1,721,556 research outputs found
An analytic study on the properties of solitary waves traveling on tensegrity-like lattices
No full textThis paper develops an analytic study on the existence and properties of solitary waves on 1D chains of lumped masses and nonlinear springs, which exhibit a mechanical response similar to that of tensegrity prisms with locking-type response under axial loading. Making use of the Weierstrass’ theory of 1D Lagrangian conservative systems, we show that such waves exist and that their shapes depend on the wave speed. A progressive localization of the traveling pulses in narrow regions of space is observed as the wave speed increases up to a limit value. A comparative analysis illustrates that the presented study is able to capture the wave dynamics observed in previous numerical studies on tensegrity mass–spring chains
On the Optimal Prediction of the Stress Field Associated with Discrete Element Models
No full textThis work presents an optimized and convergent regularization procedure for the computation of the stress field exhibited by particle systems subject to self-equilibrated short-range interactions. A regularized definition of the stress field associated with arbitrary force networks is given, and its convergence behavior in the continuum limit is demonstrated analytically, for the first time in the literature. The analyzed systems of forces describe pair interactions between lumped masses in ‘atomistic’ models of 2D elastic bodies and 3D membrane shells based on non-conforming finite element methods. We derive such force networks from polyhedral stress functions defined over arbitrary triangulations of 2D domains. The stress function associated with an unstructured force network is projected onto a structured triangulation, producing a new force network with ordered structure. The latter is employed to formulate a ‘microscopic’ definition of the Cauchy stress of the system in the continuum limit. The convergence order of such a stress measure to its continuum limit is given, as the mesh size approaches zero. Benchmark examples illustrate the application of the proposed regularization procedure to the prediction of the stress field exhibited by a variety of 2D and 3D membrane networks
Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials
No full textThis article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with microstructure. Two improvements are made in contrast to earlier approaches: First, the micro-rotations are parameterized with the help of an Euler–Rodrigues formula related to quaternions. Secondly, as main result, a novel two-pass preconditioning scheme for searching the energy-minimizing solutions based on the limited memory Broyden–Fletcher–Goldstein–Shanno quasi-Newton method is proposed that consists of a predictor step and a corrector-iteration. After outlining the necessary adaptations to the model, numerical simulations compare the performance and efficiency of the new and the old algorithm. The proposed numerical model can be effectively employed for studying the mechanical response of complicated materials featuring large size effects
Uniqueness, continuous dependence, and spatial behavior of the solution in linear porous thermoelasticity with two relaxation times
No full textThis work aims to contribute to the verification of the well-posedness question, as for the uniqueness and continuous dependence issues, for a linear thermoelastic model with two main features: (i) a porous material matrix modeled on the basis of the Cowin-Nunziato theory; (ii) a heat transfer process obeying a time-differential constitutive equation with two relaxation times, derived from the dual-phase lag theory with an appropriate selection of the Taylor series expansion orders. Imagining to deal with very small spatial scales (in the order of the micro or nanometer), we assume it is reasonable to accept that the deformations caused by temperature variations are small enough to be realistically modeled under hypotheses of linearity, thus making the mathematical theory under investigation particularly meaningful, e.g. in the study of miniaturized devices in very fast transients. The work is concluded by proving a domain of influence theorem, and with a reference to the future research activities to carry out starting from it
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