ALE-based ductile damage and fracture

Mixed methods have been used with success in finite strain elasto-plastic with damage for decades. The subsequent stage is now dealt with enrichment methods, either local such as SDA or global such as XFEM. These are only suitable for academic fracture problems. Modeling of multiple crack intersection and coalescence can more directly done by remeshing techniques. Disadvantages of these are lower mesh quality (even blade and dagger-shaped finite elements), deteriorated crack path prediction and cumbersome coding. In order to overcome these difficulties, an approach fully capable of dealing with multiple advancing cracks and self-contact is presented. This approach uses the Arbitrary Lagrangian-Eulerian method (ALE) and localized remeshing at the tips (simpler than a full remeshing) and therefore mesh quality is better during crack evolution. Our nonlocal pressure-gradient element is used with full anisotropic finite strain elasto-plasticity based on smooth Mangasarian replacement functions (without return mapping). The critical crack front is identified and propagated when Strong Ellipticity is lost at each single Gauss point

Smooth finite strain plasticity with non-local pressure support

The aim of this work is to introduce an alternative framework to solve problems of finite strain elastoplasticity including anisotropy and kinematic hardening coupled with any isotropic hyperelastic law. After deriving the constitutive equations and inequalities without any of the customary simplifications, we arrive at a new general elasto-plastic system. We integrate the elasto-plastic algebraico-differential system and replace the loading–unloading condition by a Chen–Mangasarian smooth function to obtain a non-linear system solved by a trust region method. Despite being non-standard, this approach is advantageous, since quadratic convergence is always obtained by the non-linear solver and very large steps can be used with negligible effect in the results. Discretized equilibrium is, in contrast with traditional approaches, smooth and well behaved. In addition, since no return mapping algorithm is used, there is no need to use a predictor. The work follows our previous studies of element technology and highly non-linear visco-elasticity. From a general framework, with exact linearization, systematic particularization is made to prototype constitutive models shown as examples. Our element with non-local pressure support is used. Examples illustrating the generality of the method are presented with excellent results

A new semi-implicit formulation for multiple-surface ow rules in multiplicative plasticity

We propose new integration scheme

Finite element formulation for modelling nonlinear viscoelastic elastomers

Nonlinear viscoelastic response of reinforced elastomers is modeled using a three-dimensional mixed finite element method with a nonlocal pressure field. A general second-order unconditionally stable exponential integrator based on a diagonal Padé approximation is developed and the Bergström–Boyce nonlinear viscoelastic law is employed as a prototype model. An implicit finite element scheme with consistent linearization is used and the novel integrator is successfully implemented. Finally, several viscoelastic examples, including a study of the unit cell for a solid propellant, are solved to demonstrate the computational algorithm and relevant underlying physics

Stress intensity factors computation for bending plates with extended finite element method

The modelization of bending plates with through-the-thickness cracks is investigated. We consider the Kirchhoff–Love plate model, which is valid for very thin plates. Reduced Hsieh–Clough–Tocher triangles and reduced Fraejis de Veubeke–Sanders quadrilaterals are used for the numerical discretization. We apply the eXtended Finite Element Method strategy: enrichment of the finite element space with the asymptotic bending singularities and with the discontinuity across the crack. The main point, addressed in this paper, is the numerical computation of stress intensity factors. For this, two strategies, direct estimate and J-integral, are described and tested. Some practical rules, dealing with the choice of some numerical parameters, are underlined

Stabilized four-node tetrahedron with nonlocal pressure for modeling hyperelastic materials

Non-linear hyperelastic response of reinforced elastomers is modeled using a novel three-dimensional mixed finite element method with a nonlocal pressure field. The element is unconditionally convergent and free of spurious pressure modes. Nonlocal pressure is obtained by an implicit gradient technique and obeys the Helmholtz equation. Physical motivation for this nonlocality is shown. An implicit finite element scheme with consistent linearization is presented. Finally, several hyperelastic examples are solved to demonstrate the computational algorithm including the inf–sup and verifications test

A damage-based temperature-dependent model for ductile fracture with finite strains and configurational forces

A temperature dependent model for ductile fractur