A geometrically nonlinear phase field theory accounting for dissipation, rate effects, nonlinear thermoelasticity, fracture, and other structural changes is constructed in the context of continuum thermodynamics. First, a general framework accommodating arbitrary strain energy potentials, inelastic deformation kinematics, and unlimited order parameters is formulated. Next, the framework is specialized to account for deformation physics pertinent to crystalline ceramics and minerals deformed at high rates and high pressures. Notably, a logarithmic elastic strain tensor referred to an intermediate material configuration enters the nonlinear thermoelastic potential. Order parameters represent fractures, solid–solid phase transformations, deformation twinning, or slip of partial dislocations. Thermodynamically consistent kinetics manifest in equations reminiscent of Ginzburg–Landau dynamics, wherein viscosity coefficients are most generally state- and rate-dependent. Pressure-dependent strength commensurate with frictional resistance is enabled in alternative kinetic equations for dynamic fracture with irreversibility constraints. Linearization of the model suitable for moderate volume changes but small deviatoric elastic strain and rotation is undertaken. The theory is applied to study deformation and failure of polycrystalline forms of boron carbide (B${}_4$C), titanium diboride (TiB${}_2$), and a B${}_4$C-TiB${}_2$ ceramic composite. Solutions are derived and evaluated numerically for uniaxial stress tension and compression, uniaxial strain compression, and planar shock compression. The latter analysis yields relationships among viscosity coefficients, gradient regularization lengths, and characteristics of steady plastic waveforms. Results give new insight into high-rate deformation mechanisms previously speculated in these materials.

在连续热力学的背景下构建了一种几何非线性相场理论，该理论考虑了耗散、速率效应、非线性热弹性、断裂和其他结构变化。首先，制定了一个适用于任意应变能势、非弹性变形运动学和无限阶参数的通用框架。接下来，该框架专门用于解释与在高速和高压下变形的结晶陶瓷和矿物相关的变形物理。值得注意的是，涉及中间材料配置的对数弹性应变张量进入非线性热弹性势。有序参数代表断裂、固-固相变、变形孪晶或部分位错的滑移。热力学一致的动力学表现在让人想起金茨堡-朗道动力学的方程中，其中粘度系数通常与状态和速率有关。在具有不可逆约束的动态断裂的替代动力学方程中，启用了与摩擦阻力相称的压力相关强度。模型的线性化适用于适度的体积变化，但进行小偏弹性应变和旋转。该理论被应用于研究碳化硼 (B) 多晶形式的变形和失效 模型的线性化适用于适度的体积变化，但进行小偏弹性应变和旋转。该理论被应用于研究碳化硼 (B) 多晶形式的变形和失效 模型的线性化适用于适度的体积变化，但进行小偏弹性应变和旋转。该理论被应用于研究碳化硼 (B) 多晶形式的变形和失效${}_4$C)、二硼化钛(TiB)${}_2$)，和一个 B${}_4$C-TiB${}_2$陶瓷复合材料。针对单轴应力拉伸和压缩、单轴应变压缩和平面冲击压缩，导出和数值计算解。后一种分析得出粘度系数、梯度正则化长度和稳定塑性波形特征之间的关系。结果为以前在这些材料中推测的高速率变形机制提供了新的见解。