Course10510800172 lectures
Advanced Plasticity of Solid Continua
Prof. Debasish Roy · IISc Bangalore
About
This graduate course offers a rigorous, field-theoretic treatment of plastic deformation in solid continua, grounded in finite-deformation kinematics and rational thermodynamics. We develop thermodynamically consistent constitutive closures using internal variables and the dissipation inequality, and study yielding, flow rules and hardening in both classical and modern formulations. Additive and multiplicative decompositions are treated carefully, with analytic solutions of representative boundary-value problems to build physical intuition. The course also covers numerical implementation – linearization and finite-element schemes for small-strain plasticity – and contemporary yield-free approaches. Intended for M.Tech/MS and PhD students, it equips participants with both theoretical depth and practical-cum-computational insights for research-grade modelling.
Intended audience: Research students, industry peoples
Prerequisites: B.E. or B.Tech. pursuing Master’s or PhD, with some background in the basics of Continuum Mechanics
Lectures
Week 1 Kinematics, Strain Measures, and Objectivity
- Motion, Configurations, and the Philosophy of the Continuum
- Kinematics. Line and Area Transformation
- Volume Transformations and Strain Measures
- Objectivity and Strain Measures
- Objective Strain Rates
Week 2 Balance Laws, Yielding, and Thermodynamics
- Transport and Divergence Theorems
- Balance Laws
- Physics of Yielding
- Classical Yield Criteria
- Thermodynamic Closure
- The Coleman-Noll Procedure
Week 3 Hardening, Convex Analysis, and Variational Structures
- Isotropic Hardening: Physical Insight and Thermodynamic Structure
- Kinematic Hardening: Physical Insight and Thermodynamic Structure
- Rate Independent Plasticity and Convex Analysis - Part 1
- Rate Independent Plasticity and Convex Analysis - Part 2
- Rate Independent Plasticity through Convex Analysis - Part 1
- Rate Independent Plasticity through Convex Analysis - Part 2
Week 4 Incremental Variational Frameworks, Pressure Sensitivity, and Rate-Dependent Plasticity
- Rate Independent Plasticity through Convex Analysis - Part 3
- Rate Independent Plasticity through Convex Analysis - Part 4
- Pressure Sensitive Plasticity and Rate Dependence - Part 1
- Pressure Sensitive Plasticity and Rate Dependence - Part 2
- Rate Dependent Plasticity – Perzyna Model - Part 1
- Rate Dependent Plasticity – Perzyna Model - Part 2
Week 5 Time-Discretized Variational Frameworks and Thermo-Visco-Plasticity
- Rate dependent plasticity – Time-discretized variational problem - Part 1
- Rate dependent plasticity – Time-discretized variational problem - Part 2
- Rate dependent plasticity – Time-discretized variational problem - Part 3
- Thermo-visco-plasticity: A variational route - Part 1
- Thermo-visco-plasticity: A variational route - Part 2
Week 6 Variational Rate Functionals and Computational Thermo-Visco-Plasticity
- Rate-dependent thermo-viscoplasticity & The variational problem - Part 1
- Rate-dependent thermo-viscoplasticity & The variational problem - Part 2
- Rationale behind the rate functional & Time-discretized variational update - Part 1
- Rationale behind the rate functional & Time-discretized variational update - Part 2
- Thermo-visco-plasticity: The consistent tangent stiffness - Part 1
- Thermo-visco-plasticity: The consistent tangent stiffness - Part 2
Week 7 Fully Coupled Thermo-Mechanics and Strain Gradient Plasticity
- FEM for fully coupled thermo-visco-plasticity and Strain gradient plasticity - Part 1
- FEM for fully coupled thermo-visco-plasticity and Strain gradient plasticity - Part 2
- Strain gradient plasticity – Primal formulation - Part 1
- Strain gradient plasticity – Primal formulation - Part 2
- Strain Gradient Plasticity: Dual Formulation and FEM Implementation - Part 1
- Strain Gradient Plasticity: Dual Formulation and FEM Implementation - Part 2
Week 8 Thermodynamic Dislocation Theory and the 2-Temperature Model
- Mixed FEM for Strain Gradient Plasticity; 2-Temperature Model - Part 1
- Mixed FEM for Strain Gradient Plasticity; 2-Temperature Model - Part 2
- 2-Temperature Model for Visco-plasticity - Part 1
- 2-Temperature Model for Visco-plasticity - Part 2
- 2-Temperature Viscoplasticity: Evolution Equations and Incremental Updates - Part 1
- 2-Temperature Viscoplasticity: Evolution Equations and Incremental Updates - Part 2
Week 9 2-Temperature model and distortional viscoplasticity
- Incremental Variational Approach for 2-Temperature Model - Part 1
- Incremental Variational Approach for 2-Temperature Model - Part 2
- Distortional visco-plasticity - Part 1
- Distortional visco-plasticity - Part 2
- Distortional viscoplasticity: FEM implementation - Part 1
- Distortional viscoplasticity: FEM implementation - Part 2
Week 10 Large deformation plasticity
- Large deformation plasticity: Introduction
- Large deformation plasticity: kinematics and kinetics
- Finite deformation plasticity: A Perzyna-type model - Part 1
- Finite deformation plasticity: A Perzyna-type model - Part 2
- Perzyna-Type Model for Finite-Strain Viscoplasticity - Part 1
- Perzyna-Type Model for Finite-Strain Viscoplasticity - Part 2
Week 11 Rate independent limit of finite strain viscoplasticity
- Finite-Strain Visco-plasticity & the Rate-Independent Limit - Part 1
- Finite-Strain Visco-plasticity & the Rate-Independent Limit - Part 2
- Rate independent limit of finite-strain visco-plasticity: variational formulation - Part 1
- Rate independent limit of finite-strain visco-plasticity: variational formulation - Part 2
Week 12 High strain rate loading
- Finite-strain Plasticity under high strain rates - Part 1
- Finite-strain Plasticity under high strain rates - Part 2
- Finite-strain Plasticity with High Strain Rates: The Variational Formulation - Part 1
- Finite-strain Plasticity with High Strain Rates: The Variational Formulation - Part 2
- Tensor Algebra
- Tensor calculus
- Kinematics, frame-indifference
- Piola stresses
- Constitutive relations
- code implementation demo
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IISc Bangalore
- Department
- Civil Engineering
- Teacher
- Prof. Debasish Roy
- Level
- Graduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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