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Abstract We formulate a methodology to enforce interface conditions preserving higher-order continuity across the interface. Isogeometrical methods (IGA) naturally allow us to deal with equations of higher-order omitting the usage of mixed approaches. For multi-patch analysis of Kirchhoff–Love shell elements, G 1 continuity at the interface is required and serve here as a prototypical example for a higher-order coupling conditions. When working with this class of shell elements, two different types of constraints arise: Higher-order Dirichlet conditions and higher-order patch coupling conditions. A basis modification approach is presented here, based on a least-square formulation and the incorporation of the constraints into the IGA approximation space. An alternative formulation using Lagrange multipliers which are statically condensed via a discrete Null-Space method provides additional insight into the proposed formulation. A detailed comparison with a classical mortar approach shows the similarities and differences. Eventually, numerical examples demonstrate the capabilities of the presented formulation. Highlights • Non-conform domain decomposition for Kirchhoff–Love shell elements. • Mortar approach for domain decomposition problems requiring higher continuity. • Use of an Euclidean norm on the interface to circumvent complex segmentation procedures. • Basis modification approach to incorporate the constraints. [ABSTRACT FROM AUTHOR]

Abstract Variationally consistent phase-field methods have been well established in the recent decade. A wide range of applications to brittle and ductile fracture problems could already demonstrate the ability to predict complex crack patterns in three-dimensional geometries. However, current phase-field models to ductile fracture are not formulated for both, material and geometrical non-linearities. In this contribution we present a computational framework to account for three-dimensional fracture in ductile solids undergoing large elastic and plastic deformations. The proposed model is based on a triple multiplicative decomposition of the deformation gradient and an exponential update scheme for the return map in the time discrete setting. This increases the accuracy on the entire range of the ductile material behavior encompassing elastoplasticity, hardening, necking, crack initiation and propagation. The accuracy and convergence properties are further improved by the application of a higher order phase-field regularization and a gradient enhanced plasticity model. To account for the ductile behavior at fracture, a model of the critical fracture energy density depending on the equivalent plastic strain is proposed and validated by experimental data. Highlights • We present a higher order phase-field model to non-linear ductile fracture. • A novel multiplicative triple split of the deformation gradient is introduced. • An exponential update scheme for the return map in the time discrete setting is applied. • To account for ductile fracture a novel model of the critical fracture energy is introduced. • The approach is able to account for the entire range of ductile fracture within non-linear elastoplasticity. [ABSTRACT FROM AUTHOR]

Highlights: [•] We present a Mortar based approach for thermomechanical contact problems. [•] An isogeometric approach for the discretisation is considered. [•] A consistent thermodynamical model is used. [•] Constitutive laws for the thermomechanical contact interface are applied. [Copyright &y& Elsevier]

A second gradient theory for woven fabrics is applied to Kirchhoff–Love shell elements to analyze the mechanics of fiber reinforced composite materials. In particular, we assume a continuous distribution of the fibers embedded into the shell surface, accounting for additional in-plane flexural resistances within the hyperelastic regime. For the finite element discretization we apply isogeometric methods, i.e. we make use of B-splines as basis functions omitting the usage of mixed approaches. The higher gradient formulation of the fabric is verified by a series of numerical examples, followed by suitable validation steps using experimental measurements on organic sheets. A final example using a non-flat reference geometry demonstrates the capabilities of the presented formulation. • We present a framework for the simulation of fiber reinforced composite materials. • A second gradient theory is applied to Kirchhoff–Love shell elements. • The concept of Isogemetric Analysis is adopted to account for G1-continuity. • A comprehensive verification of the implementation was carried out. • A number of experimental investigations are used to validate the proposed framework. [ABSTRACT FROM AUTHOR]

