Numerical approach to a model for quasistatic damage with spatial BV-regularization

We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems

Isogeometric Kirchhoff-Love shell formulation for elasto-plasticity

An isogeometric thin shell formulation allowing for large-strain plastic deformation is presented. A stress-based approach is adopted, which means that the constitutive equations are evaluated at different integration points through the thickness, allowing the use of general 3D material models. The plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points. The deformation of the shell structure is completely described by the deformation of its midsurface, and, furthermore, the formulation is rotation-free, which means that the discrete shell model involves only three degrees of freedom. Several numerical benchmark examples, with comparison to fully 3D solid simulations, confirm the accuracy and efficiency of the proposed formulation

Phase-field modeling of brittle fracture along the thickness direction of plates and shells

The prediction of fracture in thin-walled structures is decisive for a wide range of applications. Modeling methods such as the phase-field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase-field modeling approach. For this purpose, a new, so called “mixed-dimensional” model is introduced, which combines structural elements representing the displacement field in the two-dimensional shell midsurface with continuum elements describing a crack phase-field in the three-dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled twoand three-dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed-dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through-thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy aswell as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples

Phase-field simulation of ductile fracture in shell structures

In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff-Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, displacement and rotational continuity and C0 and C1 continuity of the phase-field, the latter required if a higher-order phase-field formulation is adopted. We study the mesh dependency of the numerical model and we show that mesh refinement allows for capturing important features of ductile fracture such as cracking along shear bands. Therefore, we investigate the effectiveness of a predictor-corrector algorithm for adaptive mesh refinement based on LR NURBS. Thanks to the adoption of time- and space-adaptivity strategies, it is possible to simulate the failure of complex structures with a reasonable computational effort. Finally, we compare the predictions of the numerical model with experimental results

Microstructure Characterization and Reconstruction in Python: MCRpy

Microstructure characterization and reconstruction (MCR) is an important prerequisite for empowering and accelerating integrated computational materials engineering. Much progress has been made in MCR recently; however, in the absence of a flexible software platform it is difficult to use ideas from other researchers and to develop them further. To address this issue, this work presents MCRpy as an easy-to-use, extensible and flexible open-source MCR software platform. MCRpy can be used as a program with graphical user interface, as a command line tool and as a Python library. The central idea is that microstructure reconstruction is formulated as a modular and extensible optimization problem. In this way, arbitrary descriptors can be used for characterization and arbitrary loss functions combining arbitrary descriptors can be minimized using arbitrary optimizers for reconstructing random heterogeneous media. With stochastic optimizers, this leads to variations of the well-known Yeong–Torquato algorithm. Furthermore, MCRpy features automatic differentiation, enabling the utilization of gradient-based optimizers. In this work, after a brief introduction to the underlying concepts, the capabilities of MCRpy are demonstrated by exemplarily applying it to typical MCR tasks. Finally, it is shown how to extend MCRpy by defining a new microstructure descriptor and readily using it for reconstruction without additional implementation effort

Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

Fracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the fracture toughness, i.e. the resistance against crack propagation, can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described

A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures

We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff-Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations for the brittle fracture part. For the application to complex multipatch structures, we propose penalty formulations for imposing all the required interface constraints, i.e., displacement (C0) and rotational (C1) continuity for the structure as well as C0 and C1 continuity for the phase field, where the latter is required only in the case of the fourth-order phase-field model. All involved penalty terms are scaled with the corresponding problem parameters to ensure a consistent scaling of the penalty contributions to the global system of equations. As a consequence, all coupling terms are controlled by one global penalty parameter, which can be set to 103 independent of the problem parameters. Furthermore, we present a multistep predictor-corrector algorithm for adaptive local refinement with LR NURBS, which can accurately predict and refine the region around the crack even in cases where fracture fully develops in a single load step, such that rather coarse initial meshes can be used, which is essential especially for the application to large structures. Finally, we investigate and compare the numerical efficiency of loosely vs. strongly staggered solution schemes and of the second- vs. fourth-order phase-field models