Imposed force in phase_field prolem

Hello all,
Normally when solving phase field problem we impose displacement as follows:

imposed displacement

load = Expression(“t”, t=0.0, degree=1)

boundary conditions

bc_load = DirichletBC(W.sub(1), load, top)
bc_fix = DirichletBC(W, Constant((0.0,0.0)), bottom)

variational problem

E_du = (g_d * inner(epsilon(v), sigma(u))) * dx

loop

u_r = 0.007
while t < tf:
inc +=1
t += deltaT
load.t = t * u_r

However, when i want to impose force instead of displacement, how the problem will change?

imposed force

force = Expression(“t”, t=0.0, degree=1)

boundary conditions

bc_fix = DirichletBC(W, Constant((0.0,0.0)), bottom)

variational problem

E_du = (g_d * inner(epsilon(v), sigma(u))) * dx - inner(force,v) * ds(top)

loop

while t < tf:
inc +=1
t += deltaT
force.t = t * …