Abstract
The fracture of ductile materials is usually preceded by considerable levels of plastic strain. After a first stage in which plastic strain strengthens the material due to the introduction and increase of dislocations (hardening), a degradation phenomenon begins to take place due to the nucleation of microcracks and microvoids. The nucleation, growth and coalescence of these defects can be modeled using the concepts of Continuum Damage Me- chanics. In this theory, a continuous damage variable is defined, which evolves coupled to plastic strain until attaining a critical value associated to rupture. Several damage models have been proposed for ductile materials, two of the most important being attributed to Gur- son and to Lemaitre. This work evaluates the effect of Lemaitre's damage model when applied to 3D trusses subjected to geometrical nonlinearities including inertial forces. To this end, two different damage evolution laws found in the literature are studied and compared. Special attention is given to unstable problems such as snap-through, in which results show that the effect of inertial forces is predominant. Furthermore, it becomes evident that for a realistic description of damage evolution and failure prediction, a different treatment must be given to tensile and compressive states. The work is closed by the discussion of damping effects on the damaged dynamic problem. It should be remarked that the evaluation of coupled plasticity and damage including geometrical nonlinearities, inertial forces and damping is a complex problem. Hence, setting these phenomena in a simple 3D truss framework makes it possible to focus on the description of physical behavior rather than on element technology complexities. This allows a clear understanding of some effects of Lemaitre's damage, paving the way for implementations using 2D and 3D continuum finite elements.
Highlights
The analysis of three-dimensional trusses subjected to large displacements is geometrically nonlinear
Several studies on Continuum Damage Mechanics have been conducted in the last decades [11, 7], until the development of the principle of equivalent deformation [9], which has led to a wide spectrum of applications in engineering
A better prediction of a convenient damage threshold could be performed with the implementation of a nonlinear hardening law, which would identify an assymptotic line correspondent to a saturated hardening
Summary
The analysis of three-dimensional trusses subjected to large displacements is geometrically nonlinear. Often the consideration of finite strains no longer resides in the linear range of material response, because of plasticity and hardening effects. Yielding affects the propagation and growth of microcracks and microvoids, characterizing an associated damage phenomenon. Several studies on Continuum Damage Mechanics have been conducted in the last decades [11, 7], until the development of the principle of equivalent deformation [9], which has led to a wide spectrum of applications in engineering
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