Abstract

This work investigates systematically strain localization and failure mechanics for elastoplastic damage solids. Two complementary methodologies, i.e., traction-based discontinuities localized in an elastic solid and strain localization of a stress-based inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity (band) forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity (band) and the orientation is determined from Mohr’s maximization postulate. If the (apparent) displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity (band). Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness/continuity upon strain localization is established for general inelastic softening solids. Application to a unified elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, i.e., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded/smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion, not given a priori, are determined consistently from the kinematic constraint. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form 2D results under plane stress condition are also given, with the classical Rankine, Mohr-Coulomb, von Mises and Drucker-Prager criteria analyzed as the illustrative examples. A generic failure criterion of either elliptic, parabolic or hyperbolic type, is then considered in a unified manner, resulting in many failure criteria frequently employed in practice.

Abstract

An important concern in sheet stamping is the risk of obtaining brittle final products that can be affected by fracture. Monte Carlo simulations presented herein show that this is governed by two main factors, namely static and dynamic friction coefficients. Whereas the latter correlates in a non-linear manner with minimum and maximum end thickness, the relationship of these design parameters to the former exhibits a bifurcation that is typical of highly non-linear phenomena, in which there is a sensitivity to small perturbations of the input values (chaos). In order to estimate the reliability of the process (i.e., the probability of obtaining brittle products due to low minimum and maximum thicknesses) with a reduced number of Monte Carlo runs, it is proposed to assimilate the problem to a pattern recognition task, due to the existence of two classes, namely robust and brittle. Among many pattern recognition algorithms that are useful to this end, use is made of support vector machines, as this incorporates the powerful tool of class margins that allow a drastic reduction of the number of simulations.

Abstract

The virtual element method (VEM), is a stabilized Galerkin scheme deriving from mimetic finite differences, which allows for very general polygonal meshes, and does not require the explicit knowledge of the shape functions within the problem domain. In the VEM, the discrete counterpart of the continuum formulation of the problem is defined by means of a suitable projection of the virtual shape functions onto a polynomial space, which allows the decomposition of the bilinear form into a consistent part, reproducing the polynomial space, and a correction term ensuring stability. In the present contribution, we outline an extended virtual element method (X-VEM) for two-dimensional elastic fracture problems where, drawing inspiration from the extended finite element method (X-FEM), we extend the standard virtual element space with the product of vector-valued virtual nodal shape functions and suitable enrichment fields, which reproduce the singularities of the exact solution. We define an extended projection operator that maps functions in the extended virtual element space onto a set spanned by the space of linear polynomials augmented with the enrichment fields. Numerical examples in 2D elastic fracture are worked out to assess convergence and accuracy of the proposed method for both quadrilateral and general polygonal meshes.

Abstract

This study analyses on comparing the static delamination behavior and mode I fracture toughness of two types of adhesives (one epoxy and one acrylic) used in a composite material with an epoxy matrix and unidirectional carbon fiber reinforcement. The material was subjected to two different degradation processes (hygrothermal and salt spray chamber), and then mode I fracture was evaluated for both materials.

The results suggest that hygrothermal exposure may have a moderate impact on the delamination behavior of the epoxy adhesive, while exposure to the salt spray environment may result in a significant loss of its delamination resistance. For the acrylic adhesive, hygrothermal exposure improved its delamination behavior, while exposure to the salt spray environment had a minor impact on its behavior. Overall, it is concluded that the type of aging has influence on the fracture behavior of both adhesives.

Abstract

This study experimentally analyses the phenomenon of delamination under static and fatigue loading in mode II using the standardized End-Notched Flexure (ENF) test. Adhesive joints made of two epoxy matrix laminates reinforced with unidirectional carbon fiber are studied, bonded with an epoxy adhesive, and subjected to environmental degradation in a saline environment for exposure periods of 1, 2, 4, and 12 weeks.

By conducting initial static tests on the joints, we identified crucial values for the rate at which energy is released under mode II conditions. These values served as a benchmark to establish the approach for dynamic fatigue testing. Our objective was to generate characteristic curves that illustrate how these adhesive joints behave when fatigue delamination begins, while also assessing the impact of varying exposure periods on their performance. To enhance result interpretation, we employed a probabilistic model rooted in the Weibull distribution to analyse the experimental data.

The results show that adhesive joints experience a decrease in their delamination resistance when exposed to a saline environment.

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