Strain Energy

In this article the identification of the material parameters occurring in isotropic and incompressible hyperelasticity relations of generalized polynomial-type is discussed. The underlying strain-energy function depends on the first and second invariant of the left Cauchy–Green tensor in the ...

In this paper, we investigate power flow in compliant mechanisms that are employed in dynamic applications. More specifically, we identify various elements of the energy storage and transfer between the input, external load, and strain energy stored within the compliant transmission. The goal is to design compliant mechanisms for dynamic applications by exploiting the inherent energy storage capability of compliant mechanisms in the most effective manner. We present a detailed case study on a flapping mechanism, in which we compare the peak input power requirement in a rigid-body mechanism with attached springs versus a distributed compliant mechanism. Through this case study, we present two approaches: (1) generative-load exploitation and (2) reactance cancellation, to describe the role of stored elastic energy in reducing the peak input power requirement. We propose a compliant flapping mechanism and its evaluation using nonlinear transient analysis. The input power needed to driv...

A class of ‘assumed strain’ mixed finite element methods for fully non-linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three-field variational formulation. The resulting class of mixed methods provides a possible extension to the non-linear regime of well-known incompatible mode formulations. In addition, this class of methods includes non-linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2-D, 3-D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.

Five series of test blocks of Pendeli marble with artificially created discontinuities of different crack densities (simulating three mutually orthogonal joint sets) were tested in uniaxial compression in order to study the effect of discontinuities on: (a) the compressive strength and the modulus of elasticity, and (b) certain fracture energy parameters expressed by the ratio W A/W V, where W A is the surface energy and W V the volume elastic strain energy. Mathematical relationships are derived similar to those suggested by other authors relating strength parameters to crack densities. Such relationships clearly show a reduction in strength with increased crack density. The experimental results obtained permit the extension of Persson's relation (which refers to ideal intact rock) to the more realistic case of discontinuous rock mass by introducing the appropriate term that takes into consideration the effect of rock mass discontinuities on the energy ratio W A/W V. A comparison between laboratory results and field observations was subsequently carried out assuming the rock mass to behave as a linearly elastic material, obeying the Hoek and Brown failure criterion. This comparison showed that laboratory results can be extended to larger scale. Furthermore, in order to predict the in situ strength and stability of a rock mass in uniaxial compression (which is of major importance in underground excavations) certain concepts are proposed based on laboratory tests, in situ investigations and first principles of linear elastic fracture mechanics.

This paper represents a first attempt to derive one-dimensional models with non-convex strain energy starting from “genuine” three-dimensional, nonlinear, compressible, elasticity theory. Following the usual method of obtaining beam theories, we show here for a constrained kinematics appropriate for long cylinders governed by a polyconvex, objective, stored energy function, that the bar model originally proposed by Ericksen [3] is obtainable but enriched by an additional term in the strain gradient. This term, characteristic of nonsimple grade-2 materials, penalizes interfacial energies and makes single-interface two-phase solutions preferred. The resulting model has been proposed by a number of authors to describe the phenomenon of necking and cold drawing in polymeric fibers and, here, we discuss its suitability to interpret also the elastic-plastic behavior of metallic tensile bars under monotone loading.

A good understanding of the mechanics of pole vaulting is fundamental to performance because this event is quite complex, with several factors occurring in sequence and/or in parallel. These factors mainly concern the velocities of the vaulter-pole system, the kinetic and potential energy of the vaulter and the strain energy stored in the pole, the force and torque applied by the athlete, and the pole design. Although the pole vault literature is vast, encompassing several fields such as medicine, sports sciences, mechanics, mathematics, and physics, the studies agree that pole vault performance is basically influenced by the energy exchange between the vaulter and pole. Ideally, as the athlete clears the crossbar, the vaulter mechanical energy must be composed of high potential energy and low kinetic energy, guaranteeing the high vertical component of the vault. Moreover, the force and torque applied by the vaulter influences this energy exchange and these factors thus must be taken into consideration in the analysis of performance. This review presents the variables that influence pole vault performance during the run-up, take-off, pole support, and free flight phases.

Marine cables under low tension and torsion on the sea floor can form highly contorted three-dimensional geometries that include loops (e.g. hockles) and tangles. These geometries arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is reviewed herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-alpha method for finite differencing in both space and time. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, through the dynamic collapse of this helix into a loop, and subsequent intertwining of the loop with multiple sites of self-contact.

One of the important considerations in the selection of a polymer blend for a practical application is how it resists crack growth and/or failure from a material flaw, under static or fatigue conditions. The blending of two or more rubbers is a useful technique to improve certain properties not inherent in a single rubber. In the present work, fatigue and