r7.02.14 Internal discontinuity elements, behavior CZM_EXPet load control

Summary:

Based on an energetic formulation presented briefly in the first part, we present a numerical model for the initiation and propagation of two-dimensional cracks. This is based on a finite element with an internal displacement discontinuity, similar to the models known under the name « embedded discontinuityfinite element » in the literature.

For this model, we detail the law of behavior used (of the Exponential Cohesive Zone Model type: keyword CZM_EXP), the properties of the finite element as well as the resolution of the problem of minimizing total energy. In addition, we describe a loading control technique making it possible to monitor possible instabilities in the overall response of the structure.

These elements can be used in 2D plane or axisymmetric only with models PLAN_ELDI and AXIS_ELDI. They are validated on the ssnop128a (documentation [V6.03.128]) and ssna115a (documentation [V6.01.115]) test cases.

Remarks:

• This documentation is largely inspired by thesis work [6]. The interested reader can refer to it for a more complete vision of the link of this model with the « Frankfurt Marigo » energy approach as well as a number of numerical results.

• The choice to group together in the same documentation the presentation of a finite element and a law of behavior is linked to the specificity of the model and is intended to facilitate its understanding.

Table of Contents

• 1. Cracking energy model
  • 1.1. General principle
  • 1.2. Reversible model
  • 1.3. Memory model
  • 1.4. Temporal discretization
• 2. Internal discontinuity model
  • 2.1. Law of behavior of the element with discontinuity: CZM_EXP
  • 2.2. Properties of the discontinuous element
  • 2.3. Minimization of total energy
• 3. Load control method
  • 3.1. Piloting control equation
• 4. ANNEXE: Calculating the tangent matrix for the discontinuous element
• 5. Bibliographical references
• 6. Description of document versions