Mathematical and computational modeling of the stomach is an emerging field of biomechanics where several complex phenomena, such as gastric electrophysiology, fluid mechanics of the digesta, and solid mechanics of the gastric wall, need to be addressed. Developing a comprehensive multiphysics model of the stomach that allows studying the interactions between these phenomena remains one of the greatest challenges in biomechanics. A coupled multiphysics model of the human stomach would enable detailed in‐silico studies of the digestion of food in the stomach in health and disease. Moreover, it has the potential to open up unprecedented opportunities in numerous fields such as computer‐aided medicine and food design. This review article summarizes our current understanding of the mechanics of the human stomach and delineates the challenges in mathematical and computational modeling which remain to be addressed in this emerging area.

We present an electro-mechanical constitutive framework for the modeling of gastric motility, including pacemaker electrophysiology and smooth muscle contractility. In this framework, we adopt a phenomenological description of the gastric tissue. Tissue electrophysiology is represented by a set of two minimal two-variable models and tissue electromechanics by an active-strain finite elasticity approach. We numerically investigate the implication of the spatial distribution of pacemaker cells on the entrainment and synchronization of the slow waves characterizing gastric motility in health and disease. On simple schematic model geometries, we demonstrate that the proposed computational framework is amenable to large scale in-silico analyses of the complex gastric motility including the underlying electro-mechanical coupling. K E Y W O R D Sactive-strain electro-mechanics, electrophysiology, finite elasticity, gastric motility Abbreviations: ICC, interstitial cell of Cajal; ICC-MY, myenteric interstitial cell of Cajal; SMC, smooth muscle cell; VDCC, voltage-dependent calcium channel; cpm, cycles per minute This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Growth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.

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Powder bed fusion additive manufacturing (PBFAM) of metals has the potential to enable new paradigms of product design, manufacturing and supply chains while accelerating the realization of new technologies in the medical, aerospace, and other industries. Currently, wider adoption of PBFAM is held back by difficulty in part qualification, high production costs and low production rates, as extensive process tuning, post-processing, and inspection are required before a final part can be produced and deployed. Physics-based modeling and predictive simulation of PBFAM offers the potential to advance fundamental understanding of physical mechanisms that initiate process instabilities and cause defects. In turn, these insights can help link process and feedstock parameters with resulting part and material properties, thereby predicting optimal processing conditions and inspiring the development of improved processing hardware, strategies and materials. This work presents recent developments of our research team in the modeling of metal PBFAM processes spanning length scales, namely mesoscale powder modeling, mesoscale melt pool modeling, macroscale thermo-solid-mechanical modeling and microstructure modeling.Ongoing work in experimental validation of these models is also summarized. In conclusion, we discuss the interplay of these individual submodels within an integrated overall modeling approach, along with future research directions. K E Y W O R D Sadditive manufacturing, defects, melt pool, microstructure, modeling and simulation, powder, powder bed fusion, residual stressesThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Many additive manufacturing (AM) technologies rely on powder feedstock, which is fused to form the final part either by melting or by chemical binding with subsequent sintering. In both cases, process stability and resulting part quality depend on dynamic interactions between powder particles and a fluid phase, i.e., molten metal or liquid binder. The present work proposes a versatile computational modeling framework for simulating such coupled microfluid-powder dynamics problems involving thermo-capillary flow and reversible phase transitions. In particular, a liquid and a gas phase are interacting with a solid phase that consists of a substrate and mobile powder particles while simultaneously considering temperature-dependent surface tension and wetting effects. In case of laser–metal interactions, the effect of rapid evaporation is incorporated through additional mechanical and thermal interface fluxes. All phase domains are spatially discretized using smoothed particle hydrodynamics. The method’s Lagrangian nature is beneficial in the context of dynamically changing interface topologies due to phase transitions and coupled microfluid-powder dynamics. Special care is taken in the formulation of phase transitions, which is crucial for the robustness of the computational scheme. While the underlying model equations are of a very general nature, the proposed framework is especially suitable for the mesoscale modeling of various AM processes. To this end, the generality and robustness of the computational modeling framework is demonstrated by several application-motivated examples representing the specific AM processes binder jetting, material jetting, directed energy deposition, and powder bed fusion. Among others, it is shown how the dynamic impact of droplets in binder jetting or the evaporation-induced recoil pressure in powder bed fusion leads to powder motion, distortion of the powder packing structure, and powder particle ejection.