Abstract We call nonlinear dilatational strain gradient elasticity the theory in which specific class of second continua is considered: those whose deformation energy depends, an objective way, on placement and determinant placement. It interesting particular case complete Toupin–Mindlin elasticity: indeed, it, only effects are due to inhomogeneous dilatation state considered deformable body. T...

In this paper, topology optimization of both geometrically and materially nonlinear structure is studied using a general displacement functional as the objective function. In order to consider large deformation, e2ective stress and strain are expressed in terms of 2nd Piolar–Kirchho2 stress tensor and Green–Lagrange strain tensor, and constitutive equation is derived from the relation between t...

We establish the feasibility of imaging the linear and nonlinear elastic properties of soft tissue using ultrasound. We report results for breast tissue where it is conjectured that these properties may be used to discern malignant tumors from benign tumors. We consider and compare three different quantities that describe nonlinear behavior, including the variation of strain distribution with o...

In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacem...

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlinear differential equations has been described. ...

This study investigates the time-dependent long-term creep strain in a composite cylinder made of glass/vinylester with a unidirectional ply. The cylinder is subjected to an internal pressure and the boundary condition is free–free and acts as thermal insulation. The classical lamination theory (CLT) is used to derive the governing equations as a second-order equation to determine the radial, c...

We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the equation governing rectilinear shear motion in the plane of the fiber reinforcement; it is a nonlinear partial differential equation for the shear strain. Special...