critical bond strain\u003c\/p\u003e\u003cp\u003eCritical bond strain dependence on compressive strains along\u003c\/p\u003e\u003cp\u003eother directions\u003c\/p\u003e\u003cp\u003eSurface effect in impact problems \u003c\/p\u003e\u003cp\u003eConvergence study for impact on a glass plate \u003c\/p\u003e\u003cp\u003eImpact on a multilayered glass system \u003c\/p\u003e\u003cp\u003eModel description \u003c\/p\u003e\u003cp\u003eA comparison between FEM and peridynamics for the elastic\u003c\/p\u003e\u003cp\u003eresponse of a multilayered system to impact\u003c\/p\u003e\u003cp\u003e13.4 Computational results for damage progression in the seven-layer\u003c\/p\u003e\u003cp\u003eglass system \u003c\/p\u003e\u003cp\u003eDamage evolution for the cross-section\u003c\/p\u003e\u003cp\u003eDamage evolution in the first layer\u003c\/p\u003e\u003cp\u003eDamage evolution in the second layer\u003c\/p\u003e\u003cp\u003eDamage evolution in the fourth layer\u003c\/p\u003e\u003cp\u003eDamage evolution in the seventh layer \u003c\/p\u003e\u003cp\u003eConclusions \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eV Multiphysics and Multiscale Modeling \u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCoupling Local and Nonlocal Models\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction\u003c\/p\u003e\u003cp\u003eEnergy-based blending schemes\u003c\/p\u003e\u003cp\u003eThe Arlequin method \u003c\/p\u003e\u003cp\u003eDescription of the coupling model\u003c\/p\u003e\u003cp\u003eA numerical example\u003c\/p\u003e\u003cp\u003eThe morphing method\u003c\/p\u003e\u003cp\u003eOverview \u003c\/p\u003e\u003cp\u003eDescription of the morphing method \u003c\/p\u003e\u003cp\u003eOne-dimensional analysis of ghost forces \u003c\/p\u003e\u003cp\u003eNumerical examples \u003c\/p\u003e\u003cp\u003eForce-based blending schemes \u003c\/p\u003e\u003cp\u003eConvergence of peridynamic models to classical models \u003c\/p\u003e\u003cp\u003eDerivation of force-based blending schemes \u003c\/p\u003e\u003cp\u003eA numerical example \u003c\/p\u003e\u003cp\u003eSummary\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eA Peridynamic model for corrosion damage\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAbstract \u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eElectrochemical Kinetics \u003c\/p\u003e\u003cp\u003eProblem formulation of 1D pitting corrosion \u003c\/p\u003e\u003cp\u003eThe peridynamic formulation for 1D pitting corrosion\u003c\/p\u003e\u003cp\u003eResults and discussion of 1D pitting corrosion \u003c\/p\u003e\u003cp\u003ePit corrosion depth proportional to square root t\u003c\/p\u003e\u003cp\u003eActivation-controlled, diffusion-controlled, and IR-controlled\u003c\/p\u003e\u003cp\u003ecorrosion \u003c\/p\u003e\u003cp\u003eCorrosion damage and the Concentration-Dependent Damage\u003c\/p\u003e\u003cp\u003e(CDD) model \u003c\/p\u003e\u003cp\u003eDamage evolution \u003c\/p\u003e\u003cp\u003eSaturated concentration \u003c\/p\u003e\u003cp\u003eFormulation and results of 2D and 3D pitting corrosion \u003c\/p\u003e\u003cp\u003ePD formulation of 2D and 3D pitting corrosion \u003c\/p\u003e\u003cp\u003eThe Concentration-Dependent Damage (CDD) model for\u003c\/p\u003e\u003cp\u003epitting corrosion: example in 2D \u003c\/p\u003e\u003cp\u003eA coupled corrosion\/damage model for pitting corrosion: 2D example \u003c\/p\u003e\u003cp\u003eDiffusivity affects the corrosion rate \u003c\/p\u003e\u003cp\u003ePitting corrosion with the CDD+DDC model in 3D \u003c\/p\u003e\u003cp\u003ePitting corrosion in heterogeneous materials: examples in 2D \u003c\/p\u003e\u003cp\u003ePitting corrosion in layer structures \u003c\/p\u003e\u003cp\u003ePitting corrosion in a material with inclusions: a 2D example \u003c\/p\u003e\u003cp\u003eConclusions \u003c\/p\u003e\u003cp\u003eAppendix \u003c\/p\u003e\u003cp\u003eConvergence study for 1D diffusion-controlled corrosion \u003c\/p\u003e\u003cp\u003eConvergence study for 2D activation-controlled corrosion\u003c\/p\u003e\u003cp\u003ewith Concentration-Dependent Damage model \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePeridynamics for Coupled Field Equations\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eIntroduction \u003c\/p\u003e\u003cp\u003eDiffusion Equation \u003c\/p\u003e\u003cp\u003eThermal diffusion \u003c\/p\u003e\u003cp\u003eMoisture diffusion \u003c\/p\u003e\u003cp\u003eElectrical conduction \u003c\/p\u003e\u003cp\u003eCoupled Field Equations \u003c\/p\u003e\u003cp\u003eThermomechanics \u003c\/p\u003e\u003cp\u003eThermal diffusion with a structural coupling term \u003c\/p\u003e\u003cp\u003eEquation of motion with a thermal coupling term \u003c\/p\u003e\u003cp\u003ePorelasticity \u003c\/p\u003e\u003cp\u003eMechanical deformation due to fluid pressure \u003c\/p\u003e\u003cp\u003eFluid flow in porous medium \u003c\/p\u003e\u003cp\u003eElectromigration \u003c\/p\u003e\u003cp\u003eHygrothermomechanics\u003c\/p\u003e\u003cp\u003eNumerical solution to peridynamic field equations \u003c\/p\u003e\u003cp\u003eCorrection of PD material parameters \u003c\/p\u003e\u003cp\u003eBoundary conditions \u003c\/p\u003e\u003cp\u003eEssential boundary conditions \u003c\/p\u003e\u003cp\u003eNatural boundary conditions\u003c\/p\u003e\u003cp\u003eExample 1\u003c\/p\u003e\u003cp\u003eExample 2 \u003c\/p\u003e\u003cp\u003eExample 3 \u003c\/p\u003e\u003cp\u003eApplications \u003c\/p\u003e\u003cp\u003eCoupled nonuniform heating and deformation \u003c\/p\u003e\u003cp\u003eCoupled nonuniform moisture and deformation in a square plate \u003c\/p\u003e\u003cp\u003eCoupled fluid pore pressure and deformation\u003c\/p\u003e\u003cp\u003eCoupled electrical, temperature, deformation, and vacancy diffusion \u003c\/p\u003e\u003cp\u003eRemarks \u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":50578093670743,"sku":"9781482230437","price":185.25,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781482230437.jpg?v=1746097868","url":"https:\/\/bookcurl.com\/products\/handbook-of-peridynamic-modeling-9781482230437","provider":"Book Curl","version":"1.0","type":"link"}