arXiv subjects

L. Angela Mihai

Publications and source records attributed to L. Angela Mihai.

21 records · Page 2Linked to original sources

arXiv2016

Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations

In isotropic finite elasticity, unlike in the linear elastic theory, a homogeneous Cauchy stress may be induced by non-homogeneous strains. To illustrate this, we identify compatible non-homogeneous three-dimensional deformations producing a homogeneous Cauchy stress on a cuboid geometry, and provide an example of an isotropic hyperelastic material, which is not rank-one convex, and for which the homogeneous stress and the associated non-homogeneous strains on a domain similar to those analysed are given explicitly.

math-ph↗

arXiv2016

Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition

In this note, we show that the Cauchy stress tensor $σ$ in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that $σ(F+ξ\otimes η)=σ(F)$ implies $ξ\otimes η=0$ under strict rank-one convexity.

math.CA↗

arXiv2016

Guaranteed upper and lower bounds on the uniform load of contact problems in elasticity

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 solutions of which are used to provide an enclosure on the uniform external load acting on the body's surface away from the contact zone.

math.AP↗