By Khemais Saanouni
Those accumulated writings assemble contemporary advances in numerical and computational points of wear mechanics with the purpose of stimulating present examine and destiny demanding situations during this box.
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Extra info for Numerical modelling in damage mechanics
In this manner, zero stiffness is avoided and it is not necessary to remove the fully damaged elements from the mesh. It is assumed that D depends on a state variable Y, which in turn depends on the strains: The basic idea of nonlocal damage models is averaging the state variable Y in the neighbourhood of each point. In this manner, the nonlocal state variable Y is obtained: The weight function a, which depends on the distance d to the point under consideration, is typically the Gaussian where the characteristic length lc is a material parameter of the nonlocal damage model, which acts as a localization limiter and can be associated to the grain size [PIJ 91].
The predictor of the isochoric left Cauchy-Green deformation tensor is then obtained through and hence the trial Kirchhoff stress tensor as Note that the ductile damage does not evolve in the predictor phase, since the hyperelastic relation is independent from wp. The next step consists in the integration of the flow rule, which is performed with a pull-back and push-forward procedure in order to ensure incremental objectivity. The objective Eulerian flow rule is pulled-back to the invariant Lagrangian configuration, after which a time discretization is carried out using an implicit Euler backward scheme.
In this paper, an implicit gradient enrichment is used, which combines the computational efficiency of gradient type theories with the integral nonlocal concept. It has been shown that such an implicit approach presents a true nonlocal character [PEE 99], in the sense that an equivalent integral format exists, in which the nonlocal variable is a long-range weighted average of field of local variables. The solution strategy for the infinitesimal case will be highlighted briefly, after which the extension towards the hyperelastoplastic formulation is scrutinized.
Numerical modelling in damage mechanics by Khemais Saanouni