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Nonlinear Structural Mechanics
Posted Apr 11, 2017, 4:57 a.m. EDT 1 Reply
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Hi,
I'd like to model 2D nonlinear deformation of the solid material with a simple rectangular geometry. I do specify the nonlinear behavior of elastic bulk and shear moduli as a function of boundary load. Simple linear function is used, i.e. solid.K = a+b*load, where basically solid.K and solid.G are changing from 5 to 10 GPa as a function of load The BC are 1) roller BC on the sides; 2) fixed bottom; and 3) boundary load at the top. The stationary study is used. I define the boundary load parameter (i.e. 10,20,30,40, 50 MPa) , and tried both parametric sweep and auxillary sweep studies. I also include geometric and force and strain nonlinearity, respectively,
I ran this study and compare with two studies of 2D linear deformation of the solid material with exactly same parameters, except my elastic bulk and shear moduli are constant solid.K = solid.G = 5GPa, and solid.K = solid.G = 10GPa, respectively. Attached are point displacement at top the vs. boundary load plots from comsol and my expected results.
It seems like I'm doing something wrong. The slope of my nonlinear deformation curve in the beginning should be equal to 5GPA, and in the end to 10GPA. But it seems like, when I specify the boundary load and solid.K and solid.G as a function of load, comsol does calculate displacement like in linear elasticity, at the given load it uses the given elastic moduli, and does not integrate the displacement. So it is not exactly nonlinear deformation. How can I correctly model the nonlinear deformation of the solid material with given nonlinear behavior of the bulk and shear moduli as a function of specified boundary load?
Thank you!
Sincerely,
AK
I'd like to model 2D nonlinear deformation of the solid material with a simple rectangular geometry. I do specify the nonlinear behavior of elastic bulk and shear moduli as a function of boundary load. Simple linear function is used, i.e. solid.K = a+b*load, where basically solid.K and solid.G are changing from 5 to 10 GPa as a function of load The BC are 1) roller BC on the sides; 2) fixed bottom; and 3) boundary load at the top. The stationary study is used. I define the boundary load parameter (i.e. 10,20,30,40, 50 MPa) , and tried both parametric sweep and auxillary sweep studies. I also include geometric and force and strain nonlinearity, respectively,
I ran this study and compare with two studies of 2D linear deformation of the solid material with exactly same parameters, except my elastic bulk and shear moduli are constant solid.K = solid.G = 5GPa, and solid.K = solid.G = 10GPa, respectively. Attached are point displacement at top the vs. boundary load plots from comsol and my expected results.
It seems like I'm doing something wrong. The slope of my nonlinear deformation curve in the beginning should be equal to 5GPA, and in the end to 10GPA. But it seems like, when I specify the boundary load and solid.K and solid.G as a function of load, comsol does calculate displacement like in linear elasticity, at the given load it uses the given elastic moduli, and does not integrate the displacement. So it is not exactly nonlinear deformation. How can I correctly model the nonlinear deformation of the solid material with given nonlinear behavior of the bulk and shear moduli as a function of specified boundary load?
Thank you!
Sincerely,
AK
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1 Reply Last Post Apr 11, 2017, 7:52 a.m. EDT
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Posted:
7 years ago
Hi,
This is exactly the expected result. Stress is proportional to strain, with the given modulus as coefficient.
This is what you could call a 'secant stiffness',
It seems like you expect a 'tangent stiffness',
Your case is somewhat strange (material properties as function of the load), but generally you need to do conversions like
or
See also the discussion about secant and tangent coefficients of thermal expansion in the user's guide.
Regards,
Henrik
This is exactly the expected result. Stress is proportional to strain, with the given modulus as coefficient.
This is what you could call a 'secant stiffness',
It seems like you expect a 'tangent stiffness',
Your case is somewhat strange (material properties as function of the load), but generally you need to do conversions like
or
See also the discussion about secant and tangent coefficients of thermal expansion in the user's guide.
Regards,
Henrik