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A computational framework for the simulation of progressive failure in composite laminates is presented. The phantom-node method (a variation to the XFEM) is used for a mesh-independent representation of matrix cracks as straight discontinuities in the displacement field. Furthermore, interface elements are used for delamination and a continuum damage model for fiber failure. The framework is validated against experimental observations for open-hole tests and compact tension tests. It is shown that different failure mechanisms are captured well, which allows for the prediction of size effects. [ABSTRACT FROM AUTHOR]

In this paper, three different approaches used to model strong discontinuities are studied: a new strong embedded discontinuity technique, designated as the discrete strong embedded discontinuity approach ( DSDA), introduced in Dias-da-Costa et al. (Eng Fract Mech 76(9):1176–1201, 2009); the generalized finite element method, ( GFEM), developed by Duarte and Oden (Tech Rep 95-05, 1995) and Belytschko and Black (Int J Numer Methods Eng 45(5):601–620, 1999); and the use of interface elements (Hillerborg et al. in Cem Concr Res 6(6): 773–781, 1976). First, it is shown that all three descriptions are based on the same variational formulation. However, the main differences between these models lie in the way the discontinuity is represented in the finite element mesh, which is explained in the paper. Main focus is on the differences between the element enrichment technique, used in the DSDA and the nodal enrichment technique adopted in the GFEM. In both cases, global enhanced degrees of freedom are adopted. Next, the numerical integration of the discretised equations in the three methods is addressed and some important differences are discussed. Two types of numerical tests are presented: first, simple academic examples are used to emphasize the differences found in the formulations and next, some benchmark tests are computed. [ABSTRACT FROM AUTHOR]

An error estimator, formulated earlier for h-adaptive strategies, is extended for use in the p-version finite element analysis. The estimation of error is based on solving a series of local problems, based on patches consisting of elements surrounding each node, with prescribed homogeneous essential boundary conditions. Unlike the original approach in which a patch was constructed based on one element, each patch in the present scheme is automatically formed based on a number of elements surrounding a corresponding node. The present scheme, based on enhancing the degree of interpolation, provides a better estimate than the original h-scheme while still preserving the original lower bound property. The capability of the new scheme is investigated in some numerical examples in terms of its global and local performance. [ABSTRACT FROM AUTHOR]

A yield function in the stress resultant space of geometrically exact beams based on the elastoplastic cross-sectional warping problem has been proposed by Herrnböck et al. (Comput Mech, 67(3):723–742, 2021). This plasticity framework has been extended with a hardening tensor to model the kinematic hardening effects in Herrnböck et al. (Comput Mech, 71(1):1–24, 2022). While this framework provides scaling for the yield surface in ideal plasticity, scaling in hardening plasticity has not yet been explored. This paper focuses on the numeric modelling of hardening beams and beam assemblies at different geometric scales. Discretization effects from the introduction of plasticity into the geometrically exact beam model are demonstrated. Furthermore, the effects of scaling are explored, and a method to mitigate undesirable effects in order to achieve a size-agnostic formulation is proposed. Consistent geometric scaling is demonstrated for two alternative scaling approaches of the yield function. [ABSTRACT FROM AUTHOR]