Plasticity and Viscoelasticity

Fertig Research Group: Multiscale Failure of Materials via YouTube

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Provider

YouTube
Pricing

Free Video
Languages

English
Duration & workload

19 hours 11 minutes
Sessions

On-Demand
Level

Advanced

Found in

Explore advanced mechanical behavior of materials through this comprehensive graduate-level course covering plasticity and viscoelasticity theory. Master fundamental concepts beginning with tensor mathematics, continuum mechanics, and kinematics before progressing to complex material constitutive relationships. Develop expertise in plastic deformation mechanisms across different material systems, including metals and other engineering materials, while learning to apply one-dimensional and three-dimensional plasticity frameworks. Study yield criteria such as von Mises and Tresca, hardening models including isotropic and kinematic approaches, and the mathematical foundations of incremental plasticity theory. Investigate viscoelastic material behavior through simple and generalized models like Maxwell and Kelvin-Voight systems, utilizing Laplace transforms and hereditary integrals to solve time-dependent problems. Apply the correspondence principle to convert elastic solutions for viscoelastic analysis, examine time-temperature superposition effects, and analyze oscillatory loading conditions including storage and loss moduli calculations. Gain practical problem-solving skills through detailed mathematical derivations, stress-strain relationships, and energy dissipation analysis essential for advanced materials engineering applications.

Syllabus

Vector Notation and Conventions
Tensor Review (Definitions)
Tensor Review (Coordinate Transformation)
1-2a: Continuum Kinematics (Reference Frames and Deformation)
1-2b: Continuum Kinematics (Lagrange Finite Strain Tensor)
1-2c: Continuum Kinematics (Meaning of the Lagrange Finite Strain Tensor)
1-2d: Continuum Kinematics (Displacement-Based Strain Formulation)
1-2e: Continuum Kinematics (Shear Strain)
Continuum Stresses (Cauchy Stress Formula)
Continuum Stresses (Principal Stresses)
Continuum Stresses (Stress Invariants)
Continuum Stresses (Hydrostatic and Deviatoric Stresses)
1-4: Equations of Motion and Equlibrium
1-5: Constitutive Law (Hooke's Law)
1-6: Linking Linear Elastic Mechanics with Plasticity
2-1a: Plasticity Mechanisms (Plastic Deformation in Metals)
2-1b: Plasticity Mechanisms (Plastic Deformation in Other Materials)
2-2a: Plasticity in a 1-D Bar (Deformation Measures)
2-2b: Plasticity in a 1-D Bar (Deformation Decomposition)
2-2c: Plasticity in a 1-D Bar (Elastic-Perfectly Plastic)
2-2d: Plasticity in a 1-D Bar (Isotropic Hardening-Part I)
2-2e: Plasticity in a 1-D Bar (Isotropic Hardening-Part II)
2-2f: Plasticity in a 1-D Bar (Kinematic Hardening)
2-3a: General (3-D) Framework for Plasticity (Yield Function)
2-3b: General (3-D) Framework for Plasticity (Consistency Condition)
2-3c: General (3-D) Framework for Plasticity (Flow Rule)
2-4a: Uniqueness and Stability (Net Stress Work and Net Complementary Stress Work)
2-4b: Uniqueness and Stability (Stress Cycle)
2-5a: Properties of Yield Surfaces (Maximum Dissipation Postulate)
2-5b: Properties of Yield Surfaces (Convexity of Surface and Normality of Plastic Strain Increment)
2-5c: Properties of Yield Surfaces (Consequences of the Normality Rule)
2-6a: Initial Yield Surfaces (Octahedral Plane)
2-6b: Initial Yield Surfaces (von Mises Yield Criterion)
2-6c: Initial Yield Surfaces (Tresca Yield Criterion)
2-6d: Initial Yield Surfaces (Yield Criteria with Hydrostatic Effects)
2-7: Subsequent Yield Surfaces
2-8a: 3D Incremental Plasticity (von Mises with Isotropic Hardening)
2-8b: 3D Incremental Plasticity (Scalar Hardening Function)
2-9: Path Dependence of Plastic Strains
2-10: Combined Isotropic and Kinematic Hardening
3-1a: Viscoelasticity Introduction (Basics)
3-1b: Viscoelasticity Introduction (Physical Mechanisms)
3-2a: Simple Viscoelastic Models (Maxwell and Kelvin-Voight Materials)
3-2b: Simple Viscoelastic Models (Creep Compliance)
3-2c: Simple Viscoelastic Models (Relaxation Modulus)
3-3a: Laplace Transform (Overview)
3-3b: Laplace Transform (Creep Compliance Example)
3-4a: Generalized Viscoelastic Models (Generalized Maxwell Model - Part I)
3-4b: Generalized Viscoelastic Models (Generalized Maxwell Model - Part II)
3-4c: Generalized Viscoelastic Models (Generalized Kelvin-Voight Model)
3-4d: Generalized Viscoelastic Models (Creep Compliance - Part I)
3-4e: Generalized Viscoelastic Models (Creep Compliance - Part II)
3-5a: Hereditary Integrals (Creep Compliance)
3-5b: Hereditary Integrals (Relaxation Modulus)
3-5c: Hereditary Integrals (Alternate Forms)
3-6a: Correspondence Principle
3-6b: Correspondence Principle (Beam Example)
3-7: Viscoelasticity in Three Dimensions
3-8: Time-Temperature Superposition
3-9a: Oscillatory Loading (Storage and Loss Moduli)
3-9b: Oscillatory Loading (Loss Tangent)
3-9c: Oscillatory Loading (Relationships between Complex Quantities)
3-10: Energy Dissipation in Viscoelastic Materials