Add Mechanics submodule

[adtzlr]

Mechanics submodule

A submodule for (solid) mechanics.

Solid Body

A umat as a user material class with two methods, one for the evaluation of the gradient and one for the hessian of the total potential energy. A solid body is built on top of it and provides convenient methods for weak-form assemblies based on linear and bilinear forms in combination with fields. In a similar way, hydrostatic pressure boundaries are supported too.

# Solid Body
S = fem.mechanics.SolidBody(umat, field)

# Assemble methods for internal force vector and stiffness matrix
r = S.vector(field) # force attribute as last assembled vector
K = S.matrix(field) # stiffness attribute as last assembled vector

# Field gradients/values and stress from latest (force) assembly or given field
F = S.extract(field) # kinematics as last evaluated extraction
P = S.gradient(field) # stress as last evaluated gradient
A = S.hessian(field) # elasticity as last evaluated hessian

# Pressure Boundary
SP = fem.mechanics.SolidBodyPressure(fieldp)
SP.update(fieldp, other_field=field)
r -= SP.vector(fieldp, pressure, resize=r)
K -= SP.matrix(fieldp, pressure, resize=K)