A polyconvex transversely-isotropic invariant-based formulation for electro-mechanics: stability, minimisers and computational implementation

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

Young Measures Generated by Ideal Incompressible Fluid Flows

In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech. Ana

Characterization of Generalized Young Measures Generated by Symmetric Gradients

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer\ue2\u80\u93Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The \ue2\u80\u9clocal\ue2\u80\u9d proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti\ue2\u80\u99s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences

Nonsmooth analysis of doubly nonlinear evolution equations

In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional,for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.Comment: 45 page

A peridynamic based machine learning model for one-dimensional and two-dimensional structures

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics based machine learning model for one and two-dimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a pre-existing crack, a two-dimensional representation of a three-point bending test, and a plate subjected to dynamic load are simulated

A phase-field approach to Eulerian interfacial energies

We analyze a phase-field approximation of a sharp-interface model for two- phase materials proposed by Šilhavý (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, pp 233–244, Springer, Dordrecht, 2010; J Elast 105:271–303, 2011). The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is defined on the deformed configuration. We discuss a functional frame allowing for the existence of phase-field minimizers and Gamma-convergence to the sharp-interface limit. As a by-product, we provide additional detail on the admissible sharp-interface con- figurations with respect to the analysis in Šilhavý (2010, 2011)