pyxfem.solidmechanics.elasticity module

Tools for Elasticity

class pyxfem.solidmechanics.elasticity.ElasticField

Bases: ABC

base class for elastic field : thing thah can evaluate displacement and stress (and strain ..) at each point xy

abstractmethod displacement(xy)

return the displacement vector at points xy

abstractmethod strain(xy)

return the strain tensor at points xy

abstractmethod stress(xy)

return the stress tensor at points xy

class pyxfem.solidmechanics.elasticity.LinearIsotropeElasticMaterial(E: float = 1.0, nu: float = 0.3, hyp2d: MaterialHypothesis = MaterialHypothesis.PLANESTRAIN, elastic_limit: float = 1.0)

Bases: object

Linear isotrope elastic material

class pyxfem.solidmechanics.elasticity.MaterialHypothesis(*values)

Bases: Enum

Enum class to define the avalaible Material hypothesis

DIM3 = 3

PLANESTRAIN = 2

PLANESTRESS = 1

class pyxfem.solidmechanics.elasticity.P1FemElasticfield(xy, t2v, vdisp, estress, trifinder=None)

Bases: ElasticField

implementation of ElasticField that use the classical P1 Fem interpolation (over triangles)

displacement(xy)

return the displacement vector at points xy

strain(xy)

return the strain tensor at points xy

stress(xy)

return the stress tensor at points xy

class pyxfem.solidmechanics.elasticity.Tensor2222CSR

Bases: object

grouping CSR matrix repesentation of order 4 tensor with base space of dimension 2

For now we have, for A a second order tensor (repesented as a 2d matrix in rowmajor storage)

• ISym: .5 (AT + A) = ISym: A -> ISym.dot(A.flatten()).reshape((2, 2))

• IxI I*trace(A) = IxI: A -> IxI.dot(A.flatten()).reshape((2, 2))

ISym = <Compressed Sparse Row sparse array of dtype 'float64' with 6 stored elements and shape (4, 4)>

IxI = <Compressed Sparse Row sparse array of dtype 'float64' with 4 stored elements and shape (4, 4)>

pyxfem.solidmechanics.elasticity.VonMises(stress2d, sigmazz)

return the von mises stress

pyxfem.solidmechanics.elasticity.YoungPoisson2LambdaMu(E, nu)

Return Lame coefficients (Lambda, mu) from Young Modulus (E) and poisson ration nu

pyxfem.solidmechanics.elasticity.planeStrainC2222CSR(*, lam: float | None = None, mu: float | None = None, mat: LinearIsotropeElasticMaterial | None = None)

Compute the C operator (tensor 4) for isotropic material such as sigma = C:eps, for plane strain isotrope assumption

input : lambda and mu Lamé’s coefficient or a linearIsotropeElasticMaterial instance.

pyxfem.solidmechanics.elasticity.stress_from_strain(strain, lamb, mu)

compute stress from plane deformation Strain. return sigma2d in voigt format and sigmazz

pyxfem.solidmechanics.elasticity.to_tensor2d(s11, s22, s12)

stack the 3 stress component in 2d tenso2r format

pyxfem.solidmechanics.elasticity.to_voigt2d(s11, s22, s12)

stack the 3 stress component in voigt format