COMPLAS 2023

A Plastic-Damage-Cracking Model for Tensorial Crack Opening

  • Daneshyar, Alireza (Technische Universität München)
  • Herrmann, Leon (Technische Universität München)
  • Oztoprak, Oguz (Technische Universität München)
  • Hug, Lisa (Technische Universität München)
  • Kollmannsberger, Stefan (Technische Universität München)

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In this talk, we propose to introduce a crack-strain field in conjunction with a damage model into the standard plasticity formulation. This allows the model to correctly differentiate between irreversible plastic strain and reversible cracking strain, which is crucial in repeated loading involving plasticity, damage, and fracture. In spite of the fact that the actual fracture process stems from forming interfaces, continuum damage mechanics provides an appealing framework for computational purposes since no special treatments---such as the injection of strong discontinuities either geometrically or mathematically---need not be invoked. By introducing stiffness degradation and permanent straining to the mechanical characteristics of solids, damage plasticity models deal with material inelasticity through a purely phenomenological point of view [1]. Nonetheless, those models have a fundamental weak spot in dealing with quasi-brittle materials [2]. Since macrocracks are represented by fully degraded regions in a smeared sense rather than by a discrete representation, the opening of crack faces coincides with inelastic straining. As a result, crack openings are interpreted as permanent deformations. Hence, macrocracks recover their stiffness under load reversal, which leads to an early closing of crack faces and the unloading branches do not exhibit stiffness degradation. We propose to treat this artificial stiffening by introducing a new strain field, termed 'cracking strain'. Based on this postulation, the conventional additive decomposition of the strain tensor is revised so that the total strain involves elastic, plastic, and cracking parts. The latter stores the state of macrocracks, enabling the model to differentiate between irreversible plastic and reversible cracking strains. In addition, owing to the tensorial nature of the cracking strain, the orientation of crack faces as well as the fracture mode is fully captured.