Stress-Strain Analysis and Constitutive Relations

Overview Stress Theory and Analysis

Definition of Stress and the Mechanism of Stress Generation in Solids

Criteria for Distinguishing Normal Stress from Shear Stress and Direction Determination

Stress Description and Calculation in Uniaxial Stress State

Definition of Plane Stress State and Common Engineering Scenarios

Plane stress state stress analysis methods (analytical method, graphical method)

Rules for Drawing the Stress Circle and Applications (Calculate Principal Stresses and Shear Stress)

Principal stress definition and the criteria for determining principal planes

Requirements for the Complex Stress Description in Three-Dimensional Stress States

The Background and Mathematical Expression of the Stress Tensor

The basic properties of the stress tensor and its invariant meaning

Stress-Strain Relationship of Ideal Plasticity Materials

Concepts and Components of the Stress Tensor

Strain Tensor and Geometric Deformation

Hooke's Law: Theory of Linear Elasticity

Generalized Hooke's Law and Material Constants

Poisson's Ratio and Young's Modulus

Shear Modulus and Bulk Modulus

Principal Stresses and Principal Strains

Stress Circle (Mohr's Circle) Analysis

Stress-Strain Curve Analysis

Isotropic and Anisotropic Materials

Definition and Physical Significance of the Stress Tensor

Distinction Between Normal Stress and Shear Stress

Proof of the Symmetry of the Stress Tensor

Concepts of Principal Stresses and Principal Directions

Stress Invariants and Their Engineering Applications

Construction and Interpretation of Mohr's Circle