the solid mechanics view on continuum elastic-viscoplastic ... · vikas srivastava m.i.t. 2 outline...

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The solid mechanics view on continuum elastic-viscoplastic

deformation

Shawn Chester, David Henann, Vikas Srivastava

M.I.T.

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Outline

• Tresca vs. Mises yield criteria• Continuum Plasticity

– Kinematics (3D, 1D large and small)– Constitutive theory– Specialization to a Bingham material

• 2D vs. 3D• 1D implementation

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Tresca vs. Mises

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1D small-deformation elastic-viscoplastic

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3D small-deformation elastic-viscoplastic

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Large-deformation kinematics

• DeformationGradient

• VelocityGradient

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Kinematical decomposition: Motivation

• Irreversible part of deformation:We assume that irreversible flow is due to the

flow of “defects” through the material structure

• Reversible part of the deformation:We assume that reversible deformation is

accommodated by stretch and rotation of the structure

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Kinematical decompositions

• Small Strain elastic-plastic

• Large Strain elastic-plastic

• In most typical cases, we assume plastic flow is incompressible

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Kinematics

• Polar decomposition

• Spectraldecomposition

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Basic Laws

• Cauchy stress,

• Conservation of linear momentum

• Conservation of angular momentum

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3D large-deformation elastic-viscoplastic

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3D large-deformation elastic-viscoplastic

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Flow rule

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Flow rule

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1D large-deformation elastic-viscoplastic

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2D vs. 3D

• General 3D model can be specialized– Plane-strain

– Plane-stress