This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of transient implicit and explicit solvers and steady-state (static) solvers and implementations for Central Processing Unit (CPU) as well as Graphics Processing Unit (GPU). The various implementations are compared on the basis of a set of benchmarks tests describing behaviors of increasing computational complexity. They include elastic vibrations, confined strain-hardening compressive response, tensile fracture, and unconfined strain-softening compressive response. Metrics of interest extracted from the simulations include macroscopic stress versus strain responses, computational times, number of iterations, and energy balance error. Pairwise comparison of final crack patterns is provided through the correlation coefficient and normalized root mean square error of the crack opening vectors. Moreover, for the most numerically challenging case of unconfined compression with sliding boundary conditions, the stability of the strain-softening response is tested by perturbing the solutions as well as changing the convergence criteria and time step size. Attached to this paper is the complete input data of the benchmark tests; this will allow researchers to run the examples and compare them with their own implementations. In addition, most of the reported implementations are publicly available in open source packages.

翻译：本文针对混凝土及其他异质准脆性材料的数值模拟，对晶格离散颗粒模型（LDPM）的多种实现方案进行了比较。比较内容涉及瞬态隐式与显式求解器、稳态（静态）求解器，以及在中央处理器（CPU）和图形处理器（GPU）上的实现。通过一组计算复杂度递增的基准测试，对各类实现方案进行了评估。这些测试包括弹性振动、约束应变硬化压缩响应、拉伸断裂以及无约束应变软化压缩响应。从模拟中提取的关键指标包括宏观应力-应变响应、计算时间、迭代次数以及能量平衡误差。最终裂纹模式的成对比较通过裂纹张开向量的相关系数和归一化均方根误差进行。此外，针对最具数值挑战性的无约束压缩与滑动边界条件工况，通过扰动解、改变收敛准则和时间步长，测试了应变软化响应的稳定性。本文附有基准测试的完整输入数据，可供研究人员运行算例并与自身实现方案进行对比。此外，文中报告的大部分实现方案已在开源软件包中公开提供。