Encyclopedia of mechanics: basic equations, continuum mechanics, finite elements, and numerical methods

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Introduction to Continuum Mechanics
Kinematics of Deformation
Tensors and the Divergence Theorem
Polar Decomposition
Finite Strain Measures
Principal Stretches and Invariants
Velocity Gradient and Material Derivative
Cauchy Stress and Traction
Balance Laws & Conservation
Constitutive Models
Work-Conjugate Stresses
Principal Stresses and von Mises
Objective Rates
Hooke’s Law
Hyperelasticity
Metal Plasticity
Fluids: Continuity and Navier–Stokes
Thermodynamics of Continua
Variational Principles
Finite Element Method (Introduction)
Element Types & Families (Chooser)
Virtual Element Method
Extended & Generalized Finite Element Methods (XFEM/GFEM)
Discontinuous Galerkin Method
Shell Elements
Truss Elements
Mesh Generation & Embedded/Unfitted Methods (FEM/FCM)
Shape Functions & Isoparametric Mapping
p-Version FEM & Lobatto Shape Functions
Numerical Integration & Gauss Quadrature
Assembly of the Global Stiffness Matrix
Boundary Conditions & Loads
Constrained FEM
Solving Linear Systems
Mixed Methods and Locking
Nonlinear FEM
Total and Updated Lagrangian
Column Buckling
Plasticity Formulations & Return Mapping
Viscoplastic Localization & Gradient Damage
Newton–Raphson Iteration in FEM
Path Following and Arc-Length
Static Condensation & Schur Complement
Time-Dependent Problems
Contact and Friction
Box Deformation: Shells and Plasticity
Steel Joint: Plasticity and Moment–Rotation
Three-Point Bending of a Hollow Profile
Inflating a Pillow
Fracture Mechanics
Linear Elastic Fracture Mechanics
Mode I, II & Mixed-Mode Cracking
Cohesive Cracking
The J-Integral
Phase-Field Modelling of Fracture
XFEM Crack Growth
Fiber-Reinforced Composites
Embedded Fiber Models
Fiber Neutrality and Rigid Line Inclusions
Composite Materials – Effective Properties
Composite Materials – Failure Modes
Multiphase Porous Materials
One-Dimensional Consolidation
Gibson Consolidation
Mandel–Cryer Effect
Heat Transfer & Multiphysics FEM
Battery Mechanics – Structural Aspects
Battery FEM – Coupled Electro-Chemo-Mechanics
Fiber-Based Electrodes
GPUs in the FEM Pipeline
GPU Programming for Engineers
Sparse Linear Algebra on GPUs
Performance Comparison: CPU vs GPU in FEM
Future of FEM: Multiscale & Multiphysics
Matrix Fundamentals (Dense & Sparse)
Sparse Formats & Performance
CPU Linear Algebra Libraries
GPU Linear Algebra Libraries
Solvers & Preconditioning
Matrix Assembly & Graph Reordering
MATLAB-like Basics for FEM
Plotting & Postprocessing (MATLAB/Python)
NumPy/SciPy Equivalents
Benchmarking & Profiling
I/O & Interchange Formats