DrRayFertigIII

Uses the consistency condition and the orthogonality of the plastic strain increment to develop the general equations for plastic flow including: yield function, plastic potential, and scalar hardening function.

Introduces consistency condition and begins to develop the functional form for the evolution of internal state variables (including plastic strain).

Begins development of incremental plasticity framework in 3-D. Focuses on strain decomposition and yield function.

Introduces the yield function for kinematic hardening and a discussion of back stress.

Develops the equations for the evolution of yield stress, introduces the plastic modulus, and introduces the concept of an effective plastic strain that can only increase.

Introduces hardening behavior and focuses specifically on the flow rule and yield function for isotropic hardening.

Introduces the constitutive law for an elastic-perfectly plastic material including: strain decomposition, yield function, and flow rule.

Discussion of additive and multiplicative decompositions of stretch ratio and strain for the purposes of separating elastic deformation from plastic deformation.

Reviews the derivation and relationship between stretch ratio, strain, and velocity gradient in 1-D.

Briefly covers plastic deformation mechanisms in polymers, ceramics, and soils.

Discusses dislocation glide, deformation twinning, and diffusion as mechanisms for plastic deformation in metals.

Develops a basic concept of eigenstrains using examples of thermal expansion and then extends the concept to plasticity to show how plastic behavior and linear elastic mechanics work together.

Introduces the full tensor form of Hooke's Law to describe a linear elastic material.

Develops equations of motion and equilibrium in 1D and in 3D.

Defines hydrostatic (spherical) and deviatoric stresses. Shows that the principal directions are the same for deviatoric and full stress tensor. Develops expression for J2 deviatoric stress invariant.

Develops the concept of stress invariants by derivation and expansion of the characteristic equation.

Develops the eigenvalue/eigenvector problem leading to principal stresses as extreme values of normal stresses.

Develops the Cauchy stress formula and definition of traction vector.

Develops a measure for shape change (shear) from deformation gradient tensor and links with off-diagonal terms in the small strain tensor.

Develops the Lagrange finite strain tensor and the small strain tensor in terms of displacement gradients.

Continuation of a discussion of the Lagrange finite strain tensor. Introduces stretch and shows how both stretch and nominal (engineering) strain are related to the Lagrange finite strain tensor.

Develops the Lagrange finite strain tensor from a basic measure of length change and the deformation gradient tensor.

Introduces Eulerian versus Lagrangian reference frames and discusses motion (rigid body and deformation) in the Lagrangian reference frame.

Develops coordinate transformation relationships for vectors and tensors

Overview of tensor representation, Kronecker delta, and permutation tensor (alternating tensor)