Many materials, such as clays, fresh concrete, and biological fluids, exhibit elasto-viscoplastic (EVP) behaviour, transitioning between solid and fluid states under varying stress conditions. Among EVP models, Saramito’s constitutive law stands out for its thermodynamic consistency, smooth solid-to-fluid transition, and ability to accurately represent diverse materials with only four easily determinable parameters. However, computational challenges have mainly confined its application to 2D or axisymmetric confined flows. This work presents an innovative partitioned Lagrangian FEM approach for the simulation of transient free-surface viscoelastic and EVP flows. The Lagrangian framework allows to naturally track free surfaces and simplifies the constitutive equation by eliminating the convective term. The solver decouples the Navier–Stokes equations (solved implicitly) from the EVP constitutive law (solved explicitly), employing an adaptive sub-stepping procedure. An advantageous splitting of the Cauchy stress tensor is used in combination with the Both Sides Diffusion (BSD) stabilization technique to prevent issues linked to the ellipticity loss in the momentum equation, also for low solvent-polymer viscosity ratios. The FEM solver has been integrated within the Particle Finite Element Method (PFEM), an updated Lagrangian formulation equipped with an efficient re-meshing scheme, to simulate free-surface flows, large deformations in soft solids, and topological changes of the domain. Benchmark tests in 2D and 3D, including gravity-induced spreading, impacting drops, and dam-break scenarios are used to validate the framework and highlight the versatility of Saramito’s model, which can also successfully reproduce a wide range of simpler sub-cases, including viscoelastic, viscoplastic, and EVP behaviours.

中文翻译：

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用于模拟粘弹性和弹-粘塑性自由表面流的分区拉格朗日有限元方法

许多材料，如粘土、新混凝土和生物流体，都表现出弹性-粘塑性 （EVP） 行为，在不同的应力条件下在固体和流体状态之间转换。在 EVP 模型中，Saramito 本构定律因其热力学一致性、平稳的固液转变以及仅使用四个易于确定的参数即可准确表示不同材料的能力而脱颖而出。然而，计算挑战主要局限于其应用在 2D 或轴对称受限流中。这项工作提出了一种创新的分区拉格朗日有限元方法，用于模拟瞬态自由表面粘弹性和 EVP 流动。拉格朗日框架允许自然地跟踪自由表面，并通过消除对流项简化了本构方程。求解器采用自适应子步进程序，将 Navier-Stokes 方程（隐式求解）与 EVP 本构定律（显式求解）解耦。柯西应力张量的有利分裂与两侧扩散 （BSD） 稳定技术结合使用，以防止与动量方程中的椭圆度损失相关的问题，也适用于低溶剂-聚合物粘度比。FEM 求解器已集成到粒子有限元法 （PFEM） 中，这是一种更新的拉格朗日公式，配备了高效的重新网格划分方案，用于模拟自由表面流、软固体中的大变形以及域的拓扑变化。 2D 和 3D 基准测试，包括重力诱导的扩散、冲击滴落和溃坝场景，用于验证框架并突出 Saramito 模型的多功能性，该模型还可以成功再现各种更简单的子情况，包括粘弹性、粘塑性和 EVP 行为。