Nonlocal formulation - TrabBoneNL3d

The model is regularized by the over-nonlocal formulation with damage driven by a combination of local and nonlocal cumulated plastic strain

$\displaystyle \hat{\kappa} = (1-m)\kappa + m\bar{\kappa},$ (219)

where $ m$ is a dimensionless material parameter (typically $ m>1$) and

$\displaystyle \bar{\kappa}(x) = \int\limits_V \alpha(x,s)\kappa(s)\,{\rm d}s$ (220)

is the nonlocal cumulated plastic strain. The nonlocal weight function is defined as

$\displaystyle \alpha(x,s) = \frac{\alpha_0(\Vert x-s\Vert )}{\int\limits_V\alpha_0(\Vert x-t\Vert )\,{\rm d}t}$ (221)

where

(222)

Parameter $ R$ is related to the internal length of the material. The model description and parameters are summarized in Tab. 47.

Table 47: Nonlocal formulation of anisotropic elastoplastic model with isotropic damage - summary.
Description Nonlocal anisotropic elastoplastic model with isotropic damage
Record Format TrabBoneNL3d (in) # d(rn) # eps0(rn) # nu0(rn) # mu0(rn) # expk(rn) # expl(rn) # m1(rn) # m2(rn) # rho(rn) # sig0pos(rn) # sig0neg(rn) # chi0pos(rn) # chi0neg(rn) # tau0(rn) # plashardfactor(rn) # expplashard(rn) # expdam(rn) # critdam(rn) # m(rn) # R(rn) #
Parameters - material number
  - d material density
  - eps0 Young modulus (at zero porosity)
  - nu0 Poisson ratio (at zero porosity)
  - mu0 shear modulus (at zero porosity)
  - m1 first eigenvalue of the fabric tensor
  - m2 second eigenvalue of the fabric tensor
  - rho volume fraction of the solid phase
  - sig0pos yield stress in tension
  - tau0 yield stress in shear
  - chi0pos interaction coefficient in tension
  - chi0neg interaction coefficient in compression
  - plashardfactor hardening parameter
  - expplashard exponent in the hardening law
  - expdam exponent in the damage law
  - critdam critical damage
  - expk exponent $ k$ in the expression for elastic stiffness
  - expl exponent $ l$ in the expression for elastic stiffness
  - expq exponent in the expression for tensor
  - expp exponent $ p$ in the expression for tensor
  - m over-nonlocal parameter
  - R nonlocal interaction radius
Supported modes 3dMat


Borek Patzak
2018-01-02