Tangent stiffness matrix

About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.

Numerical Modeling of Transient Creep in Polycrystalline Ice

Abstract: Transient creep, an important deformation mechanism for polycrystalline ice at quasi‐static strain rates, is characterized by rate and temperature sensitivity, by isotropic and kinematic strain hardening, as well as by fabric and deformation‐induced anisotropy A physically based constitutive model, using internal state variables, has been developed by Shyam Sunder and Wu (1989a, b) to describe the multiaxial behavior of ice undergoing transient creep To solve boundary value problems using this constitutive theory requires the numerical time integration of a coupled set of stiff and highly nonlinear first‐order differential equations A closed‐form Newton‐Raphson (tangent) formulation, in conjunction with the α‐method of integration, is developed to solve the constitutive equations The fully consistent constitutive Jacobian matrix that is used to assemble the finite element tangent stiffness matrix is also established in closed form This algorithm is implemented as a subroutine in the finite element pr

Modified cyclic micromechanical model for concrete

Abstract: A detailed cyclic micromechanical model based on the micromechanics of granular material is proposed for concrete. In the current study, concrete is idealized to have two kinds of contacts; aggregate-aggregate and aggregate- mortar contacts. The behavior of these contacts is examined and distinguished for both cyclic and virgin loadings. Finally, an explicit formula which expresses the tangent stiffness matrix of the material as a summation of the contributions of all contacts inside any representative volume is derived. Moreover, the nonhomogeniety of the microstructure and the nonuniformity of strain distribution are considered. This is in contrast to Bazant's microplane model in which concrete has been treated as a homogenous brittle aggregate material having a single kind of contact with uniform strain distribution.

Application of vectorial rotational variables in large displacement analysis of structures

Abstract: Publisher Summary The chapter explains that the introduction of vectorial rotational variables in the large displacement analysis brings several advantages: these vectorial rotational variables are commutative and additive, so a consistent result can be easily achieved during updating the rotation description in the incremental/iterative solution procedure; all local variables can be obtained from global variables by applying a vector transformation matrix; symmetric-consistent tangent stiffness matrices can be achieved in the local and global systems, provided the equations of equilibrium are work-conjugate with the adopted displacement and rotation parameters; large incremental step can be adopted in the incremental loading process; and the rotational variables can describe the element large displacement response accurately. Verification examples provided in the chapter demonstrate that the proposed unified co-rotational approach provide accurate predictions of the large displacement response of two-dimensional/three-dimensional framed structures as well as curved shell problems, providing computational efficiency through the use of a symmetric tangent stiffness matrix and step-insensitivity.

On the Differentiation Formulae for Sine, Tangent, and Inverse Tangent

Abstract: SummaryWe prove the derivative formula for sine via a geometric argument and the symmetric derivative, and then use similar techniques for tangent and inverse tangent.

On vectorized MATLAB implementation of elastoplastic problems

Abstract: We propose an effective and flexible way to assemble tangent stiffness matrices in MATLAB. Our technique is applied to elastoplastic problems formulated in terms of displacements and discretized by the finite element method. The tangent stiffness matrix is repeatedly assembled in each time step and in each iteration of the semismooth Newton method. We consider von Mises and Drucker-Prager yield criteria, linear and quadratic finite elements in two and three space dimensions. Our codes are vectorized and available for download. Comparisons with other available MATLAB codes show, that our technique is also efficient for purely elastic problems. In elastoplasticity, the assembly times are linearly proportional to the number of integration points.