Non linear constitutive law

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@bleyerj Hi, thankyou for the reply.

Sorry for not being clear. Yes, I am solving a 1d axial force problem.
To get started with modelling non linear constitutive laws, I took cube of the strain

I have actually tried it solving this way but from energy formulation following Defining non-linear constitutive laws

from dolfin import *
from dolfin.cpp.mesh import *
from mshr import *
#import matplotlib.pyplot as plt
import numpy as np

L = 40.
H = 10.

res = 100

base = Rectangle(Point(0,0), Point(L,H))

mesh = generate_mesh(base, res)
x = SpatialCoordinate(mesh)
V = VectorFunctionSpace(mesh, 'Lagrange', degree=1)

class Left_face(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and near(x[0],0)
     
class Right_face(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and near(x[0],L)

left_face = Left_face()
right_face = Right_face()

u = Function(V, name='Displacement')

eps = sym(grad(u))

E_0 = 2e5
E_1 = E_0/100

sigma = (E_0*eps + (E_1*(eps**3)))

bc1 = DirichletBC(V, Constant((0,0)), sub_domains, 1)
#bc = DirichletBC(V, Constant((0.,0.)), left_face)

f1 = Constant((100,0)) 
du = TrialFunction(V)
u_ = TestFunction(V)
l = dot(f1,u)*ds(2) 

# Energy:
energy = (0.5*inner(sigma,eps) - l)*dx



# Solve with homogeneous Dirichlet boundary conditions:
solve(derivative(energy,u)==0, u, bc1)

I was getting an error “Cannot take the power of a non-scalar expression .”

I guess I was not using ufl properly. I will do the appropriate changes and try the same again