Damage models are developed within the continuum damage mechanics frameworkwhich allows the description of material degeneration with general constitutiveequations. The difficulty in the description of damage behaviour increases withincreasing complexity of the material behaviour. This is especially true when it comesto composite materials which have an orthotropic material behaviour. The conventionaldescription of damage, i.e. the local continuum damage mechanics description, leadsto strain-softening behaviour which is characterised by a decline in stress withsimultaneously increasing strain.Due to strain-softening the tangent stiffness becomes negative which forces the wavespeed to become imaginary in dynamic problems. Consequently the partial differentialequations governing the dynamic problem change from hyperbolic to elliptic and,therefore, the initial boundary value problem no longer has a unique solution. Due tothis the physical meaning becomes unrealistic. Strain-softening is limited to an infinitelysmall area in which waves are not able to propagate in a process called wave trapping.A displacement discontinuity in an area of width zero (localisation zone) develops. Thestrain becomes infinite in this zone and is accompanied with a zero stress. Areasoutside the softening zone are not able to interact with the strain-softening domain. Asa consequence the strain-softening domain acts similar to a free boundary at whichwaves reflect. The implementation of local continua with strain-softening behaviour infinite element codes leads to additional numerical problems. Strain-softening behaviourmanifests itself in the smallest area possible which is a single point in analyticalconsiderations. This area is defined by the element discretisation in finite elementcodes. Therefore, strain-softening leads to a pronounced mesh sensitivity of results inaddition to mathematical and physical issues.This work aims to find a solution which removes problems associated to strain-softening. Its aim is to represent material behaviour due to damage realistically andenable numerical results to convergence to a unique solution.The strain-softening problem is the focus of this work. It was investigated using a 1Dwave propagation problem described by Bažant and Belytschko [1]. This simpleexperiment allows for an easy comparison of analytical and numerical results andtherefore gives an insight into the problems connected to strain-softening.Furthermore, regularisation methods, specifically nonlocal and viscous methods, wereinvestigated. Regularisation methods add additional terms to constitutive equationswhich keep the initial boundary value problem well-posed and enable a unique solutionindependent of the element discretisation. It was found that these methods are indeedcapable of regulating the softening problem; however, they add additional difficulties inthe description of material behaviour.A new approach to the strain-softening issues, unique at this point of time, wasdeveloped in this work which implements damage as an equivalent damage force. Thisapproach is able to keep the initial boundary value problem stable and converge to aunique solution without adding additional terms in the constitutive equations, such asregularisation methods. This new approach to strain-softening was implemented for anisotropic material with scalar damage variable in DYNA3D successfully. Numericalresults converged to a unique solution and were physically reasonable. The concept ofan equivalent damage force was further developed to orthotropic material behaviour.This made an advanced representation, using an 8th rank damage tensor, necessary.The 8th rank damage tensor is able to represent anisotropic damage and it is also themost general damage representation possible.
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