相关论文: Relaxation theorems in nonlinear elasticity

We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.

Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…

Nonlinear elastic theory studies the elastic constants of a material (such as Young's modulus or bulk modulus) as a power series in the applied load. The inverse bulk modulus K, for example depends on the compression P: $ {1/ K(P)} = c_0 +…

The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…

The rigorous derivation of linear elasticity from finite elasticity by means of Gamma-convergence is a well-known result, which has been extended to different models also beyond the elastic regime. However, in these results the applied…

We consider a deposition model in which balls rain down at random towards a 2-dimensional surface, roll downwards over existing adsorbed balls, are adsorbed if they reach the surface, and discarded if not. We prove a spatial law of large…

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…

Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…

Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…

This study is an introduction to the theory of three-dimensional consolidation. The point of departure in the description are the basic equations of elasticity (i.e. constitutive law, equations of equilibrium in terms of stresses, and the…

In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced…

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show…

In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…

We give an overview of relaxation and 3d-2d passage theorems in hyperelasticity in the framework of the multidimensional calculus of variations. Some open questions are addressed. This paper, which is an expanded version of the…

We extend classical Flory-Rehner theory for the expansion and compression of porous materials such as cross-linked polymer networks. The theory includes volume exclusion, affinity with the solvent, and finite stretching of the polymer…

Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the…

A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…

Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…

A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot strains, truncated at quadratic order. The primary motivation is the desire for a clean separation between stretching and bending energies for…

In this paper we revisit the mathematical foundations of nonlinear viscoelasticity. We study the underlying geometry of viscoelastic deformations, and in particular, the intermediate configuration. Starting from the multiplicative…