Related papers: Stable numerics for finite-strain elasticity
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the…
Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we present Si I under large strain in terms of Lagrangian strain by an…
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…
This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…
Recently, a widely applicable system of hyperbolic partial differential equations has been derived that enables the deterministic computation of a full heterogeneous stress field from a measured deformation field, for example, from a strain…
The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a…
It is well known that Cauchy problem for Laplace equations is an ill-posed problem in Hadamard's sense. Small deviations in Cauchy data may lead to large errors in the solutions. It is observed that if a bound is imposed on the solution,…
The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is…
The variational static formulation contributed in [International Journal of Engineering Science 143, 73-91 (2019)] is generalized in the present paper to model axial and flexural dynamic behaviors of elastic nano-beams by nonlocal strain…
This paper presents a consistent computational framework for multiscale 1st order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. Based on the principle of multiscale virtual…
We investigate a finite element formulation of the exponentiated Hencky-logarithmic model whose strain energy function is given by \[ W_\mathrm{eH}(\boldsymbol{F}) = \dfrac{\mu}{k}\, e^{\displaystyle k \left\lVert\mbox{dev}_n…
Elastic constants are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic constants…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
Tensile instability, often observed in smoothed particle hydrodynamics (SPH), is a numerical artifact that manifests itself by unphysical clustering or separation of particles. The instability originates in estimating the derivatives of the…
A finite-strain formulation is developed, implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder. This constitutive model (as well as…
Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This…
We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…
This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…