isogeometric and extended finite element methods Borst, René de creator author. 18n 0 e "5.4.4 Weak Forms and Discretization"" -- ""5.4.5 Example Calculations"" -- "" References"" -- ""6 Fracture Modeling Using Isogeometric Analysis"" -- ""6.1 Basis Functions in Isogeometric Analysis"" -- ""6.1.1 Univariate B-Splines"" -- ""6.1.2 Univariate Non-Uniform Rational B-Splines"" -- ""6.1.3 Multivariate B-Splines and NURBS Patches"" -- ""6.2 Isogeometric Finite Elements"" -- ""6.3 Isogeometric Analysis for Poroelasticity"" -- ""6.3.1 Formulation Using B©℗♭zier Extraction"" -- ""6.3.2 Local Mass Conservation and Minimum Time Step"" -- ""6.3.3 Unequal Orders of Interpolation"" -- ""6.4 Discontinuities in B-Splines and NURBS"" -- ""6.5 An Isogeometric Interface Element"" -- ""6.5.1 B©℗♭zier Extraction"" -- ""6.5.2 Spatial Integration"" -- ""6.5.3 An Isogeometric Interface Element for Porous Media"" -- ""6.6 Cohesive Crack Propagation"" -- "" References"" -- ""7 Phase-Field Methods for Fracture"" -- ""7.1 The Phase-Field Approach to Brittle Fracture"" -- ""7.1.1 The Phase-Field Approximation"" -- ""7.1.2 Brittle Fracture"" -- ""7.1.3 Discretization and Linearization"" -- ""7.1.4 Internal Length Scale and Degradation Function"" -- ""7.1.5 G-Convergence"" -- ""7.2 A Phase-Field Method for Cohesive Fracture"" -- ""7.2.1 Kinematics"" -- ""7.2.2 Discretization and Linearization"" -- ""7.2.3 Order of the Interpolations"" -- ""7.3 Phase-Field Approaches for Fracture in Porous Media"" -- "" References"" -- ""Index""." René de Borst. "Front Cover"" -- ""Computational Methods for Fracture in Porous Media"" -- ""Copyright"" -- ""Dedication"" -- ""Contents"" -- ""About the Author"" -- ""Preface"" -- ""Acknowledgment"" -- ""1 Introduction"" -- ""1.1 Fracture in Porous Media"" -- ""1.2 The Representation of Cracks and Fluid Flow in Cracks"" -- ""1.3 Purpose and Scope"" -- "" References"" -- ""2 Fractured or Fracturing, Fully or Partially Saturated Porous Media"" -- ""2.1 Mass and Momentum Balance in a Porous Medium"" -- ""2.2 A Saturated Porous Medium"" -- ""2.2.1 Balance Equations and Constitutive Equations"" -- ""2.2.2 Weak Forms"" -- ""2.3 Unsaturated Porous Medium"" -- ""2.3.1 Balance Equations and Constitutive Equations"" -- ""2.3.2 Weak Forms"" -- ""2.4 Modeling of Mass Transport Within Cracks"" -- ""2.4.1 Fully Open Cracks"" -- ""2.4.2 Partially Open Cracks"" -- ""2.4.3 Fluid Flow Normal to the Crack"" -- "" References"" -- ""3 Fracture Mechanics"" -- ""3.1 Linear Elastic Fracture Mechanics"" -- ""3.2 Cohesive Zone Models"" -- "" References"" -- ""4 Interface Elements"" -- ""4.1 Standard Interface Elements"" -- ""4.1.1 Interface Kinematics"" -- ""4.1.2 Constitutive Relation for the Interface"" -- ""4.1.3 Internal Force Vector and Tangential Stiffness Matrix"" -- ""4.1.4 Numerical Integration of Interface Elements"" -- ""4.2 Poromechanical Interface Elements"" -- ""4.2.1 Interface Elements With a Continuous Pressure"" -- ""4.2.2 Interface Elements With a Discontinuous Pressure"" -- ""4.2.3 An Independent Pressure in the Interface"" -- ""4.3 Remeshing Techniques"" -- "" References"" -- ""5 The Extended Finite Element Method"" -- ""5.1 The Partition-of-Unity Concept"" -- ""5.2 Extension to Fluid-Saturated Porous Media"" -- ""5.2.1 Continuous Pressure Field"" -- ""5.2.2 Discontinuous Pressure Field"" -- ""5.3 Extension to Dynamics"" -- ""5.4 Large Deformations"" -- ""5.4.1 Nonlinear Kinematics"" -- ""5.4.2 Balance Equations"" -- ""5.4.3 Constitutive Equations""." Includes bibliographical references at the end of each chapters and index. Fracture mechanics Mathematical models 9780081009178 MiAaPQ |a2508 20251112200007.0 u7432 eng