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Damage of an elastic body undergoing large deformations by a "hard-device" loading possibly combined with an impact (modeled by a unilateral frictionless contact) of another, ideally rigid body is formulated as an activated, rate-independent process. The damage is assumed to absorb a specific and prescribed amount of energy. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on a part of the boundary. Rigorous analysis by time discretization is performed.

We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total energy, determine the corresponding Euler–Lagrange conditions and prove, by means of direct methods of calculus of variations, the existence of curled local minimizers. Moreover, we prove some sufficient conditions for stability and instability of solutions of the Euler–Lagrange, that can be applied to numerically found curled shapes.

Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may be necessary in some problems involving extremely large distortions. If a standard updated formulation is implemented in SPH zero energy modes are activated and spoil the solution. It is important to note that the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization technique is incorporated to the updated formulation to obtain an improved method without mechanisms.

We present an extended radial point interpolation method (XRPIM) for modeling cracks and material interfaces in two-dimensional elasto-static problems. Therefore, partition of unity enrichment is incorporated into RPIM. We employ both step enrichment and crack tip enrichment for cracks. The studies are restricted to stationary cracks though the method can be extended easily to moving boundaries. We compare the results to the extended finite element method to show the superiority of our method. We show for two selected problems that the error is of magnitudes lower compared to XFEM simulations.

We present a Smoothed Finite Element Methods (SFEM) for thermo-mechanical impact problems. The smoothing is applied to the strains and the standard finite element approach is used for the temperature field. The SFEM allows for highly accurate results and large deformations. No isoparametric mapping is needed; the shape functions are computed in the physical domain. Moreover, no derivatives of the shape functions must be computed. We implemented a visco-plastic constitutive model and validate the method by comparing numerical results to experimental data.

We present impact simulations with the Smoothed Finite Element Method (SFEM). Therefore, we develop the SFEM in the context of explicit dynamic applications based on diagonalized mass matrix. Since SFEM is not based on the isoparametric concept and is based on line integration rather than domain integration, it is very promising for events involving large deformations and severe element distortion as they occur in high dynamic events such as impacts. For some benchmark problems, we show that SFEM is superior to standard FEM for impact events. To our best knowledge, this is the first time SFEM is applied in the context of impact analysis based on explicit time integration.

In this paper, a general model of elastic (non-dissipative) behavior is developed. This model belongs to a class of models, developed for the description of complex bodies, in which the local state is assumed to be determined not only by the deformation, but also by a family of additional material parameters. The latter, unlike some additional structures used in the mechanics of complex bodies (e.g., directors, order parameters, internal degrees of freedom), are not considered as interactions of microscopic nature; rather they are considered as variables of macroscopic nature that describe the internal structure of the material, while their rates describe the evolution of the internal structure in the course of deformation. Accordingly, these variables are assumed to evolve continuously with time in a manner that guaranties the reversibility of the applied dynamical process. A covariant theory for the continuum in question is derived by means of invariance properties of the global form of the spatial energy balance equation, under the superposition of arbitrary spatial diffeomorphisms. In particular, it is shown that the assumption of spatial covariance of the equation of balance of energy yields the standard conservation and balance laws of classical mechanics but it does not yield the standard Doyle–Ericksen formula. In fact, the "Doyle–Ericksen formula" derived in this work, has some extra terms in it, which are related directly to the internal structure of the material, as the latter is controlled by the additional parameters. In a similar manner, by assuming the absolute temperature as an additional state variable and by employing the invariance properties of the local form of the spatial balance of energy under superimposed spatial diffeomorphisms, which also include a temperature rescaling, a nonisothermal covariant constitutive theory is naturally obtained. A formal comparison of the proposed elastic material with the standard hyperelastic (Green elastic) solid is also presented.

The mechanical properties of Ogden material under biaxial deformation are obtained by using the bubble inflation technique. First, pressure inside the bubble and height at the hemispheric pole are recorded during bubble inflation experiment. Thereafter, Ogden's theory of hyperelasticity is employed to define the constitutive model of flat circular thermoplastic membranes (CTPMs) and nonlinear equilibrium equations of the inflation process are solved using finite difference method with deferred corrections. As a last step, a neuronal algorithm artificial neural network (ANN) model is employed to minimize the difference between calculated and measured parameters to determine material constants for Ogden model. This technique was successfully implemented for acrylonitrile-butadiene-styrene (ABS), at typical thermoforming temperatures, 145°C. When solving for the bubble inflation, the recorded pressure is applied uniformly on the structure. During the process inflation, the pressure is not uniform inside the bubble, thus full gas dynamic equations need to be solved to get the appropriate nonuniform pressure to be applied on the structure. In order to simulate the inflation process accurately, computational fluid dynamics in a moving fluid domain as well as fluid structure interaction (FSI) algorithms need to be performed for accurate pressure prediction and fluid structure interface coupling. Fluid structure interaction solver is then required to couple the dynamic of the inflated gas to structure motion. Recent development has been performed for the simulation of gas dynamic in a moving domain using arbitrary Lagrangian Eulerian (ALE) techniques.