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Tangent stabilised large strain isotropic elasticity was recently proposed by Poya et al. [1] wherein by working directly with principal stretches the entire eigenstructure of constitutive and geometric/initial stiffness terms were found in closed-form, giving fresh insights into exact convexity conditions of highly non-convex functions in discrete settings. Consequently, owing to these tangent eigenvalues an analytic tangent stabilisation was proposed bypassing incumbent numerical approaches routinely used in nonlinear finite element analysis. This formulation appears to be extremely robust for quasi-static simulation of complex deformations even with no load increments and time stepping while still capturing instabilities automatically in ways that are infeasible for path-following techniques in practice. In this work, we generalise the notion of tangent stabilised elasticity to virtually all known invariant formulations of nonlinear elasticity. We show that, closed-form eigen-decomposition of tangents is easily available irrespective of invariant formulation or integrity basis. In particular, we work out closed-form tangent eigensystems for isotropic Total Lagrangian deformation gradient (F )-based and right Cauchy-Green (C)-based as well as Updated Lagrangian left Cauchy-Green (b)-based formulations and present their exact convexity conditions postulated in terms of their corresponding tangent and initial stiffness eigenvalues. In addition, we introduce the notion of geometrically stabilised polyconvex large strain elasticity for models that are materially stable but exhibit geometric instabilities for whom we construct their initial stiffness in a spectrally-decomposed form analytically. We further extend this framework to the case of transverse isotropy where once again, closed-form tangent eigensystems are found for common transversely isotropic invariants.

We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of stable systems can be efficiently computed using the algebraic versions of improved inclusion-exclusion formulas and sum of disjoint products.

In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material behavior at finite deformations are calibrated to different synthetically generated datasets, including an analytical isotropic potential, a homogenised rank-one laminate, and a homogenised metamaterial with a spherical inclusion. Subsequently, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Scenarios with large electrically induced deformations and instabilities are particularly challenging and thus necessitate extensive investigations of the PANN constitutive models in the context of finite element analyses. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. In all cases studied, the PANN models yield excellent prediction qualities and a stable numerical behavior even in highly nonlinear scenarios. This can be traced back to the PANN models excellent performance in learning both the first and second derivatives of the ground truth electro-elastic potentials, even though it is only calibrated on the first derivatives. Overall, this work demonstrates the applicability of PANN constitutive models for the efficient and robust simulation of engineering applications of composite electro-elastic materials.

Intensity Modulated Radiation Therapy is an effective cancer treatment. Models based on the Generalized Equivalent Uniform Dose (gEUD) provide radiation plans with excellent planning target volume coverage and low radiation for organs at risk. However, manual adjustment of the parameters involved in gEUD is required to ensure that the plans meet patient-specific physical restrictions. This paper proposes a radiotherapy planning methodology based on bi-level optimization. We evaluated the proposed scheme in a real patient and compared the resulting irradiation plans with those prepared by clinical planners in hospital devices. The results in terms of efficiency and effectiveness are promising.

Searching for potential active compounds in large databases is a necessary step to reduce time and costs in modern drug discovery pipelines. Such virtual screening methods seek to provide predictions that allow the search space to be narrowed down. Although cheminformatics has made great progress in exploiting the potential of available big data, caution is needed to avoid introducing bias and provide useful predictions with new compounds. In this work, we propose the decision-support tool ALMERIA (Advanced Ligand Multiconformational Exploration with Robust Interpretable Artificial Intelligence) for estimating compound similarities and activity prediction based on pairwise molecular contrasts while considering their conformation variability. The methodology covers the entire pipeline from data preparation to model selection and hyperparameter optimization. It has been implemented using scalable software and methods to exploit large volumes of data -- in the order of several terabytes -- , offering a very quick response even for a large batch of queries. The implementation and experiments have been performed in a distributed computer cluster using a benchmark, the public access DUD-E database. In addition to cross-validation, detailed data split criteria have been used to evaluate the models on different data partitions to assess their true generalization ability with new compounds. Experiments show state-of-the-art performance for molecular activity prediction (ROC AUC: $0.99$, $0.96$, $0.87$), proving that the chosen data representation and modeling have good properties to generalize. Molecular conformations -- prediction performance and sensitivity analysis -- have also been evaluated. Finally, an interpretability analysis has been performed using the SHAP method.

Typical computational techniques for vascular biomechanics represent the blood vessel wall via either a membrane, a shell, or a 3D solid element. Each of these formulations has its trade offs concerning accuracy, ease of implementation, and computational costs. Despite the widespread use of these formulations, a systematic comparison on the performance and accuracy of these formulations for nonlinear vascular biomechanics is lacking. Therefore, the decision regarding the optimal choice often relies on intuition or previous experience, with unclear consequences of choosing one approach over the other. Here, we present a systematic comparison among three different formulations to represent vessel wall: (i) a nonlinear membrane model, (ii) a nonlinear, rotation-free shell model, and (iii) a nonlinear 3D solid model. For the 3D solid model, we consider two different implementations employing linear and quadratic interpolation. We present comparison results in both idealized and subject-specific mouse geometries. For the idealized cylindrical geometry, we compare our results against the axisymmetric solution for three different wall thickness to radius ratio. Subsequently, a comparison of these approaches is presented in an idealized bifurcation model for regionally varying wall thickness. Lastly, we present the comparison results for a subject-specific mouse geometry with regionally varying material properties and wall thickness, while incorporating the effect of external tissue surrounding the vessel wall.

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated as a convex neural network. In this way, the model fulfills the polyconvexity condition which ensures material stability, as well as thermodynamic consistency, objectivity, material symmetry, and growth conditions. Depending on the considered invariants, this physics-augmented machine learning model can either be applied for compressible or nearly incompressible material behavior, as well as for arbitrary material symmetry classes. The applicability and versatility of the approach is demonstrated by calibrating it on transversely isotropic data generated with an analytical potential, as well as for the effective constitutive modeling of an analytically homogenized, transversely isotropic rank-one laminate composite and a numerically homogenized cubic metamaterial. These examinations show the excellent generalization properties that physics-augmented neural networks offer also for multi-physical material modeling such as nonlinear electro-elasticity.

The fabrication of evermore sophisticated miniaturised soft robotic components made up of Electro-Active Polymers (EAPs) is constantly demanding parallel development from the in-silico simulation point of view. The incorporation of crystallographic anisotropic micro-architectures, within an otherwise nearly uniform isotropic soft polymer matrix, has shown great potential in terms of advanced three-dimensional actuation (i.e. stretching, bending, twisting), especially at large strains, that is, beyond the onset of geometrical pull-in instabilities. To accommodate for this in-silico response, this paper presents a phenomenological invariant-based polyconvex transversely isotropic framework for the simulation of EAPs at large strains. This research expands previous work developed by Gil and Ortigosa for isotropic EAPs with the help of the pioneering work by Schr\"{o}eder and Neff in the context of polyconvexity for materials endowed with crystallographic architectures in single physics mechanics. The paper also summarises key important results both in terms of the existence of minimisers and material stability. In addition, a series of numerical examples is presented in order to demonstrate the effect that the anisotropic orientation and the contrast of material properties, as well as the level of deformation and electric field, have upon the response of the EAP when subjected to large three-dimensional stretching, bending and torsion, including the possible development of wrinkling.

We present the design and implementation of a \texttt{C++} class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is implemented within the open-source \verb|CoCoALib| library and provides functions to compute system reliability and bounds. The algorithms we present may be applied to general systems with independent components having identical or non-identical probability distributions., Comment: 28 pages