material nonlinearity: nonlinear elasticity elasto-plasticity visco-elasticity visco-plasticity...
Post on 25-Feb-2016
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•Material nonlinearity: •nonlinear elasticity •elasto-plasticity •visco-elasticity •visco-plasticity
•Geometric nonlinearity: •elastic instability •large strain (Green Lagrange, Almansi’s )•coupled material-geometry nonlinearity (large strain)
•Contact analysis •Frictionless contact
•Dynamic structural analysis •Implicit and explicit methods of solution
Different Nonlinear Analysis
0 01
Coordinate Systems
The configuration of the body is referred to a cartesian base system,which is fixed in space. The coordinates of a particle P in the referenece
configuration are indicated by ( x , 02 3
t t t1 2 3
t 0i i
x , x ). Under action of loads after time t the particle P moves to a new position whose base position
are indicated by ( x , x , x ) then the transformation is
x x ti
0 0 0 t t t1 2 3 1 2 3
t t 0i i i
0 0 01 2 3
t t1 2
u
maps the location of P( x , x , x ) to P( x , x , x )where
u x x
Remarks
Coordinates ( x , x , x ) are called material coordinates
and coordinates ( x , x ,
t3x )are called spatial coordinates
where
Right Cauchy-Green Deformation TensorLeft Cauchy-Green Deformation Tensor
Right Stretch Tensor
0 0 0t t tX R U
X
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