Borjesson, E.

Fagerstrom, M.

Remmers, J.

Scipedia

8th ECCOMAS Thematic Conference on the Mechanical Response of Composites: COMPOSITES 2021M. Fagerström & G. Catalanotti (Editors)AN ARC-LENGTH SOLVER WITH DISSIPATION PATH-FOLLOWINGFOR COMPLEX ANALYSIS OF BRITTLE FAILURE AND STABILITYOF COMPOSITE STRUCTURES.Elias I. Börjesson1∗, Martin Fagerström1 and Joris J.C. Remmers21 Dept. Industrial and Materials Science, Chalmers University of Technology, Gothenburg, Sweden2 Dept. Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands∗ elias.borjesson@chalmers.seThe failure of laminated, fibre-reinforced structures generally involves the interaction of severalfailure mechanisms, many of them with a brittle behaviour including rapid softening. The dam-age models used to simulate these failure mechanisms often creates numerical difficulties forthe solution method. For example, standard Newton solvers are generally unsuitable for caseswhere rapid failure occurs in parts of the structure. A remedy often resorted to in the literature,is to include dynamical effects via implicit or explicit time integration. However, an alternativeapproach, not penalised by requiring very small time steps, mass-scaling and/or introducingunwanted inertia or other dynamical effects, is to adopt an arc-length based quasi-static solver.Much research has been made in the field of arc-length solvers, and there is now a range ofavailable methods. Traditional approaches base the equilibrium path-following constraint on thenorm of the incremental displacement vector (i.e. an arc-parameter). These methods performwell for problems exhibiting geometrical non-linearities, but have difficulties converging whenmaterial instabilities are involved. In order to remedy this, a path-following constraint basedon the energy release rate for geometrically linear continuum damage was proposed in [1]. Themethod calculates the energy release rate using global quantities (such as internal force anddisplacement vectors), and was shown to give robust and stable convergence for problems withadvanced stages of damage. The methods was later extended in [2] to include geometricallynon-linearity, with plasticity and damage computations.In the current contribution, we reformulate the dissipation based path-following equation pro-posed in [1], from being calculated with global quantities, to instead being determined fromthe material dissipation. This has the added benefit of unifying the path-following constraintfor all types of dissipative problems, and no adjustment of the solver to specific problem cases(linear/non-linear, plasticity/damage etc.) is needed. The stability and robustness of the solveris showcased in numerical examples with composite structures that experience large non-lineardamage behaviour and damage driven buckling.References[1] Gutiérrez, M.A. (2004). Energy release control for numerical simulations of failure inquasi-brittle solids. Communications in Numerical Methods in Engineering, 20, 19-29.[2] Verhoosel, C. V., Remmers, J.J.C., Gutiérrez, M. A. (2009). A dissipation-based arc-lengthmethod for robust simulation of brittle and ductile failure. International Journal for Nu-merical Methods in Engineering, 77, 1290–1321

An Arc-Length Solver with Dissipation Path-Following for Complex Analysis of Brittle Failure and Stability of Composite Structures

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An Arc-Length Solver with Dissipation Path-Following for Complex Analysis of Brittle Failure and Stability of Composite Structures

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