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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]
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!