MVSS有限元求解器是一个高效的,具有国际先进水平的快速直接求解器。本文针对通用有限元代码的结构和特点,把MVSS做了模块化封装,使之很容易结合到通用有限元程序中,使程序的求解能力和求解效率提高2-10倍以上。

The analytical stress-strain relation with heterogeneous parameters is derived for the heterogeneous brittle materials under a uniaxial extensional load, in which the distributions of the elastic modulus and the failure strength are assumed to be statistically independent. This theoretical solution gives an approximate estimate of the equivalent stress-strain relations for 3-D heterogeneous materials. In one-dimensional cases it may provide comparatively accurate results. The theoretical solution can help us to explain how the heterogeneity influences the mechanical behaviors. Further, a numerical approach is developed to model the non-linear behavior of three-dimensional heterogeneous brittle materials. The lattice approach and statistical techniques are applied to simulate the initial heterogeneity of heterogeneous materials. The load increment in each loading stage is adaptively determined so that the better approximation of the failure process can be realized. When the maximum tensile principal strain exceeds the failure strain, the elements are considered to be broken, which can be carried out by replacing its Young's modulus with a very small value. A 3-D heterogeneous brittle material specimen is simulated during a full failure process. The numerical results are in good agreement with the analytical solutions and experimental data.

By using the lattice model combined with finite element methods and statistical techniques, a numerical approach is developed to establish mechanical models of three-dimensional heterogeneous brittle materials. A special numerical code is introduced, in which a lattice model and statistical approaches are used to simulate the initial heterogeneity of material properties. The size of displacement-load step is adaptively determined so that only few elements would fail in each load step. When the tensile principal strain in an element exceeds the ultimate strain of this element, the element is considered broken and its Young's modulus is set to be very low. Some important behaviors of heterogeneous brittle materials are indicated using this code. Load-displacement curves and figures of three-dimensional fracture patterns are also numerically obtained, which are similar to those observed in laboratory tests.