Evolving discontinuities and cohesive fracture

Multi-scale methods provide a new paradigm in many branches of sciences, including applied mechanics. However, at lower scales continuum mechanics can become less applicable, and more phenomena enter which involve discon- tinuities. The two main approaches to the modelling of discontinuities are briefly reviewed, followed by an in-depth discussion of cohesive models for fracture. In this discussion emphasis is put on a novel approach to incorporate triaxi- ality into cohesive-zone models, which enables for instance the modelling of crazing in polymers, or of splitting cracks in shear-critical concrete beams. This is followed by a discussion on the representation of cohesive crack models in a continuum format, where phase-field models seem promising

Efficient modelling of delamination growth using adaptive isogeometric continuum shell elements

The computational efficiency of CAE tools for analysing failure progression in large layered composites is key. In particular, efficient approximation and solution methods for delamination modelling are crucial to meet today’s requirements on virtual development lead times. For that purpose, we present here an adaptive continuum shell element based on the isogeometric analysis framework, suitable for the modelling of arbitrary delamination growth. To achieve an efficient procedure, we utilise that, in isogeometric analysis, the continuity of the approximation field easily can be adapted via so-called knot insertion. As a result, the current continuum shell provides a basis for an accurate but also computationally efficient prediction of delamination growth in laminated composites. Results show that the adaptive modelling framework works well and that, in comparison to a fully resolved model, the adaptive approach gives significant time savings even for simple analyses where major parts of the domain exhibit delamination growth

An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results.</p

Model for the Scaling of Stresses and Fluctuations in Flows near Jamming

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.Comment: 4 pages, 5 figures (revised text and one new figure). To appear in Phys. Rev. Let

A generalised path-following solver for robust analysis of material failure

When analysing complex structures with advanced damage or material models, it is important to use a robust solution method in order to trace the full equilibrium path. In light of this, we propose a new path-following solver based on the integral of the rate of dissipation in each material point, for solving problems exhibiting large energy dissipating mechanisms. The method is a generalisation and unification of previously proposed dissipation based path-following solvers, and makes it possible to describe a wider range of dissipation mechanisms, such as large strain plasticity. Furthermore, the proposed method makes it possible to, in a straightforward way, combine the effects from multiple dissipation mechanisms in a simulation. The capabilities of the solver are demonstrated on four numerical examples, from which it can be concluded that the proposed method is both versatile and robust, and can be used in different research domains within computational structural mechanics and material science

An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results.</p

An adaptive isogeometric shell element for the prediction of initiation and growth of multiple delaminations in curved composite structures

In order to model prominent failure modes experienced by multi-layered composites, a fine through-thickness discretisation is needed. If the structure also has large in-plane dimensions, the computational cost of the model becomes large. In light of this, we propose an adaptive isogeometric continuum shell element for the analysis of multi-layered structures. The key is a flexible and efficient method for controlling the continuity of the out-of-plane approximation, such that fine detail is only applied in areas of the structure where it is required. We demonstrate how so-called knot insertion can be utilised to automatise an adaptive refinement of the shell model at arbitrary interfaces, thereby making it possible to model multiple initiation and growth of delaminations. Furthermore, we also demonstrate that the higher-order continuity of the spline-based approximations allows for an accurate recovery of transverse stresses on the element level, even for doubly-curved laminates under general load. With this stress recovery method, critical areas of the simulated structures can be identified, and new refinements (cracks) can be introduced accordingly. In a concluding numerical example of a cantilever beam with two initial cracks, we demonstrate that the results obtained with the adaptive isogeometric shell element show good correlation with experimental data

An efficient ray tracing methodology for the numerical analysis of powder bed additive manufacturing processes

This paper presents a ray tracing model to simulate the laser-powder bed interaction for additive manufacturing processes. Ray tracing is a technique that is able to accurately and efficiently capture the interaction of light with multiple objects with complex geometries made of different materials. In the proposed methodology the laser energy distribution is modelled by a finite number of rays which are traced through the powder bed that is modelled as stacked spherical particles. The proposed ray tracing methodology addresses the reflection and refraction of light using the Fresnel equations and its absorption using a Beer–Lambert law. Simulations of a stationary laser on a powder bed show that for metallic materials the effect of polarisation of the light on the energy distribution in the powder bed is negligible. In addition, it is demonstrated that the refracted rays are fully absorbed by single powder particles. The illumination results of a stationary polarised laser under a range of incident angles indicate a significant absorption difference at high angles. In order to increase computational efficiency, a closed form relation for an equivalent homogenised volumetric laser heat source has been derived, whereby the shape and power profile of the laser matches the ray tracing results. Simulating single scan lines by varying power, spot size and speed demonstrates that the model accurately captures a moving laser in a DEM simulation, revealing the relations between single scan line dimensions and printer settings.</p

An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results