Small-distortion constitutive laws are often extemporaneously generalized to large deformations by merely applying them in the unrotated material frame or, equivalently, by using polar rates. This approach does render the resulting constitutive model indifferent to large superimposed rigid rotations, but it may lead to incorrect predictions for both the magnitude and direction of stress wheneve...

We present a simple method to determine the persistence length of short submicrometer microtubule ends from their stochastic trajectories on kinesin-coated surfaces. The tangent angle of a microtubule trajectory is similar to a random walk, which is solely determined by the stiffness of the leading tip and the velocity of the microtubule. We demonstrate that even a single-microtubule trajectory...

We apply a nonlinear-nonlocal field theory for numerical calculation of quasistatic fracture. The model is given by regularized nonlinear pairwise potential in peridynamic formulation. function an explicit formula with first and second derivatives. This fact allows us to write the entries tangent stiffness matrix explicitly thereby saving computational costs during assembly matrix. validate our...

Ligaments are regularly subjected to repetitive loading in vivo. Typically, mechanical studies focus on repetitive loading protocols of short duration, while those characterizing damage accumulation over a longer duration (i.e., fatigue studies) are lacking. The aims of this study were as follows: (a) to demonstrate that damage does accumulate in ligament tissue subjected to repetitive loading ...

A methodology for computationally efficient formulation of the tangent stiffness matrix consistent with incrementally objective algorithms for integrating finite deformation kinematics and with closest point projection algorithms for integrating material response is developed in the context of finite deformation plasticity. Numerical experiments illustrate an excellent performance of the propos...

We show that the recently proposed confining string theory describes smooth surfaces with long-range correlations for the normal components of tangent vectors. These long-range correlations arise as a consequence of a " frustrated antiferromagnetic " interaction whose two main features are non-locality and a negative stiffness.

[A] matrix with constants describing the anisotropy of the material [B] strain matrix [BL] linear strain matrix [BNL] nonlinear strain matrix c speed of sound d rate of deformation tensor dp plastic rate of deformation D elastic constitutive tensor [D] matrix of the elastic constitutive tensor [DT] matrix form of the constitutive tensor ds lengths of the vector dx dS lengths of the vector dX dv...

Tensile properties of the larval cuticle of Manduca sexta were measured during the fifth instar. It was found that as the larvae grew and the cuticle thickened, the tangent modulus (intrinsic stiffness) for the cuticle declined rapidly. The extensibility of the cuticle during the growth period remained relatively high and fairly constant, while the flexural stiffness remained low. Subsequently,...

A numerical method is presented for stability analysis of cable–bar structures. An optimization problem is formulated to find the minimum value of the incremental total potential energy that depends on the direction of the incremental displacements. The penalty method with slack variables is used for representing the discontinuity in member stiffness. The tangent stiffness matrix is shifted to ...

A new technique for computation structural instability points using the finite element method is presented. The approach is based on the estimation of critical displacement pattern by writing an approximation of the tangent stiffness singularity condition at the instability point. The critical load is subsequently computed by using a secant load-displacement relationship. Details of this proced...