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what is C? S-S0=C:(ε-α(T-T_ref )-ε0)
Posted Oct 25, 2015, 6:12 p.m. EDT 1 Reply
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Hello
can you explain to me please what is C in this equation.
S-S0=C:(ε-α(T-T_ref )-ε0)
Thanks
can you explain to me please what is C in this equation.
S-S0=C:(ε-α(T-T_ref )-ε0)
Thanks
1 Reply Last Post Oct 26, 2015, 2:53 a.m. EDT
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Posted:
9 years ago
Hi
for me C is here the stiffness tensor, check the units:
s the stress (s0 initial) in [Pa], epsilon (eps0 the initial) the strain [1], alpha the thermal expansion [m/m/K], T & Tref the temperature [K], hence C is in [Pa]. The ":" is the tensor product
Studying the notation here I recommend to read through books like: "Elasticity" by M.H. Sadd, or "Continuum Mechanics and Thermodynamics" by E. Tadmor and R. Miller (several volumes), or "Modelling of mechanical Systems: Structural Elements" by F. Axisa and P. Trompette (several volumes), or "Advanced Mechanics of Continua" K.S. Surana, or the classical "Theory of Elasticity" of Timoshenko.
For tensor I recommend: Vectors and Tensors in Engineering and Physics, or "Tensor Calculus for Physics" by D.E: Neuenschwander, or the appropriate chapter of "The Mechanical and Thermodynaical Theory of Plasticity", by M. Negahban, or "Non-Linear Finite Element Analysis of Solids and Structures" by R de Borst et al
--
Good luck
Ivar
for me C is here the stiffness tensor, check the units:
s the stress (s0 initial) in [Pa], epsilon (eps0 the initial) the strain [1], alpha the thermal expansion [m/m/K], T & Tref the temperature [K], hence C is in [Pa]. The ":" is the tensor product
Studying the notation here I recommend to read through books like: "Elasticity" by M.H. Sadd, or "Continuum Mechanics and Thermodynamics" by E. Tadmor and R. Miller (several volumes), or "Modelling of mechanical Systems: Structural Elements" by F. Axisa and P. Trompette (several volumes), or "Advanced Mechanics of Continua" K.S. Surana, or the classical "Theory of Elasticity" of Timoshenko.
For tensor I recommend: Vectors and Tensors in Engineering and Physics, or "Tensor Calculus for Physics" by D.E: Neuenschwander, or the appropriate chapter of "The Mechanical and Thermodynaical Theory of Plasticity", by M. Negahban, or "Non-Linear Finite Element Analysis of Solids and Structures" by R de Borst et al
--
Good luck
Ivar