A Unified Determinant-Preserving Formulation for Compressible/Incompressible Finite Viscoelasticity.
A Unified Determinant-Preserving Formulation for Compressible/Incompressible Finite Viscoelasticity.
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可压缩/不可压缩有限粘弹性的统一行列式保持公式。
DOI：
10.1016/j.jmps.2023.105312
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发表时间：
2023
影响因子：
5.3
通讯作者：
Masud,Arif
中科院分区：
文献类型：
--
作者：
Wijaya,IgnasiusPA;Lopez-Pamies,Oscar;Masud,Arif
本文提出了一个制定旁边的数值解算法来描述的机械响应的机构进行任意准静态有限变形的粘弹性材料的一大类。具有一个统一的配方，适用于广泛的高度可压缩，几乎不可压缩，完全不可压缩的软有机材料在一个数值上易于处理的方式的目的，粘弹性描述在拉格朗日设置由两个潜在的混合配方。在这个公式中，变形场，一个压力场，从勒让德变换，和一个内部变量的状态F v，描述的粘性部分的变形是独立的领域。与粘性变形是体积保持过程的实验证据相一致，要求内部变量F v满足约束条件det F v= 1。为了解决由此产生的初边值问题，提出了一种数值求解算法，该算法是基于有限元（FE）离散的空间和有限差分离散的时间。具体而言，变分多尺度有限元方法，允许任意组合的形状函数的变形和压力场。为了处理具有挑战性的非凸约束det F v= 1，引入了一种新的时间积分方案，该方案允许将任何显式或隐式选择方案转换为保持约束det F v= 1不变的稳定方案。一系列的测试案例，展示了拟议的配方的能力。
This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide range of highly compressible, nearly incompressible, and fully incompressible soft organic materials in a numerically tractable manner, the viscoelasticity is described within a Lagrangian setting by a two-potential mixed formulation. In this formulation, the deformation field, a pressure field that ensues from a Legendre transform, and an internal variable of state F v that describes the viscous part of the deformation are the independent fields. Consistent with the experimental evidence that viscous deformation is a volume-preserving process, the internal variable F v is required to satisfy the constraint det F v= 1. To solve the resulting initial–boundary-value problem, a numerical solution algorithm is proposed that is based on a finite-element (FE) discretization of space and a finite-difference discretization of time. Specifically, a Variational Multiscale FE method is employed that allows for an arbitrary combination of shape functions for the deformation and pressure fields. To deal with the challenging non-convex constraint det F v= 1, a new time integration scheme is introduced that allows to convert any explicit or implicit scheme of choice into a stable scheme that preserves the constraint det F v= 1 identically. A series of test cases is presented that showcase the capabilities of the proposed formulation.