Add math.solve_2d(A, b)

[adtzlr]

for two-dimensional problems.

See discussion #741.

Example

import numpy as np
import tensortrax as tr
from tensortrax.math import trace
from tensortrax.math.linalg import inv
from tensortrax.math.special import dev, from_triu_1d, triu_1d

import felupe as fem

mesh = fem.Rectangle(n=3)
region = fem.RegionQuad(mesh)
field = fem.FieldContainer([fem.FieldPlaneStrain(region, dim=2)])
boundaries, loadcase = fem.dof.uniaxial(field, clamped=True)

@fem.constitution.isochoric_volumetric_split
def finite_strain_viscoelastic_newton(C, Cin, mu, eta, dtime):
    "Finite Strain Viscoelastic material formulation."

    def evolution(Ci, Cin, C, mu, eta, dtime):
        "Viscoelastic evolution equation."
        return mu / eta * dev(C @ inv(Ci)) @ Ci - (Ci - Cin) / dtime

    # update of state variables by evolution equation
    Cin = from_triu_1d(Cin, like=C)
    Ci = fem.newtonrhapson(
        x0=Cin,
        fun=tr.function(evolution, ntrax=C.ntrax),
        jac=tr.jacobian(evolution, ntrax=C.ntrax),
        solve=fem.math.solve_2d,
        args=(Cin, C.x, mu, eta, dtime),
        verbose=0,
        tol=1e-2,
    ).x

    # first invariant of elastic part of right Cauchy-Green deformation tensor
    I1 = trace(C @ inv(Ci))

    # strain energy function and state variable
    return mu / 2 * (I1 - 3), triu_1d(Ci)

umat = fem.Hyperelastic(
    finite_strain_viscoelastic_newton, mu=1.0, eta=1.0, dtime=0.1, nstatevars=6
)
solid = fem.SolidBodyNearlyIncompressible(umat, field, bulk=5000)
solid.results.statevars[[0, 3, 5]] += 1

move = fem.math.linsteps([0, 0.3], num=3)
step = fem.Step(
    items=[solid], ramp={boundaries["move"]: move}, boundaries=boundaries
)
job = fem.CharacteristicCurve(steps=[step], boundary=boundaries["move"]).evaluate()

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.48%. Comparing base (c98f213) to head (b4decc8).
Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #742   +/-   ##
=======================================
  Coverage   97.48%   97.48%           
=======================================
  Files          95       96    +1     
  Lines        5163     5173   +10     
=======================================
+ Hits         5033     5043   +10     
  Misses        130      130           

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