Phase-field methods to regularize sharp interfaces represent a well established technique nowadays. In fracture mechanics, recent works have shown the capability of the method for brittle as well as ductile problems formulated within the fully non-linear regime. In this contribution, we introduce a framework to simulate porous-ductile fracture in isotropic thermo-elasto-plastic solids undergoing large deformations. Therefore, a modified Gurson–Tvergaard–Needleman GTN-type plasticity model is combined with a phase-field fracture approach to account for a temperature-dependent growth of voids on micro-scale followed by crack initiation and propagation on macro-scale. The multi-physical formulation is completed by the incorporation of an energy transfer into the thermal field such that the temperature distribution depends on the evolution of the plastic strain and the crack phase-field. Eventually, this physically comprehensive fracture formulation is validated by experimental data. • We present a novel framework for the simulation of non-linear porous-ductile fracture. • A phase-field fracture approach is combined with a thermoelastoplasticity formulation. • A modified GTN-type model is introduced to account for the growth of micro-voids. • The multi-physical formulation rests on an energy transfer into thermal field. • The capabilities of the analysis for complex material behavior are demonstrated. [ABSTRACT FROM AUTHOR]

A crosspoint modification for general C n continuous mortar coupling conditions is presented. In particular, we modify the extended mortar method as introduced in Schuß et al. (2019) and Dittmann et al. (2019) to deal with crosspoints as they arise in multi-patch geometries. This modification is constructed in such a way, that we decouple the Lagrange multipliers at the crosspoint to avoid a global coupling condition across all interfaces. Moreover, we recast the underlying B-Splines such that they preserve the higher order best approximation property across the interface and the crosspoint. A detailed investigation is presented in the context of second order thermal problems, fourth order Cahn–Hilliard and sixth order Swift–Hohenberg formulations. • Extended mortar method for C n continuous coupling conditions. • Crosspoint modification for IGA. • Best approximation property across the interface and the crosspoint. • Application to fourth-order Cahn–Hilliard and sixth-order Swift–Hohenberg problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new Galerkin based formulation for transient continuum problems, governed by partial differential equations in space and time. Therefore, we aim at a direct finite element discretization of the space–time, suitable for massive parallel analysis of the arising large-scale problem. The proposed formulation is applied to thermal, mechanical and fluid systems, as well as to a Kuramoto–Sivashinsky problem, representing the general class of higher-order formulations in material science using NURBS based shape functions. We verify whenever possible the conservation properties of the formulation. Finally, a series of examples demonstrate the applicability to all systems presented in this paper. [ABSTRACT FROM AUTHOR]

While the interest in higher-order models in physics and mechanics grows, their numerical simulation still poses a challenge, especially for arbitrary shaped three-dimensional domains. This contribution presents the mathematical framework as well as the application to different problems in the field of material science, fracture mechanics and diffusion problems. All models under consideration require at least C 1 continuity, which prevents the application of standard finite element analysis and local mesh refinements. Introducing isogeometric analysis (IGA) for the discretization in a finite element framework enables us to deal with these requirements. Moreover, a general hierarchical refinement scheme based on a subdivision projection is presented here for one, two and three dimensional simulations. This technique allows to enhance the approximation space using finer splines on each level but preserves the partition of unity as well as the continuity properties of the original discretization. Using this mathematical framework, the improved convergence of a Kuramoto–Sivashinsky model, a mesh-adapted thermal diffusion simulation and computations of a priori unknown crack propagation in different fracture modes underline the versatility of the presented hierarchical refinement scheme. [ABSTRACT FROM AUTHOR]

In this paper we investigate variationally consistent Mortar contact algorithms applied to a phase-field approach to brittle fracture. Phase-field approaches allow for an efficient simulation of complex fracture problems, as they arise in contact and impact situations. To improve accuracy and convergence, a fourth-order phase-field model is considered, requiring C 1 continuity throughout the domain. An isogeometrical framework is used for the spatial discretisation subject to hierarchical refinements to resolve local features. This reduces the computational effort tremendously, as will be shown in a series of representative examples. [ABSTRACT FROM AUTHOR]

Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy–Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn–Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu–Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials. [ABSTRACT FROM AUTHOR]