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 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 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

Bifurcation analysis versus maximum force criteria in formability limit assessment of stretched metal sheets

The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches are identical for particular loading paths and constitutive models, they are generally different, which is even the case for elasticity, confirming the distinct nature of the two concepts. Closed-form expressions of the critical stress and strain states are derived for both criteria in elasto-plasticity and rigid-plasticity for a variety of hardening models. The resulting useful formulas in rigidplasticity are shown to also accurately represent the elasto-plastic critical states for small ratios of the hardening modulus with respect to Young's modulus. Finally, the well-known expression of Swift's diffuse necking criterion, whose foundations are attributed in the literature to the maximum force principle, is shown here to originate from the bifurcation approach instead, providing a sound justification for it

An elasto-viscoplastic constitutive model for the rate-dependent behavior of polyvinylidene fluoride

To model the engineering performance of components made of polyvinylidene fluoride (PVDF), the 3D elasto-viscoplastic Eindhoven glassy polymer (EGP) model is extended to describe the rate-dependent behavior of PVDF. Careful analysis of the intrinsic behavior of PVDF revealed that the postyield compressive response shows a strain rate-dependence that evolves with increasing deformation. The extension of the constitutive model captures the deformation-dependent evolution of the activation volume and the rate-factor, which describes the driving stress. Given the significant temperature-dependent behavior, the model has been characterized for different temperatures (23, 55 and 75 °C). The accuracy of the model has been validated by means of tension and creep experiments at these temperatures. The constitutive model is implemented in finite element simulations and the results are compared with the experiments. It is shown that the proposed model allows for an accurate prediction of the short- and long-term rate-dependent behavior of PVDF.</p