Hyperelastic Media Research Articles

Nonlinear elastic finite fracture mechanics: Modeling mixed-mode crack nucleation in structural glazing silicone sealants

Requiring both stress and energy conditions to be met simultaneously proved key to modeling brittle crack formation at singular and nonsingular stress concentrations in linear elastic materials. The present work extends this so-called coupled stress and energy criterion to brittle crack nucleation in hyperelastic media using the example of silicone adhesives. For this purpose, we provide a comprehensive constitutive as well as fracture mechanical characterization of the structural silicone adhesive DOWSIL™ 993 using a large set of experiments and propose a mixed-mode failure model for crack initiation in nonlinear elastic materials. Characterized in independent experiments, the model is used to determine critical loads of hyperelastic adhesive bonds in both shear and tension dominated configurations. For any of the examined adhesive joint configurations the model predicts and explains size effects and agrees well with experimental findings. We study stable and unstable crack propagation observed in video recordings of our experiments. It is shown that crack initiation, crack growth and crack arrest are caused by nonmonotonic energy release rates and can be predicted. Effects of excess energy available after crack nucleation and initial unstable crack growth are discussed.

An all-speed relaxation scheme for gases and compressible materials

We present a novel relaxation scheme for the simulation of compressible material flows at all speeds. An Eulerian model describing gases, fluids and elastic solids with the same system of conservation laws is adopted. The proposed numerical scheme is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in all different Mach regimes. The scheme is validated by simulating gas and liquid flows with different Mach numbers. The simulation of the deformation of compressible solids is also approached, assessing the ability of the scheme in approximating material waves in hyperelastic media.

A coupled Eulerian–Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries

We present a coupled Eulerian–Lagrangian (CEL) formulation aimed at modeling the moving interface of hyperelastic materials undergoing large to extreme deformations. This formulation is based on an Eulerian description of kinematics of deformable bodies together with an updated Lagrangian formulation for the transport of the deformation gradient tensor. The extended finite element method (XFEM) is used to discretize the mechanical equilibrium and deformation gradient transport equations in a two-phase domain. A mixed interpolation scheme (biquadratic for the velocity and bilinear for the deformation gradient) is adopted to improve the accuracy of the numerical formulation. The interface describing the deformed shape of the body is represented by the level set function and is evolved using the grid based particle method. The performance of the scheme is explored in two-dimensions in the compressible regime. For an adequate spatial and temporal discretization, our numerical results are in good agreement with theory and with numerical results from the traditional Lagrangian formulation (in Abaqus). The advantage of the proposed formulation is that material motion is not coupled with that of the mesh; this eliminates the issues of mesh distortion and the need for remeshing associated with Lagrangian formulations when bodies undergo very large distortions. It is therefore well adapted to describe the motion of complex fluids and soft matter whose physical properties are intermediate between conventional liquids and solids.

Hyper-twist

In this paper, we introduce ‘hyper-twist’, a distortion technique for the production of abstract artistic forms (see Figure 1). It is developed via exploiting the theoretical feature of deforming an infinite space filled with a hyper-elastic media. Any object placed within this space can change its shape as a result of the distortion of the space. Based on this developed theoretic insight, we have produced a computer program where point sources are used to control the form and extent of distortion. These sources perform a similar function to forces exerting on a soft body. By qualifying them with a distortion tensor, they define the patterns of the resultant distortions. Linking this representation with time, temporal effects can be produced. Our work, incorporating physics into a digital creation, presents a new form of algorithmic art.

Effective Hyperelastic Behaviour of Fiber Reinforced Polymer Composite Materials

The macroscopic hyperelastic behavior of fiber reinforced polymer composites is studied using the micromechanical model and finite deformation theory. It is assumed that the fiber and matrix are hyperelastic media and undergoing finite deformation. The local fields of a representative volume element are calculated by the hyperelastic finite element method. Then an averaging procedure is used to find the homogenized stress and strain and the macroscopic curves of stress-strain are obtained. The several microstructural parametric effects on the macroscopic hyperelastic behavior are considered. The numerical examples show the hyperelastic behavior and deformation of the composites.

Uniqueness in Inverse Problems for Elastic Media with Residual Stress

We consider dynamic inverse problems for bounded, three-dimensional elastic media with residual stress. In fact, we consider more general (nonclassical) linear hyperelastic media with the property that wave propagation occurs along the geodesics of Riemannian metrics. We show that the travel times of wave propagation through the object, together with entry and exit locations and directions, are determined by the Dirichlet-to-Neumann map in the absence of caustics and when the characteristic cones do not intersect. It follows by a boundary rigidity result of Lassas et al. (Lassas, M., Sharafutdinov, V., Uhlmann, G. ([2003]). Semiglobal boundary rigidity for Riemannian metrics. Math. Ann. 325(4):767–793.) that, under certain conditions, the geometry of the wave paths through the medium is determined up to the pullback by diffeomorphisms that fix the boundary. We also prove that the Dirichlet-to-Neumann map determines the six independent parameters at the boundary that describe the material properties of elastic media with residual stress.

Three-wave interaction and second harmonic generation in one-phase and two-phase hyperelastic media

We have applied the method of slowly varying amplitudes to the equations describing plane waves in one- phase and two-phase hyperelastic media. As a result, we have obtained the evolution equations for the complex amplitudes and Manley-Rowe power relations for both media. We have taken into account three-wave interaction and have established the spatial synchronization conditions (index matching conditions) for the triplet. We briefly analyze the second harmonic generation problem.