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classical elasticity

Cemal Basaran's picture

A unified mechanics theory-based model for temperature and strain rate dependent proportionality limit stress of mild steel

Strain rate and temperature dependent elastic limit of mild steel is investigated by developing a dislocation incipient motion-based proportionality limit stress model. Temperature effect on strain energy of an edge dislocation is modeled by using unified mechanics theory. Unified mechanics theory-based index, called thermodynamic state index, is used to model thermally assisted degradation of strain energy. Kinetic energy due to thermal vibrations is added to the kinetic energy of an accelerating dislocation.

Anisotropic stiffness of isotropic material

Dear colleagues,


Consider a simple non-linear elastic material with stress given as

σ = D(εdev) εdev + B εiso

where εdev is the norm of εdev, D is a function of εdev and B is constant. The material is isotropic since the principal directions of  σ and ε will coincide.

If we differentiate σ wrt ε to obtain the material stiffness the form of the stiffness tensor will be

Kamyar M Davoudi's picture

Stresses and Strains

In classical elasticity, we know that at the interface of two different materials, traction stresses and non-traction strains are cotinuous. Traction stresss are continuous according to Newton's third law, but why non-traction strains are continuous?

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