Module-1: Basics of Plasticity
Week 1: Introduction to Plasticity and Elastic Stress-Strain Relations
Lec-01 : Introduction to plasticity: Plastic behavior of materials, elastic and plastic strains, elastic, perfectly plastic, and hardening behavior. Definition of Elastic range, Yield stress, Yield surface, and admissible stress state. Introduction to Hardening and Softening Behavior. Introduction to Haigh Westergard coordinates.
Lec-02 : Stress-Strain Relations: Elastic constants, isotropy, homogeneity, and Mohr's Circle. Material Types: Introduction to anisotropic, monoclinic, and orthotropic materials.
Week 2: Fundamentals of Yield and Failure Criteria
Lec-03 : Failure Criterion for Pressure-Independent Materials - Tresca, Von mises
Lec-04 : Failure Criterion for Pressure-Dependent Materials- Mohr Columb, Rankine, and Drucker-Prager, Failure criteria for anisotropic materials
Week 3: Foundations of Plasticity and Plastic Stress-Strain Relations
Lec-05 : Kuhn-Tucker loading and unloading Conditions, State of stress in a plastic process.
Lec-06 : Stress-Strain Relations for Perfectly Plastic Materials Flow rule/normality condition- Associated and Non-Associative flow rules.
Lec-07 : Stress-Strain Relations for Work-Hardening Materials Hardening Rule, Work Hardening, and Strain Hardening Rules. Hardening Parameter. Internal Hardening variables and Potential function. Consistency Conditions, Incremental elastic stress-strain relations, Simple 1D model for rate-independent plasticity for isotropic, kinematic, and Mixed hardening cases.
Module-2: Application of Plasticity in Metals, Reinforced Concrete & Composites
Week 4: Metal Plasticity, Concrete Plasticity and Elasto-Plastic Metal Matrix Composites
Lec-08 :
Implementation in Metals: Formulation of the elastic-plastic matrix, finite element formulation, numerical algorithms for solving nonlinear equations, and numerical implementation of elastic-plastic incremental constitutive relations. Bounding surface theory and its extension to anisotropic cases.
Lec-09 :
Implementation in Concretes: Introduction, Failure Criteria, Plasticity Modeling: Hardening Behaviour and Softening Behavior
Lec-10 : Elasto-Plastic Metal Matrix Composites: Effective stresses, strains, and yield function, constitutive relations, stresses in the damage composite system, damage evolution, and both elastic and elasto-plastic constitutive relations in damaged composite systems.
Week 5: Concrete Elasticity and Failure Criteria
Lec-11 : Linear-Elastic Brittle-Fracture Models: Linear-elastic isotropic stress-strain relations for uncracked concrete, transversely isotropic stress-strain relations for cracked concrete, linear-elastic fracture analyses of undersea pressure-resistant concrete structures, fracture analyses of beams, and inelastic analysis of reinforced concrete panels.
Lec-12 :
Nonlinear-Elastic Fracture Models: Isotropic nonlinear-elastic stress-strain relations, general formulation of hyperelastic models, and the formulation of a third-order hyperelastic constitutive model. Incremental stress-strain relations, hypoelastic models, and an orthotropic hypoelastic constitutive model for concrete.
Lec-13 :
Failure Criteria of Concrete: Stress and strain invariants, and characteristics of the failure surface of concrete. One-parameter, two-parameter, three-parameter, four-parameter, and a five-parameter model, along with a fracture model for concrete.
Week 6: Fracture Models for Concrete
Lec-14 :
Elastic Perfectly Plastic Fracture Models: criteria of loading and unloading, elastic-strain-increment tensor, and plastic-strain-increment tensor, elastic perfectly plastic concrete models, Prandtl-Reuss material (J2 theory), Drucker-Prager material, Mohr-Coulomb material with a tension cutoff, and William-Warnke material.
Lec-15 :
Limit Analysis of Perfect Plasticity: theorems of limit analysis, a plasticity model for concrete, splitting tests on cylinders, shear resistance of joints, shear in beams with vertical stirrups, punching shear of reinforced concrete slabs, and the load-carrying capacity of concrete pavements.
Lec-16 :
Elastic-Hardening Plastic-Fracture Models: loading function, concept of effective stress and strain, hardening rule, flow rule, and Drucker's stability postulate, incremental stress-strain relations, Drucker-Prager material with isotropic hardening and softening, von Mises material with mixed hardening, and three-parameter models for concrete displaying isotropic and independent hardening in tension and compression.
