A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law

一种用于动态线性粘弹性的稳定DG-POD降阶方法

A stable DG-POD reduced-order method for dynamic linear viscoelasticity

本文提出一种稳定DG-POD降阶方法，用于动态线性粘弹性问题，可高效实现长时间模拟，数值实验验证其收敛性与精度，且计算成本显著降低。

基于Green-Naghdi运动学假设和广义应变的有限粘弹性建模

Modeling finite viscoelasticity based on the Green-Naghdi kinematic assumption and generalized strains

本文提出一种基于Green-Naghdi运动学假设和广义应变的有限粘弹性建模框架，避免了争议性的中间构型，通过不同应变分离非弹性变形，构建了可校准的本构理论，并经实验和有限元分析验证了其有效性与优势。

完全混合有限元方法用于粘弹性与反应-扩散模型耦合

Fully mixed finite element methods for the coupling of viscoelasticity and reaction-diffusion models

本文提出并分析了一种完全混合有限元方法，用于粘弹性组织中钙信号传导的双向耦合机械化学模型，通过混合变量和弱对称性处理，建立了适定性和最优误差估计，并数值验证了收敛速率。

A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model

The stress-strain constitutive law for viscoelastic materials such as soft tissues, metals at high temperature, and polymers, can be written as a Volterra integral equation of the second kind with a \emph{fading memory} kernel. This integral relationship yields current stress for a given strain history and can be used in the momentum balance law to derive a mathematical model for the resulting deformation. We consider such a dynamic linear viscoelastic model problem resulting from using a \textit{Dirichlet-Prony} series of decaying exponentials to provide the fading memory in the Volterra kern…

Mittag-Leffler Euler integrator for a stochastic fractional order equation with additive noise

Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here as the Mittag-Leffler Euler integrator, is used for the temporal discretization, while the spatial discretization is performed by the spectral Galerkin method. The temporal rate of strong convergence is found to be (almost) twice compared to when the backward Euler method is used together with a convolution quadrature for time discretization. Numerical expe…

一大类有限黏弹性模型的Abaqus实现

Abaqus implementation of a large family of finite viscoelasticity models

本文提出一个Abaqus UMAT子程序，用于实现涵盖非高斯弹性与非线性黏性的有限黏弹性本构模型，通过高阶显式Runge-Kutta格式求解约束ODE，并验证了准确性与收敛性。

二阶超几何方程含记忆项的Galerkin近似存在性与收敛性

Existence and convergence of Galerkin approximation for second order hyperbolic equations with memory

研究含记忆项的二阶超几何初始边界值偏微分方程，通过Picard迭代证明Galerkin近似的存在性和唯一性，并利用能量法推导出有限元近似的最优阶先验误差估计。

An Efficient and Accurate Method for Modeling Nonlinear Fractional Viscoelastic Biomaterials

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelasticity, current biomechanical models in the computation community often assume only hyperelasticity. Fractional viscoelastic constitutive models have been successfully used in literature to capture the material response. However, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic con…

一种用于波传播分数阶粘弹性模型的快速全离散混合有限元格式

A fast fully discrete mixed finite element scheme for fractional viscoelastic models of wave propagation

针对分数阶偏微分方程数值求解内存与计算成本高的问题，本文提出波传播分数阶粘弹性模型的快速全离散混合有限元格式，通过拉普拉斯变换、SOE近似结合混合有限元与Newmark格式，显著降低复杂度并经实验验证。

基于物理信息神经网络的流变学时间分数阶微分方程反演框架

Physics-Informed Neural Network based inverse framework for time-fractional differential equations for rheology

本研究将物理信息神经网络（PINNs）拓展至时间分数阶导数反问题，针对反常扩散与分数阶粘弹性本构方程两类问题，设计定制残差损失函数，在含噪数据与生物组织实验中均实现10%以内的预测相对误差。