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finite elasticity

Solving incompressible finite elasticity without tears

Solving incompressible elasticity has been quite challenging numerically. The conventional approach for handling incompressibility is the so-called penalty method. A volumetric energy term enters into the strain energy and penalizes the volumetric deformation. One straightforward issue is that the penalty parameter goes directly into the tangent matrix. The bigger the penalty parameter, the worse the condition number of the matrix. This is really a manifestation of the ill-posedness of theories based on the Helmholtz free energy, in my opinion [3].

Cauchy's first law of motion

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Hi All

I'm a bioengineering PhD student, I just started reading on the finite elasticity theory and have a question regarding to the governing equation.

As I understand, Cauchy's first law of motion is the governing equation for finite elasticity. For steady-state (no acceleration), the equation is:

dσ/dx=F

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