Module-3: Plasticity based damage model for Concrete & Inelastic response of Composite MaterialsWeek 7: Mechanisms and Representation of Material Damage Models
Lec-17 :
Material Damage and Continuum Damage Mechanics microscopic mechanisms of damage, including scales of damage phenomena, physical mechanisms, and damage in fracture problems, concept of the representative volume element and continuum damage mechanics, including the notion of continuum damage mechanics.
Lec-18 :
Mechanical Representation of Damage and Damage Variables modeling techniques of damage, including effective area reduction, variations in elastic modulus, and void volume fraction, mechanical representation of damage states using scalar, vector, and higher-order damage variables, along with effective stress tensors, hypotheses of mechanical equivalence, and elastic constitutive equations for damaged materials.
Lec-19 :
Thermodynamics of Damaged Material fundamentals of thermodynamics, including the state variables, the first and second laws of thermodynamics, and Gibbs relations, thermodynamic constitutive theory of inelasticity with internal variables, dissipation potentials, and the evolution equations of internal variables, generalized standard materials and the quasi-standard thermodynamic approach.
Week 8: Inelastic Damage Mechanics: Constitutive Models, Energy Criteria, and Anisotropic Damage Behavior
Lec-20 :
Inelastic Constitutive Equations for Materials with Isotropic Damage One-dimensional and three-dimensional inelastic constitutive equations, including elastic-plastic, viscoplastic deformation, internal variables, thermodynamic potentials, and damage evolution.
Lec-21 :
Strain Energy Release and Stress Criteria in Damage DevelopmentStrain energy release, energy dissipation in elastic-plastic damage, stress triaxiality, stress sign effects, and stress criterion for ductile damage.
Lec-22 :
Inelastic Damage Theory and Anisotropic Damage ModelsInelastic damage theory based on total energy equivalence, thermodynamic potentials, dissipation potentials, and anisotropic damage theory using second-order symmetric and brittle damage models.
Week 9: Elastic-Plastic Damage and Ductile Fracture Mechanics
Lec-23 :
Constitutive and Evolution Equations of Elastic-Plastic Damage: Constitutive and evolution equations of elastic-plastic isotropic damage, ductile damage, brittle damage, and quasi-brittle damage, Elaboration of the two-scale damage model, threshold values for damage initiation, and critical fracture values.
Lec-24 :
Ductile Damage, Fracture and Application to Metal Forming: Ductile damage analysis approaches, Lemaitre’s ductile damage model, extension of the model, and finite element analysis of ductile fracture, Application to metal forming processes, including fracture limits of sheet metal forming, forging, blanking processes, and fatigue life assessment of cold working tools.
Week 10: Coupled Damage and Plasticity Models for metals and Composites
Lec-25 :
Damage and Plasticity in Metals stress and strain rate transformations between damaged and undamaged states, effective stress tensors, backstress tensors, elastic strain, and plastic strain rates, damage effect tensor, constitutive models, damage evolution, plastic deformation, coupling of damage and plastic deformation, application to void growth (Gurson’s model), effective spin tensor, example of ductile fracture.
Lec-26 :
A Coupled Anisotropic Damage Model for the Inelastic Response of Composite Materials theoretical formulation, constitutive equations for composite materials, computational aspects, covering program flow, plastic corrector algorithm, damage corrector algorithm, implementation of the viscoplastic damage model, including flow of the program, viscoplastic corrector algorithm, and results for viscoplastic damage analysis.
Module-4: Plasticity for high-strain-rate behaviour of concrete
Week 11: Fundamentals of Blast and Impact and Crack Growth: Plasticity and Rate Effects
Lec-27 : Basics of Blast and Impact Models
Lec-28 : Plasticity and Rate Effects During Crack Growth covers viscoelastic crack growth, steady crack growth in elastic-plastic materials, high strain rate crack growth in a plastic solid, fracture mode transition due to rate effects, ductile void growth, and microcracking and fragmentation. It includes topics on plastic strain on the crack line, growth criteria, toughness-speed relationships, crack arrest, and time-dependent strength under pulse loading.
Week 12: Computational Aspects of Plasticity
Lec-29 : Fundamentals of Return Mapping Algorithms
Lec-30 : Introduction to hyper elastic, Viscoelastic, and Visco plastic Materials
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