We offer an alternate derivation for the symmetric-hyperbolic formulation of the equations of motion for a hyperelastic material with polyconvex stored energy. The derivation makes it clear that the expanded system is equivalent, for weak solutions, to the original system. We consider motions with variable as well as constant temperature. In addition, we present equivalent Eulerian equations of...

We prove that the Cauchy problem for a certain sixth order hyperelastic dispersive equation is globally well-posed in a natural space. We also show that there exist solitary wave solutions u(x, y, t) = φc(x − ct, y) that come from an associated variational problem. Such solitary waves are nonlinearly stable in the sense that if a solution is initially close to the set of such solitary waves, it...

We propose a reformulation of ideal magnetohydrodynamics written in the lagrangian variable as an enlarged system of hyperelastic type, with a specific potential. We study the hyperbolicity of the model and prove that the acoustic tensor is positive for all directions which are non orthogonal to the magnetic field. The consequences for eulerian ideal magnetohydrodynamics and for numerical discr...

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on handling the nonlinearity of the fluid and structure sub-problems, the nearincompressibility of materials, the stabilization of employed finite element discretizat...

Abstract This paper presents a critical review of the nonlinear dynamics hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. Hyperelasticity requires specific constitutive laws describe mechanical properties different materials, which are characterised by relationship between stress and strain. Due recent recognition hig...

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on handling the nonlinearity of the fluid and structure sub-problems, the nearincompressibility of materials, the stabilization of employed finite element discretizat...

In this paper, the problem of large pure bending deformations of membrane is considered. The membrane is a sector of torus with a closed cross-section. This membrane is called a curved tube for short. We consider the homogenous, incompressible, isotropic and hyperelastic material. The external load is a constant pressure and bending couples acting at the edges. The equilibrium equations reduce ...

We propose a mathematical model for m-dimensional nonlinear hyperelastic bodies moving in R for all m ≤ n, which enables frictionless contacts or self-contacts but not (self-)intersection. To this end, we de ne a set of admissible deformations, and prove the existence of at least one minimizer of the energy, under suitable assumptions on the stored energy. Moreover, we give a partial equivalenc...

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with a rigid surface or with an elastic substrate. The model problems take the form of two continuous optimization problems with inequality constraints, the solu...

This paper concerns the behavior of hyperelastic energies depending on an internal parameter. First, the situation in which the internal parameter is a function of the gradient of the deformation is presented. Second, two models where the parameter describes the activation of skeletal muscle tissue are analyzed. In those models, the activation parameter depends on the strain and it is important...