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Solution methods for failure analysis of massive structural elements

Abstract : The thesis studies: the methods for failure analysis of solids and structures, and the embedded strong discontinuity finite elements for modelling material failures in quasi brittle 2d solids. As for the failure analysis, the consistently linearized path-following method with quadratic constraint equation is first presented and studied in detail. The derived path-following method can be applied in the nonlinear finite element analysis of solids and structures in order to compute a highly nonlinear solution path. However, when analysing the nonlinear problems with the localized material failures (i.e. materialsoftening), standard path-following methods can fail. For this reason we derived new versions of the pathfollowing method, with other constraint functions, more suited for problems that take into account localized material failures. One version is based on adaptive one-degree-of-freedom constraint equation, which proved to be relatively successful in analysing problems with the material softening that are modelled by the embedded-discontinuity finite elements. The other versions are based on controlling incremental plastic dissipation or plastic work in an inelastic structure. The dissipation due to crack opening and propagation, computed by e.g. embedded discontinuity finite elements, is taken into account. The advantages and disadvantages of the presented path-following methods with different constraint equations are discussed and illustrated on a set of numerical examples. As for the modelling material failures in quasi brittle 2d solids (e.g. concrete), several embedded strong discontinuity finite element formulations are derived and studied. The considered formulations are based either on: (a) classical displacement-based isoparametric quadrilateral finite element or (b) on quadrilateral finite element enhanced with incompatible displacements. In order to describe a crack formation and opening, the element kinematics is enhanced by four basic separation modes and related kinematic parameters. The interpolation functions that describe enhanced kinematics have a jump in displacements along the crack. Two possibilities were studied for deriving the operators in the local equilibrium equations that are responsible for relating the bulk stresses with the tractions in the crack. For the crack embedment, the major-principle-stress criterion was used, which is suitable for the quasi brittle materials. The normal and tangential cohesion tractions in the crack are described by two uncoupled, nonassociative damage-softening constitutive relations. A new crack tracing algorithm is proposed for computation of crack propagation through the mesh. It allows for crack formation in several elements in a single solution increment. Results of a set of numerical examples are provided in order to assess the performance of derived embedded strong discontinuity quadrilateral finite element formulations, the crack tracing algorithm, and the solution methods.
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Andjelka Stanic. Solution methods for failure analysis of massive structural elements. Mechanics [physics.med-ph]. Université de Technologie de Compiègne, 2017. English. ⟨NNT : 2017COMP2383⟩. ⟨tel-01806122⟩

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