113 - constitutive equations

13 - constitutive equations -

2constitutive equations

constitutive equations instructural analysis, constitutive rela-tions connect applied stresses or forces tostrains or deformations. the constitutiverelations for linear materials are linear.more generally, in physics, a constitutiveequation is a relation between two physicalquantities (often tensors) that is specificto a material, and does not follow directlyfrom physical law. some constitutiveequations are simply phenomenological;others are derived from first principles.

constitutive equations

3constitutive equations

constitutive equationsor equations of state bring in the charac-terization of particular materials withincontinuum mechanics. mathematically, thepurpose of these relations is to supplyconnections between kinematic, mechanicaland thermal fields. physically, constitu-tive equations represent the various formsof idealized material response which serveas models of the behavior of actualsubstances.

constitutive equations

Chadwick „Continuum mechanics“ [1976]

4constitutive equations

tensor analysis - basic derivatives

5constitutive equations

tensor analysis - basic derivatives

6constitutive equations

neo hooke‘ian elasticity

• definition of stress

• free energy

• definition of tangent operator

7constitutive equations

neo hooke‘ian elasticity

• definition of stress

• free energy

• definition of tangent operator

8constitutive equations

neo hooke‘ian elasticity

• definition of stress

• free energy

undeformedpotato

deformedpotato

9constitutive equations

neo hooke‘ian elasticity

• definition of stress

• free energy

undeformedpotato

mashedpotatoes

• remember! mashing potatoes is not an elastic process!

10constitutive equations

neo hooke‘ian elasticity

• free energy

undeformedpotato

deformedpotato

• large strain - lamé parameters and bulk modulus

• small strain - young‘s modulus and poisson‘s ratio