Modular implementation framework of partitioned path-following strategies: Formulation, algorithms and application to the finite element software Cast3M

Oliveira, Hugo Luiz; Rastiello, Giuseppe; Millard, Alain; Bitar, Ibrahim; Richard, Benjamin

doi:10.1016/j.advengsoft.2021.103055

Cited by 2 publications

(5 citation statements)

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“…For the CNDI method, interpreting ∆τ is even more straightforward; it can be chosen, for instance, to exactly reproduce experimental loading conditions (e.g., to impose the same rate of variation of the Crack Mouth Opening 7 An example is the notched beam three-point bending test. In this case, controlling the simulation through the CMOD is an effective choice (see, e.g., [39]). Moreover, it may lead to a "smoother" damage evolution compared to a direct displacement control method.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, it may lead to a "smoother" damage evolution compared to a direct displacement control method. 8 Concerning CPU time, Oliveria et al [39] observed for a three-point bending test (without snap-back, to have a reference solution obtained through a standard incremental solver with direct displacement control) that the number of iterations to converge is lower when using path-following methods than when directly imposing displacements. In other words, the additional computational effort associated with the path-following algorithm can be partly justified by an accelerated convergence of the solving algorithm.…”

Section: Discussionmentioning

confidence: 99%

“…Remark 5. Since the constraint equation ( 26) is independent of the Lagrange multipliers [38], deriving the partitioned formulation is straightforward [39].…”

Section: Dirichlet Boundary Conditionsmentioning

confidence: 99%

“…To circumvent this issue, some FE softwares (e.g., Cast3M [40] and CodeAster [41]) use a slightly different formalism based on the introduction of two sets of Lagrange multipliers [42]. The resulting discretized linearized system to be solved is still non-symmetric, but no zero values are present on the diagonal of the stiffnesslike operator [38,39].…”

Section: Dirichlet Boundary Conditionsmentioning

confidence: 99%

“…where ∆d n is the accumulated displacement variation at the last converged time step. Alternatively, one may write [22,39]:…”

Section: Constraint Equationmentioning

confidence: 99%

See 4 more Smart Citations

Path-following methods for unstable structural responses induced by strain softening: a critical review

Rastiello¹,

Oliveira²,

Millard³

2022

Comptes Rendus. Mécanique

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Path-following methods for describing unstable structural responses induced by strain-softening are discussed. The main ingredients of the formalisms introduced by Riks and Crisfield for arc-length methods for geometrical non-linearities are presented. A link between two ways (monolithic and partitioned) of solving the resulting augmented equilibrium problem is discussed based on the Sherman-Morrison formula. The original monolithic approach assumes that the path-following constraint equation is differentiable with respect to the unknown displacement field and load factor. However, when dealing with material nonlinearities, it is often preferred to consider constraint equations controlling the maximum of a field defined on the computational domain (e.g., a scalar strain measure, the rate of variation of an internal variable of the constitutive model). In that case, differentiability cannot be guaranteed due to the presence of the maximum operator. This makes only the partitioned formulation usable. Several path-following constraint equations from the literature are presented, and the corresponding implementations in the finite element method are discussed. The different formulations are compared based on a simple two-dimensional test case of damage localization in a beam submitted to tension. A test case involving multiple snap-backs is illustrated, finally, to show the robustness of the considered formulations.Résumé. Des techniques de pilotage indirect du chargement pour décrire des réponses structurelles instables induites par l'adoucissement en déformation sont discutées. Après avoir rappelé les principaux ingrédients des formalismes introduits par Riks et Crisfield pour les méthodes de longueur d'arc pour le traitement de

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Remark 5. Since the constraint equation ( 26) is independent of the Lagrange multipliers [38], deriving the partitioned formulation is straightforward [39].…”

Section: Dirichlet Boundary Conditionsmentioning

confidence: 99%